id	sid	tid	token	lemma	pos
concept-2276	1	1	which	which	PRON
concept-2276	1	2	on	on	ADP
concept-2276	1	3	-	-	PUNCT
concept-2276	1	4	base	base	NOUN
concept-2276	1	5	percentage	percentage	NOUN
concept-2276	1	6	shows	show	VERB
concept-2276	1	7	the	the	DET
concept-2276	1	8	highest	high	ADJ
concept-2276	1	9	true	true	ADJ
concept-2276	1	10	ability	ability	NOUN
concept-2276	1	11	of	of	ADP
concept-2276	1	12	a	a	DET
concept-2276	1	13	baseball	baseball	NOUN
concept-2276	1	14	player	player	NOUN
concept-2276	1	15	?	?	PUNCT
concept-2276	2	1	january	january	PROPN
concept-2276	2	2	31	31	NUM
concept-2276	2	3	,	,	PUNCT
concept-2276	2	4	2018	2018	NUM
concept-2276	2	5	abstract	abstract	NOUN
concept-2276	2	6	this	this	DET
concept-2276	2	7	paper	paper	NOUN
concept-2276	2	8	looks	look	VERB
concept-2276	2	9	at	at	ADP
concept-2276	2	10	the	the	DET
concept-2276	2	11	true	true	ADJ
concept-2276	2	12	on	on	ADP
concept-2276	2	13	-	-	PUNCT
concept-2276	2	14	base	base	NOUN
concept-2276	2	15	ability	ability	NOUN
concept-2276	2	16	of	of	ADP
concept-2276	2	17	a	a	DET
concept-2276	2	18	baseball	baseball	NOUN
concept-2276	2	19	player	player	NOUN
concept-2276	2	20	given	give	VERB
concept-2276	2	21	their	their	PRON
concept-2276	2	22	on	on	ADP
concept-2276	2	23	-	-	PUNCT
concept-2276	2	24	base	base	NOUN
concept-2276	2	25	percentage	percentage	NOUN
concept-2276	2	26	.	.	PUNCT
concept-2276	3	1	unlike	unlike	ADP
concept-2276	3	2	a	a	DET
concept-2276	3	3	typical	typical	ADJ
concept-2276	3	4	proportion	proportion	NOUN
concept-2276	3	5	estimation	estimation	NOUN
concept-2276	3	6	problem	problem	NOUN
concept-2276	3	7	where	where	SCONJ
concept-2276	3	8	one	one	PRON
concept-2276	3	9	is	be	AUX
concept-2276	3	10	able	able	ADJ
concept-2276	3	11	to	to	PART
concept-2276	3	12	make	make	VERB
concept-2276	3	13	an	an	DET
concept-2276	3	14	analysis	analysis	NOUN
concept-2276	3	15	based	base	VERB
concept-2276	3	16	on	on	ADP
concept-2276	3	17	knowing	know	VERB
concept-2276	3	18	the	the	DET
concept-2276	3	19	number	number	NOUN
concept-2276	3	20	of	of	ADP
concept-2276	3	21	successes	success	NOUN
concept-2276	3	22	and	and	CCONJ
concept-2276	3	23	number	number	NOUN
concept-2276	3	24	of	of	ADP
concept-2276	3	25	trials	trial	NOUN
concept-2276	3	26	,	,	PUNCT
concept-2276	3	27	this	this	DET
concept-2276	3	28	problem	problem	NOUN
concept-2276	3	29	only	only	ADV
concept-2276	3	30	gives	give	VERB
concept-2276	3	31	us	we	PRON
concept-2276	3	32	the	the	DET
concept-2276	3	33	proportion	proportion	NOUN
concept-2276	3	34	of	of	ADP
concept-2276	3	35	successes	success	NOUN
concept-2276	3	36	rounded	round	VERB
concept-2276	3	37	to	to	ADP
concept-2276	3	38	three	three	NUM
concept-2276	3	39	decimal	decimal	ADJ
concept-2276	3	40	places	place	NOUN
concept-2276	3	41	.	.	PUNCT
concept-2276	4	1	this	this	DET
concept-2276	4	2	paper	paper	NOUN
concept-2276	4	3	presents	present	VERB
concept-2276	4	4	two	two	NUM
concept-2276	4	5	different	different	ADJ
concept-2276	4	6	bayesian	bayesian	NOUN
concept-2276	4	7	models	model	NOUN
concept-2276	4	8	for	for	ADP
concept-2276	4	9	finding	find	VERB
concept-2276	4	10	the	the	DET
concept-2276	4	11	highest	high	ADJ
concept-2276	4	12	true	true	ADJ
concept-2276	4	13	on	on	ADP
concept-2276	4	14	-	-	PUNCT
concept-2276	4	15	base	base	NOUN
concept-2276	4	16	ability	ability	NOUN
concept-2276	4	17	.	.	PUNCT
concept-2276	5	1	the	the	DET
concept-2276	5	2	first	first	ADJ
concept-2276	5	3	bayesian	bayesian	NOUN
concept-2276	5	4	model	model	NOUN
concept-2276	5	5	considers	consider	VERB
concept-2276	5	6	modeling	model	VERB
concept-2276	5	7	the	the	DET
concept-2276	5	8	distribution	distribution	NOUN
concept-2276	5	9	of	of	ADP
concept-2276	5	10	times	time	NOUN
concept-2276	5	11	on	on	ADP
concept-2276	5	12	-	-	PUNCT
concept-2276	5	13	base	base	NOUN
concept-2276	5	14	,	,	PUNCT
concept-2276	5	15	plate	plate	NOUN
concept-2276	5	16	appearances	appearance	NOUN
concept-2276	5	17	and	and	CCONJ
concept-2276	5	18	probability	probability	NOUN
concept-2276	5	19	of	of	ADP
concept-2276	5	20	being	be	AUX
concept-2276	5	21	on	on	ADP
concept-2276	5	22	-	-	PUNCT
concept-2276	5	23	base	base	NOUN
concept-2276	5	24	as	as	ADP
concept-2276	5	25	a	a	DET
concept-2276	5	26	prior	prior	ADJ
concept-2276	5	27	distribution	distribution	NOUN
concept-2276	5	28	and	and	CCONJ
concept-2276	5	29	then	then	ADV
concept-2276	5	30	finding	find	VERB
concept-2276	5	31	a	a	DET
concept-2276	5	32	posterior	posterior	ADJ
concept-2276	5	33	distribution	distribution	NOUN
concept-2276	5	34	given	give	VERB
concept-2276	5	35	an	an	DET
concept-2276	5	36	observed	observed	ADJ
concept-2276	5	37	on	on	ADP
concept-2276	5	38	-	-	PUNCT
concept-2276	5	39	base	base	NOUN
concept-2276	5	40	percentage	percentage	NOUN
concept-2276	5	41	.	.	PUNCT
concept-2276	6	1	the	the	DET
concept-2276	6	2	second	second	ADJ
concept-2276	6	3	bayesian	bayesian	NOUN
concept-2276	6	4	model	model	NOUN
concept-2276	6	5	looks	look	VERB
concept-2276	6	6	into	into	ADP
concept-2276	6	7	the	the	DET
concept-2276	6	8	distribution	distribution	NOUN
concept-2276	6	9	of	of	ADP
concept-2276	6	10	hits	hit	NOUN
concept-2276	6	11	,	,	PUNCT
concept-2276	6	12	walks	walk	NOUN
concept-2276	6	13	,	,	PUNCT
concept-2276	6	14	hit	hit	NOUN
concept-2276	6	15	-	-	PUNCT
concept-2276	6	16	by	by	ADP
concept-2276	6	17	-	-	PUNCT
concept-2276	6	18	pitches	pitch	NOUN
concept-2276	6	19	,	,	PUNCT
concept-2276	6	20	plate	plate	NOUN
concept-2276	6	21	appearances	appearance	NOUN
concept-2276	6	22	and	and	CCONJ
concept-2276	6	23	probability	probability	NOUN
concept-2276	6	24	of	of	ADP
concept-2276	6	25	getting	get	VERB
concept-2276	6	26	on	on	ADP
concept-2276	6	27	-	-	PUNCT
concept-2276	6	28	base	base	NOUN
concept-2276	6	29	and	and	CCONJ
concept-2276	6	30	then	then	ADV
concept-2276	6	31	creating	create	VERB
concept-2276	6	32	a	a	DET
concept-2276	6	33	simulation	simulation	NOUN
concept-2276	6	34	of	of	ADP
concept-2276	6	35	baseball	baseball	NOUN
concept-2276	6	36	players	player	NOUN
concept-2276	6	37	to	to	PART
concept-2276	6	38	see	see	VERB
concept-2276	6	39	their	their	PRON
concept-2276	6	40	true	true	ADJ
concept-2276	6	41	ability	ability	NOUN
concept-2276	6	42	given	give	VERB
concept-2276	6	43	a	a	DET
concept-2276	6	44	particular	particular	ADJ
concept-2276	6	45	on	on	ADP
concept-2276	6	46	-	-	PUNCT
concept-2276	6	47	base	base	NOUN
concept-2276	6	48	percentage	percentage	NOUN
concept-2276	6	49	.	.	PUNCT
concept-2276	7	1	after	after	ADP
concept-2276	7	2	implementing	implement	VERB
concept-2276	7	3	the	the	DET
concept-2276	7	4	two	two	NUM
concept-2276	7	5	models	model	NOUN
concept-2276	7	6	,	,	PUNCT
concept-2276	7	7	it	it	PRON
concept-2276	7	8	turns	turn	VERB
concept-2276	7	9	out	out	ADP
concept-2276	7	10	that	that	SCONJ
concept-2276	7	11	the	the	DET
concept-2276	7	12	highest	high	ADJ
concept-2276	7	13	reasonable	reasonable	ADJ
concept-2276	7	14	on	on	ADP
concept-2276	7	15	-	-	PUNCT
concept-2276	7	16	base	base	NOUN
concept-2276	7	17	percentage	percentage	NOUN
concept-2276	7	18	that	that	PRON
concept-2276	7	19	shows	show	VERB
concept-2276	7	20	a	a	DET
concept-2276	7	21	player	player	NOUN
concept-2276	7	22	’s	’s	PART
concept-2276	7	23	true	true	ADJ
concept-2276	7	24	ability	ability	NOUN
concept-2276	7	25	is	be	AUX
concept-2276	7	26	around	around	ADP
concept-2276	7	27	.4	.4	NUM
concept-2276	7	28	.	.	PUNCT
concept-2276	8	1	i.	i.	PROPN
concept-2276	8	2	introduction	introduction	NOUN
concept-2276	8	3	on	on	ADP
concept-2276	8	4	-	-	PUNCT
concept-2276	8	5	base	base	NOUN
concept-2276	8	6	percentage	percentage	NOUN
concept-2276	8	7	(	(	PUNCT
concept-2276	8	8	obp	obp	PROPN
concept-2276	8	9	)	)	PUNCT
concept-2276	8	10	,	,	PUNCT
concept-2276	8	11	defined	define	VERB
concept-2276	8	12	as	as	ADP
concept-2276	8	13	the	the	DET
concept-2276	8	14	ratio	ratio	NOUN
concept-2276	8	15	obp	obp	PROPN
concept-2276	8	16	≡	≡	PROPN
concept-2276	8	17	h+bb+hbp	h+bb+hbp	NOUN
concept-2276	8	18	ab+bb+hbp+sf	ab+bb+hbp+sf	ADP
concept-2276	8	19	where	where	SCONJ
concept-2276	8	20	h	h	NOUN
concept-2276	8	21	,	,	PUNCT
concept-2276	8	22	bb	bb	PROPN
concept-2276	8	23	,	,	PUNCT
concept-2276	8	24	hbp	hbp	PROPN
concept-2276	8	25	,	,	PUNCT
concept-2276	8	26	ab	ab	PROPN
concept-2276	8	27	,	,	PUNCT
concept-2276	8	28	and	and	CCONJ
concept-2276	8	29	sf	sf	PROPN
concept-2276	8	30	is	be	AUX
concept-2276	8	31	a	a	DET
concept-2276	8	32	player	player	NOUN
concept-2276	8	33	’s	’s	PART
concept-2276	8	34	hits	hit	NOUN
concept-2276	8	35	,	,	PUNCT
concept-2276	8	36	walks	walk	NOUN
concept-2276	8	37	,	,	PUNCT
concept-2276	8	38	hit	hit	NOUN
concept-2276	8	39	-	-	PUNCT
concept-2276	8	40	by	by	ADP
concept-2276	8	41	-	-	PUNCT
concept-2276	8	42	pitches	pitch	NOUN
concept-2276	8	43	,	,	PUNCT
concept-2276	8	44	at	at	ADP
concept-2276	8	45	bats	bat	NOUN
concept-2276	8	46	and	and	CCONJ
concept-2276	8	47	sacrifice	sacrifice	NOUN
concept-2276	8	48	flies	fly	VERB
concept-2276	8	49	respectively	respectively	ADV
concept-2276	8	50	,	,	PUNCT
concept-2276	8	51	is	be	AUX
concept-2276	8	52	one	one	NUM
concept-2276	8	53	of	of	ADP
concept-2276	8	54	the	the	DET
concept-2276	8	55	main	main	ADJ
concept-2276	8	56	statistics	statistic	NOUN
concept-2276	8	57	used	use	VERB
concept-2276	8	58	to	to	PART
concept-2276	8	59	measure	measure	VERB
concept-2276	8	60	a	a	DET
concept-2276	8	61	baseball	baseball	NOUN
concept-2276	8	62	player	player	NOUN
concept-2276	8	63	’s	’s	PART
concept-2276	8	64	offensive	offensive	ADJ
concept-2276	8	65	capacity	capacity	NOUN
concept-2276	8	66	.	.	PUNCT
concept-2276	9	1	according	accord	VERB
concept-2276	9	2	to	to	ADP
concept-2276	9	3	the	the	DET
concept-2276	9	4	bestseller	bestseller	NOUN
concept-2276	9	5	moneyball	moneyball	NOUN
concept-2276	9	6	(	(	PUNCT
concept-2276	9	7	lewis	lewis	PROPN
concept-2276	9	8	2003	2003	NUM
concept-2276	9	9	)	)	PUNCT
concept-2276	9	10	,	,	PUNCT
concept-2276	9	11	among	among	ADP
concept-2276	9	12	the	the	DET
concept-2276	9	13	different	different	ADJ
concept-2276	9	14	statistics	statistic	NOUN
concept-2276	9	15	used	use	VERB
concept-2276	9	16	to	to	PART
concept-2276	9	17	measure	measure	VERB
concept-2276	9	18	a	a	DET
concept-2276	9	19	player	player	NOUN
concept-2276	9	20	’s	’s	ADV
concept-2276	9	21	hitting	hit	VERB
concept-2276	9	22	ability	ability	NOUN
concept-2276	9	23	,	,	PUNCT
concept-2276	9	24	obp	obp	PROPN
concept-2276	9	25	is	be	AUX
concept-2276	9	26	one	one	NUM
concept-2276	9	27	of	of	ADP
concept-2276	9	28	the	the	DET
concept-2276	9	29	better	well	ADJ
concept-2276	9	30	measurements	measurement	NOUN
concept-2276	9	31	.	.	PUNCT
concept-2276	10	1	however	however	ADV
concept-2276	10	2	,	,	PUNCT
concept-2276	10	3	one	one	NUM
concept-2276	10	4	of	of	ADP
concept-2276	10	5	the	the	DET
concept-2276	10	6	things	thing	NOUN
concept-2276	10	7	that	that	PRON
concept-2276	10	8	can	can	AUX
concept-2276	10	9	be	be	AUX
concept-2276	10	10	deceiving	deceive	VERB
concept-2276	10	11	about	about	ADP
concept-2276	10	12	obp	obp	PROPN
concept-2276	10	13	is	be	AUX
concept-2276	10	14	the	the	DET
concept-2276	10	15	true	true	ADJ
concept-2276	10	16	ability	ability	NOUN
concept-2276	10	17	of	of	ADP
concept-2276	10	18	a	a	DET
concept-2276	10	19	player	player	NOUN
concept-2276	10	20	given	give	VERB
concept-2276	10	21	their	their	PRON
concept-2276	10	22	obp	obp	NOUN
concept-2276	10	23	.	.	PUNCT
concept-2276	11	1	it	it	PRON
concept-2276	11	2	may	may	AUX
concept-2276	11	3	be	be	AUX
concept-2276	11	4	that	that	SCONJ
concept-2276	11	5	the	the	DET
concept-2276	11	6	player	player	NOUN
concept-2276	11	7	’s	’s	PART
concept-2276	11	8	obp	obp	NOUN
concept-2276	11	9	was	be	AUX
concept-2276	11	10	achieved	achieve	VERB
concept-2276	11	11	with	with	ADP
concept-2276	11	12	a	a	DET
concept-2276	11	13	very	very	ADV
concept-2276	11	14	small	small	ADJ
concept-2276	11	15	sample	sample	NOUN
concept-2276	11	16	size	size	NOUN
concept-2276	11	17	.	.	PUNCT
concept-2276	12	1	for	for	ADP
concept-2276	12	2	1	1	NUM
concept-2276	12	3	example	example	NOUN
concept-2276	12	4	,	,	PUNCT
concept-2276	12	5	just	just	ADV
concept-2276	12	6	by	by	ADP
concept-2276	12	7	solely	solely	ADV
concept-2276	12	8	looking	look	VERB
concept-2276	12	9	at	at	ADP
concept-2276	12	10	the	the	DET
concept-2276	12	11	numbers	number	NOUN
concept-2276	12	12	,	,	PUNCT
concept-2276	12	13	one	one	PRON
concept-2276	12	14	would	would	AUX
concept-2276	12	15	probably	probably	ADV
concept-2276	12	16	assume	assume	VERB
concept-2276	12	17	that	that	SCONJ
concept-2276	12	18	a	a	DET
concept-2276	12	19	player	player	NOUN
concept-2276	12	20	with	with	ADP
concept-2276	12	21	.833	.833	NUM
concept-2276	12	22	obp	obp	PROPN
concept-2276	12	23	is	be	AUX
concept-2276	12	24	better	well	ADJ
concept-2276	12	25	than	than	ADP
concept-2276	12	26	a	a	DET
concept-2276	12	27	player	player	NOUN
concept-2276	12	28	with	with	ADP
concept-2276	12	29	a	a	DET
concept-2276	12	30	.398	.398	NUM
concept-2276	12	31	obp	obp	NOUN
concept-2276	12	32	.	.	PUNCT
concept-2276	13	1	however	however	ADV
concept-2276	13	2	,	,	PUNCT
concept-2276	13	3	it	it	PRON
concept-2276	13	4	is	be	AUX
concept-2276	13	5	very	very	ADV
concept-2276	13	6	much	much	ADV
concept-2276	13	7	possible	possible	ADJ
concept-2276	13	8	for	for	SCONJ
concept-2276	13	9	a	a	DET
concept-2276	13	10	player	player	NOUN
concept-2276	13	11	to	to	PART
concept-2276	13	12	achieve	achieve	VERB
concept-2276	13	13	a	a	DET
concept-2276	13	14	.833	.833	NUM
concept-2276	13	15	obp	obp	NOUN
concept-2276	13	16	just	just	ADV
concept-2276	13	17	by	by	ADP
concept-2276	13	18	getting	get	VERB
concept-2276	13	19	on	on	ADP
concept-2276	13	20	-	-	PUNCT
concept-2276	13	21	base	base	NOUN
concept-2276	13	22	5	5	NUM
concept-2276	13	23	out	out	ADP
concept-2276	13	24	of	of	ADP
concept-2276	13	25	6	6	NUM
concept-2276	13	26	times	time	NOUN
concept-2276	13	27	and	and	CCONJ
concept-2276	13	28	more	more	ADV
concept-2276	13	29	likely	likely	ADJ
concept-2276	13	30	than	than	ADP
concept-2276	13	31	not	not	PART
concept-2276	13	32	,	,	PUNCT
concept-2276	13	33	the	the	DET
concept-2276	13	34	player	player	NOUN
concept-2276	13	35	probably	probably	ADV
concept-2276	13	36	got	get	VERB
concept-2276	13	37	a	a	DET
concept-2276	13	38	.833	.833	NUM
concept-2276	13	39	obp	obp	NOUN
concept-2276	13	40	in	in	ADP
concept-2276	13	41	this	this	DET
concept-2276	13	42	fashion	fashion	NOUN
concept-2276	13	43	.	.	PUNCT
concept-2276	14	1	however	however	ADV
concept-2276	14	2	,	,	PUNCT
concept-2276	14	3	in	in	ADP
concept-2276	14	4	order	order	NOUN
concept-2276	14	5	for	for	SCONJ
concept-2276	14	6	a	a	DET
concept-2276	14	7	player	player	NOUN
concept-2276	14	8	to	to	PART
concept-2276	14	9	get	get	VERB
concept-2276	14	10	a	a	DET
concept-2276	14	11	.398	.398	NUM
concept-2276	14	12	obp	obp	NOUN
concept-2276	14	13	,	,	PUNCT
concept-2276	14	14	one	one	PRON
concept-2276	14	15	would	would	AUX
concept-2276	14	16	need	need	VERB
concept-2276	14	17	to	to	PART
concept-2276	14	18	bat	bat	VERB
concept-2276	14	19	at	at	ADV
concept-2276	14	20	least	least	ADV
concept-2276	14	21	161	161	NUM
concept-2276	14	22	times	time	NOUN
concept-2276	14	23	,	,	PUNCT
concept-2276	14	24	which	which	PRON
concept-2276	14	25	shows	show	VERB
concept-2276	14	26	a	a	DET
concept-2276	14	27	high	high	ADJ
concept-2276	14	28	degree	degree	NOUN
concept-2276	14	29	of	of	ADP
concept-2276	14	30	skill	skill	NOUN
concept-2276	14	31	since	since	SCONJ
concept-2276	14	32	this	this	DET
concept-2276	14	33	percentage	percentage	NOUN
concept-2276	14	34	is	be	AUX
concept-2276	14	35	sustained	sustain	VERB
concept-2276	14	36	upon	upon	SCONJ
concept-2276	14	37	a	a	DET
concept-2276	14	38	high	high	ADJ
concept-2276	14	39	amount	amount	NOUN
concept-2276	14	40	of	of	ADP
concept-2276	14	41	batting	batting	NOUN
concept-2276	14	42	opportunities	opportunity	NOUN
concept-2276	14	43	.	.	PUNCT
concept-2276	15	1	in	in	ADP
concept-2276	15	2	this	this	DET
concept-2276	15	3	paper	paper	NOUN
concept-2276	15	4	,	,	PUNCT
concept-2276	15	5	we	we	PRON
concept-2276	15	6	will	will	AUX
concept-2276	15	7	look	look	VERB
concept-2276	15	8	at	at	ADP
concept-2276	15	9	which	which	PRON
concept-2276	15	10	obp	obp	PROPN
concept-2276	15	11	’s	’s	PART
concept-2276	15	12	show	show	VERB
concept-2276	15	13	the	the	DET
concept-2276	15	14	highest	high	ADJ
concept-2276	15	15	amount	amount	NOUN
concept-2276	15	16	of	of	ADP
concept-2276	15	17	true	true	ADJ
concept-2276	15	18	ability	ability	NOUN
concept-2276	15	19	p	p	NOUN
concept-2276	15	20	,	,	PUNCT
concept-2276	15	21	where	where	SCONJ
concept-2276	15	22	a	a	DET
concept-2276	15	23	higher	high	ADJ
concept-2276	15	24	true	true	ADJ
concept-2276	15	25	ability	ability	NOUN
concept-2276	15	26	indicating	indicate	VERB
concept-2276	15	27	a	a	DET
concept-2276	15	28	better	well	ADJ
concept-2276	15	29	player	player	NOUN
concept-2276	15	30	.	.	PUNCT
concept-2276	16	1	the	the	DET
concept-2276	16	2	way	way	NOUN
concept-2276	16	3	that	that	PRON
concept-2276	16	4	we	we	PRON
concept-2276	16	5	will	will	AUX
concept-2276	16	6	approach	approach	VERB
concept-2276	16	7	this	this	DET
concept-2276	16	8	problem	problem	NOUN
concept-2276	16	9	is	be	AUX
concept-2276	16	10	by	by	ADP
concept-2276	16	11	turning	turn	VERB
concept-2276	16	12	real	real	ADJ
concept-2276	16	13	world	world	NOUN
concept-2276	16	14	baseball	baseball	NOUN
concept-2276	16	15	data	datum	NOUN
concept-2276	16	16	into	into	ADP
concept-2276	16	17	models	model	NOUN
concept-2276	16	18	by	by	ADP
concept-2276	16	19	using	use	VERB
concept-2276	16	20	random	random	ADJ
concept-2276	16	21	variables	variable	NOUN
concept-2276	16	22	and	and	CCONJ
concept-2276	16	23	probability	probability	NOUN
concept-2276	16	24	distribution	distribution	NOUN
concept-2276	16	25	functions	function	NOUN
concept-2276	16	26	of	of	ADP
concept-2276	16	27	these	these	DET
concept-2276	16	28	random	random	ADJ
concept-2276	16	29	variables	variable	NOUN
concept-2276	16	30	.	.	PUNCT
concept-2276	17	1	these	these	DET
concept-2276	17	2	probability	probability	NOUN
concept-2276	17	3	density	density	NOUN
concept-2276	17	4	functions	function	NOUN
concept-2276	17	5	would	would	AUX
concept-2276	17	6	retain	retain	VERB
concept-2276	17	7	the	the	DET
concept-2276	17	8	important	important	ADJ
concept-2276	17	9	details	detail	NOUN
concept-2276	17	10	that	that	SCONJ
concept-2276	17	11	the	the	DET
concept-2276	17	12	real	real	ADJ
concept-2276	17	13	world	world	NOUN
concept-2276	17	14	data	data	NOUN
concept-2276	17	15	contains	contain	VERB
concept-2276	17	16	.	.	PUNCT
concept-2276	18	1	a	a	DET
concept-2276	18	2	random	random	ADJ
concept-2276	18	3	variable	variable	NOUN
concept-2276	18	4	x	x	PUNCT
concept-2276	18	5	is	be	AUX
concept-2276	18	6	a	a	DET
concept-2276	18	7	variable	variable	NOUN
concept-2276	18	8	whose	whose	DET
concept-2276	18	9	possible	possible	ADJ
concept-2276	18	10	values	value	NOUN
concept-2276	18	11	are	be	AUX
concept-2276	18	12	outcomes	outcome	NOUN
concept-2276	18	13	of	of	ADP
concept-2276	18	14	random	random	ADJ
concept-2276	18	15	events	event	NOUN
concept-2276	18	16	.	.	PUNCT
concept-2276	19	1	we	we	PRON
concept-2276	19	2	use	use	VERB
concept-2276	19	3	an	an	DET
concept-2276	19	4	uppercase	uppercase	ADJ
concept-2276	19	5	letter	letter	NOUN
concept-2276	19	6	x	x	VERB
concept-2276	19	7	to	to	PART
concept-2276	19	8	refer	refer	VERB
concept-2276	19	9	to	to	ADP
concept-2276	19	10	the	the	DET
concept-2276	19	11	random	random	ADJ
concept-2276	19	12	variable	variable	NOUN
concept-2276	19	13	itself	itself	PRON
concept-2276	19	14	and	and	CCONJ
concept-2276	19	15	we	we	PRON
concept-2276	19	16	use	use	VERB
concept-2276	19	17	a	a	DET
concept-2276	19	18	lowercase	lowercase	NOUN
concept-2276	19	19	letter	letter	NOUN
concept-2276	19	20	x	x	PART
concept-2276	19	21	to	to	PART
concept-2276	19	22	refer	refer	VERB
concept-2276	19	23	to	to	ADP
concept-2276	19	24	the	the	DET
concept-2276	19	25	possible	possible	ADJ
concept-2276	19	26	value	value	NOUN
concept-2276	19	27	that	that	SCONJ
concept-2276	19	28	the	the	DET
concept-2276	19	29	random	random	ADJ
concept-2276	19	30	variable	variable	NOUN
concept-2276	19	31	can	can	AUX
concept-2276	19	32	take	take	VERB
concept-2276	19	33	on	on	ADP
concept-2276	19	34	.	.	PUNCT
concept-2276	20	1	probability	probability	NOUN
concept-2276	20	2	density	density	NOUN
concept-2276	20	3	functions	function	NOUN
concept-2276	20	4	are	be	AUX
concept-2276	20	5	real	real	ADV
concept-2276	20	6	valued	value	VERB
concept-2276	20	7	functions	function	NOUN
concept-2276	20	8	fx1,x2,	fx1,x2,	NOUN
concept-2276	20	9	...	...	PUNCT
concept-2276	20	10	,xn(x1	,xn(x1	PUNCT
concept-2276	20	11	,	,	PUNCT
concept-2276	20	12	x2	x2	PROPN
concept-2276	20	13	,	,	PUNCT
concept-2276	20	14	...	...	PUNCT
concept-2276	20	15	,	,	PUNCT
concept-2276	20	16	xn	xn	PROPN
concept-2276	20	17	)	)	PUNCT
concept-2276	20	18	such	such	ADJ
concept-2276	20	19	that	that	DET
concept-2276	20	20	fx1,x2,	fx1,x2,	NOUN
concept-2276	20	21	...	...	PUNCT
concept-2276	20	22	,xn(x1	,xn(x1	PUNCT
concept-2276	20	23	,	,	PUNCT
concept-2276	20	24	x2	x2	PROPN
concept-2276	20	25	,	,	PUNCT
concept-2276	20	26	...	...	PUNCT
concept-2276	20	27	,	,	PUNCT
concept-2276	20	28	xn	xn	PROPN
concept-2276	20	29	)	)	PUNCT
concept-2276	20	30	>	>	X
concept-2276	20	31	0	0	PUNCT
concept-2276	21	1	for	for	ADP
concept-2276	21	2	all	all	DET
concept-2276	21	3	random	random	ADJ
concept-2276	21	4	variables	variable	NOUN
concept-2276	21	5	x1	x1	PROPN
concept-2276	21	6	,	,	PUNCT
concept-2276	21	7	x2	x2	PROPN
concept-2276	21	8	,	,	PUNCT
concept-2276	21	9	...	...	PUNCT
concept-2276	21	10	,	,	PUNCT
concept-2276	21	11	xn	xn	PROPN
concept-2276	21	12	and	and	CCONJ
concept-2276	21	13	∫	∫	PROPN
concept-2276	21	14	∞	∞	PROPN
concept-2276	21	15	−∞	−∞	X
concept-2276	21	16	∫	∫	PROPN
concept-2276	21	17	∞	∞	PROPN
concept-2276	21	18	−∞	−∞	PROPN
concept-2276	21	19	...	...	PUNCT
concept-2276	21	20	∫	∫	PROPN
concept-2276	21	21	∞	∞	PROPN
concept-2276	21	22	−∞	−∞	ADP
concept-2276	21	23	fx1,x2,	fx1,x2,	NOUN
concept-2276	21	24	...	...	PUNCT
concept-2276	21	25	,xn(x1	,xn(x1	PUNCT
concept-2276	21	26	,	,	PUNCT
concept-2276	21	27	x2	x2	PROPN
concept-2276	21	28	,	,	PUNCT
concept-2276	21	29	...	...	PUNCT
concept-2276	21	30	,	,	PUNCT
concept-2276	21	31	xn)dx1dx2	xn)dx1dx2	PROPN
concept-2276	21	32	...	...	PUNCT
concept-2276	21	33	dxn	dxn	ADJ
concept-2276	21	34	=	=	SYM
concept-2276	21	35	1	1	NUM
concept-2276	21	36	.	.	PUNCT
concept-2276	22	1	with	with	ADP
concept-2276	22	2	probability	probability	NOUN
concept-2276	22	3	density	density	NOUN
concept-2276	22	4	functions	function	NOUN
concept-2276	22	5	,	,	PUNCT
concept-2276	22	6	we	we	PRON
concept-2276	22	7	can	can	AUX
concept-2276	22	8	create	create	VERB
concept-2276	22	9	conditional	conditional	ADJ
concept-2276	22	10	distribution	distribution	NOUN
concept-2276	22	11	functions	function	NOUN
concept-2276	22	12	which	which	PRON
concept-2276	22	13	are	be	AUX
concept-2276	22	14	probability	probability	NOUN
concept-2276	22	15	density	density	NOUN
concept-2276	22	16	functions	function	NOUN
concept-2276	22	17	with	with	ADP
concept-2276	22	18	extra	extra	ADJ
concept-2276	22	19	information	information	NOUN
concept-2276	22	20	given	give	VERB
concept-2276	22	21	with	with	ADP
concept-2276	22	22	one	one	NUM
concept-2276	22	23	or	or	CCONJ
concept-2276	22	24	more	more	ADJ
concept-2276	22	25	of	of	ADP
concept-2276	22	26	the	the	DET
concept-2276	22	27	variables	variable	NOUN
concept-2276	22	28	in	in	ADP
concept-2276	22	29	the	the	DET
concept-2276	22	30	original	original	ADJ
concept-2276	22	31	distribution	distribution	NOUN
concept-2276	22	32	function	function	NOUN
concept-2276	22	33	.	.	PUNCT
concept-2276	23	1	we	we	PRON
concept-2276	23	2	can	can	AUX
concept-2276	23	3	also	also	ADV
concept-2276	23	4	create	create	VERB
concept-2276	23	5	marginal	marginal	ADJ
concept-2276	23	6	distribution	distribution	NOUN
concept-2276	23	7	functions	function	NOUN
concept-2276	23	8	which	which	PRON
concept-2276	23	9	are	be	AUX
concept-2276	23	10	probability	probability	NOUN
concept-2276	23	11	density	density	NOUN
concept-2276	23	12	functions	function	NOUN
concept-2276	23	13	that	that	PRON
concept-2276	23	14	isolate	isolate	VERB
concept-2276	23	15	one	one	NUM
concept-2276	23	16	of	of	ADP
concept-2276	23	17	the	the	DET
concept-2276	23	18	variables	variable	NOUN
concept-2276	23	19	through	through	ADP
concept-2276	23	20	aggregating	aggregate	VERB
concept-2276	23	21	the	the	DET
concept-2276	23	22	other	other	ADJ
concept-2276	23	23	variables	variable	NOUN
concept-2276	23	24	.	.	PUNCT
concept-2276	24	1	the	the	DET
concept-2276	24	2	models	model	NOUN
concept-2276	24	3	presented	present	VERB
concept-2276	24	4	will	will	AUX
concept-2276	24	5	use	use	VERB
concept-2276	24	6	conditional	conditional	ADJ
concept-2276	24	7	distributions	distribution	NOUN
concept-2276	24	8	and	and	CCONJ
concept-2276	24	9	marginal	marginal	ADJ
concept-2276	24	10	distributions	distribution	NOUN
concept-2276	24	11	to	to	PART
concept-2276	24	12	fit	fit	VERB
concept-2276	24	13	the	the	DET
concept-2276	24	14	real	real	ADJ
concept-2276	24	15	world	world	NOUN
concept-2276	24	16	data	datum	NOUN
concept-2276	24	17	in	in	ADP
concept-2276	24	18	an	an	DET
concept-2276	24	19	appropriate	appropriate	ADJ
concept-2276	24	20	way	way	NOUN
concept-2276	24	21	.	.	PUNCT
concept-2276	25	1	sections	section	NOUN
concept-2276	25	2	2	2	NUM
concept-2276	25	3	and	and	CCONJ
concept-2276	25	4	3	3	NUM
concept-2276	25	5	will	will	AUX
concept-2276	25	6	present	present	VERB
concept-2276	25	7	two	two	NUM
concept-2276	25	8	different	different	ADJ
concept-2276	25	9	models	model	NOUN
concept-2276	25	10	to	to	PART
concept-2276	25	11	approach	approach	VERB
concept-2276	25	12	the	the	DET
concept-2276	25	13	same	same	ADJ
concept-2276	25	14	problem	problem	NOUN
concept-2276	25	15	.	.	PUNCT
concept-2276	26	1	the	the	DET
concept-2276	26	2	goal	goal	NOUN
concept-2276	26	3	is	be	AUX
concept-2276	26	4	to	to	PART
concept-2276	26	5	create	create	VERB
concept-2276	26	6	such	such	DET
concept-2276	26	7	a	a	DET
concept-2276	26	8	model	model	NOUN
concept-2276	26	9	that	that	SCONJ
concept-2276	26	10	if	if	SCONJ
concept-2276	26	11	we	we	PRON
concept-2276	26	12	made	make	VERB
concept-2276	26	13	a	a	DET
concept-2276	26	14	simulation	simulation	NOUN
concept-2276	26	15	out	out	ADP
concept-2276	26	16	of	of	ADP
concept-2276	26	17	this	this	DET
concept-2276	26	18	model	model	NOUN
concept-2276	26	19	,	,	PUNCT
concept-2276	26	20	we	we	PRON
concept-2276	26	21	would	would	AUX
concept-2276	26	22	obtain	obtain	VERB
concept-2276	26	23	fake	fake	ADJ
concept-2276	26	24	data	datum	NOUN
concept-2276	26	25	that	that	PRON
concept-2276	26	26	would	would	AUX
concept-2276	26	27	be	be	AUX
concept-2276	26	28	reasonably	reasonably	ADV
concept-2276	26	29	similar	similar	ADJ
concept-2276	26	30	to	to	ADP
concept-2276	26	31	the	the	DET
concept-2276	26	32	real	real	ADJ
concept-2276	26	33	world	world	NOUN
concept-2276	26	34	baseball	baseball	NOUN
concept-2276	26	35	data	datum	NOUN
concept-2276	26	36	.	.	PUNCT
concept-2276	27	1	section	section	NOUN
concept-2276	27	2	4	4	NUM
concept-2276	27	3	will	will	AUX
concept-2276	27	4	present	present	VERB
concept-2276	27	5	the	the	DET
concept-2276	27	6	necessary	necessary	ADJ
concept-2276	27	7	methods	method	NOUN
concept-2276	27	8	to	to	PART
concept-2276	27	9	calculate	calculate	VERB
concept-2276	27	10	the	the	DET
concept-2276	27	11	posterior	posterior	ADJ
concept-2276	27	12	true	true	ADJ
concept-2276	27	13	ability	ability	NOUN
concept-2276	27	14	p	p	NOUN
concept-2276	27	15	given	give	VERB
concept-2276	27	16	the	the	DET
concept-2276	27	17	obp	obp	NOUN
concept-2276	27	18	information	information	NOUN
concept-2276	27	19	as	as	ADV
concept-2276	27	20	well	well	ADV
concept-2276	27	21	as	as	ADP
concept-2276	27	22	the	the	DET
concept-2276	27	23	information	information	NOUN
concept-2276	27	24	that	that	PRON
concept-2276	27	25	we	we	PRON
concept-2276	27	26	created	create	VERB
concept-2276	27	27	with	with	ADP
concept-2276	27	28	both	both	CCONJ
concept-2276	27	29	our	our	PRON
concept-2276	27	30	models	model	NOUN
concept-2276	27	31	in	in	ADP
concept-2276	27	32	sections	section	NOUN
concept-2276	27	33	2	2	NUM
concept-2276	27	34	and	and	CCONJ
concept-2276	27	35	3	3	NUM
concept-2276	27	36	.	.	X
concept-2276	27	37	section	section	NOUN
concept-2276	27	38	5	5	NUM
concept-2276	27	39	will	will	AUX
concept-2276	27	40	give	give	VERB
concept-2276	27	41	the	the	DET
concept-2276	27	42	results	result	NOUN
concept-2276	27	43	of	of	ADP
concept-2276	27	44	our	our	PRON
concept-2276	27	45	calculations	calculation	NOUN
concept-2276	27	46	as	as	ADV
concept-2276	27	47	well	well	ADV
concept-2276	27	48	as	as	ADP
concept-2276	27	49	analyze	analyze	VERB
concept-2276	27	50	some	some	PRON
concept-2276	27	51	of	of	ADP
concept-2276	27	52	the	the	DET
concept-2276	27	53	results	result	NOUN
concept-2276	27	54	’	'	PUNCT
concept-2276	27	55	highlights	highlight	NOUN
concept-2276	27	56	.	.	PUNCT
concept-2276	28	1	all	all	PRON
concept-2276	28	2	of	of	ADP
concept-2276	28	3	the	the	DET
concept-2276	28	4	major	major	ADJ
concept-2276	28	5	computations	computation	NOUN
concept-2276	28	6	were	be	AUX
concept-2276	28	7	handled	handle	VERB
concept-2276	28	8	by	by	ADP
concept-2276	28	9	r	r	NOUN
concept-2276	28	10	,	,	PUNCT
concept-2276	28	11	a	a	DET
concept-2276	28	12	statistical	statistical	ADJ
concept-2276	28	13	program	program	NOUN
concept-2276	28	14	.	.	PUNCT
concept-2276	29	1	the	the	DET
concept-2276	29	2	data	datum	NOUN
concept-2276	29	3	that	that	PRON
concept-2276	29	4	we	we	PRON
concept-2276	29	5	used	use	VERB
concept-2276	29	6	was	be	AUX
concept-2276	29	7	taken	take	VERB
concept-2276	29	8	from	from	ADP
concept-2276	29	9	www.baseballreference.com	www.baseballreference.com	NOUN
concept-2276	29	10	where	where	SCONJ
concept-2276	29	11	we	we	PRON
concept-2276	29	12	recorded	record	VERB
concept-2276	29	13	the	the	DET
concept-2276	29	14	offensive	offensive	ADJ
concept-2276	29	15	statistics	statistic	NOUN
concept-2276	29	16	of	of	ADP
concept-2276	29	17	non	non	NOUN
concept-2276	29	18	-	-	NOUN
concept-2276	29	19	pitchers	pitcher	NOUN
concept-2276	29	20	who	who	PRON
concept-2276	29	21	had	have	VERB
concept-2276	29	22	at	at	ADP
concept-2276	29	23	2	2	NUM
concept-2276	29	24	least	least	ADV
concept-2276	29	25	one	one	NUM
concept-2276	29	26	at	at	ADP
concept-2276	29	27	bat	bat	NOUN
concept-2276	29	28	during	during	ADP
concept-2276	29	29	the	the	DET
concept-2276	29	30	2015	2015	NUM
concept-2276	29	31	and	and	CCONJ
concept-2276	29	32	2016	2016	NUM
concept-2276	29	33	seasons	season	NOUN
concept-2276	29	34	(	(	PUNCT
concept-2276	29	35	which	which	PRON
concept-2276	29	36	were	be	AUX
concept-2276	29	37	the	the	DET
concept-2276	29	38	two	two	NUM
concept-2276	29	39	most	most	ADV
concept-2276	29	40	recent	recent	ADJ
concept-2276	29	41	complete	complete	ADJ
concept-2276	29	42	data	datum	NOUN
concept-2276	29	43	available	available	ADJ
concept-2276	29	44	)	)	PUNCT
concept-2276	29	45	.	.	PUNCT
concept-2276	30	1	players	player	NOUN
concept-2276	30	2	who	who	PRON
concept-2276	30	3	had	have	VERB
concept-2276	30	4	at	at	ADV
concept-2276	30	5	least	least	ADJ
concept-2276	30	6	one	one	NUM
concept-2276	30	7	at	at	ADP
concept-2276	30	8	bat	bat	NOUN
concept-2276	30	9	for	for	ADP
concept-2276	30	10	more	more	ADJ
concept-2276	30	11	than	than	ADP
concept-2276	30	12	one	one	NUM
concept-2276	30	13	team	team	NOUN
concept-2276	30	14	in	in	ADP
concept-2276	30	15	a	a	DET
concept-2276	30	16	particular	particular	ADJ
concept-2276	30	17	season	season	NOUN
concept-2276	30	18	appear	appear	VERB
concept-2276	30	19	in	in	ADP
concept-2276	30	20	the	the	DET
concept-2276	30	21	data	datum	NOUN
concept-2276	30	22	multiple	multiple	ADJ
concept-2276	30	23	times	time	NOUN
concept-2276	30	24	,	,	PUNCT
concept-2276	30	25	once	once	ADV
concept-2276	30	26	for	for	ADP
concept-2276	30	27	each	each	DET
concept-2276	30	28	team	team	NOUN
concept-2276	30	29	.	.	PUNCT
concept-2276	31	1	there	there	PRON
concept-2276	31	2	were	be	VERB
concept-2276	31	3	about	about	ADV
concept-2276	31	4	700	700	NUM
concept-2276	31	5	players	player	NOUN
concept-2276	31	6	who	who	PRON
concept-2276	31	7	met	meet	VERB
concept-2276	31	8	this	this	DET
concept-2276	31	9	criterion	criterion	NOUN
concept-2276	31	10	per	per	ADP
concept-2276	31	11	season	season	NOUN
concept-2276	31	12	so	so	SCONJ
concept-2276	31	13	we	we	PRON
concept-2276	31	14	had	have	VERB
concept-2276	31	15	about	about	ADV
concept-2276	31	16	1400	1400	NUM
concept-2276	31	17	players	player	NOUN
concept-2276	31	18	’	'	PUNCT
concept-2276	31	19	statistics	statistic	NOUN
concept-2276	31	20	to	to	PART
concept-2276	31	21	work	work	VERB
concept-2276	31	22	with	with	ADP
concept-2276	31	23	.	.	PUNCT
concept-2276	31	24	ii	ii	PROPN
concept-2276	31	25	.	.	PUNCT
concept-2276	32	1	the	the	DET
concept-2276	32	2	first	first	ADJ
concept-2276	32	3	proposed	propose	VERB
concept-2276	32	4	model	model	NOUN
concept-2276	32	5	the	the	DET
concept-2276	32	6	first	first	ADJ
concept-2276	32	7	model	model	NOUN
concept-2276	32	8	will	will	AUX
concept-2276	32	9	use	use	VERB
concept-2276	32	10	bayesian	bayesian	NOUN
concept-2276	32	11	statistics	statistic	NOUN
concept-2276	32	12	to	to	PART
concept-2276	32	13	model	model	VERB
concept-2276	32	14	the	the	DET
concept-2276	32	15	true	true	ADJ
concept-2276	32	16	ability	ability	NOUN
concept-2276	32	17	of	of	ADP
concept-2276	32	18	a	a	DET
concept-2276	32	19	player	player	NOUN
concept-2276	32	20	given	give	VERB
concept-2276	32	21	an	an	DET
concept-2276	32	22	obp	obp	NOUN
concept-2276	32	23	thorough	thorough	NOUN
concept-2276	32	24	a	a	DET
concept-2276	32	25	formula	formula	NOUN
concept-2276	32	26	that	that	PRON
concept-2276	32	27	measures	measure	VERB
concept-2276	32	28	the	the	DET
concept-2276	32	29	true	true	ADJ
concept-2276	32	30	ability	ability	NOUN
concept-2276	32	31	in	in	ADP
concept-2276	32	32	relation	relation	NOUN
concept-2276	32	33	to	to	ADP
concept-2276	32	34	information	information	NOUN
concept-2276	32	35	relevant	relevant	ADJ
concept-2276	32	36	to	to	ADP
concept-2276	32	37	on	on	ADP
concept-2276	32	38	-	-	PUNCT
concept-2276	32	39	base	base	NOUN
concept-2276	32	40	percentage	percentage	NOUN
concept-2276	32	41	.	.	PUNCT
concept-2276	33	1	bayesian	bayesian	NOUN
concept-2276	33	2	statistics	statistic	NOUN
concept-2276	33	3	studies	study	VERB
concept-2276	33	4	the	the	DET
concept-2276	33	5	probabilities	probability	NOUN
concept-2276	33	6	of	of	ADP
concept-2276	33	7	events	event	NOUN
concept-2276	33	8	occurring	occurring	AUX
concept-2276	33	9	given	give	VERB
concept-2276	33	10	one	one	NUM
concept-2276	33	11	has	have	VERB
concept-2276	33	12	relevant	relevant	ADJ
concept-2276	33	13	information	information	NOUN
concept-2276	33	14	about	about	ADP
concept-2276	33	15	the	the	DET
concept-2276	33	16	event	event	NOUN
concept-2276	33	17	before	before	ADP
concept-2276	33	18	making	make	VERB
concept-2276	33	19	the	the	DET
concept-2276	33	20	actual	actual	ADJ
concept-2276	33	21	calculation	calculation	NOUN
concept-2276	33	22	.	.	PUNCT
concept-2276	34	1	the	the	DET
concept-2276	34	2	probability	probability	NOUN
concept-2276	34	3	calculated	calculate	VERB
concept-2276	34	4	without	without	ADP
concept-2276	34	5	the	the	DET
concept-2276	34	6	information	information	NOUN
concept-2276	34	7	is	be	AUX
concept-2276	34	8	called	call	VERB
concept-2276	34	9	the	the	DET
concept-2276	34	10	prior	prior	ADJ
concept-2276	34	11	probability	probability	NOUN
concept-2276	34	12	and	and	CCONJ
concept-2276	34	13	the	the	DET
concept-2276	34	14	probability	probability	NOUN
concept-2276	34	15	calculated	calculate	VERB
concept-2276	34	16	using	use	VERB
concept-2276	34	17	the	the	DET
concept-2276	34	18	updated	update	VERB
concept-2276	34	19	information	information	NOUN
concept-2276	34	20	is	be	AUX
concept-2276	34	21	called	call	VERB
concept-2276	34	22	the	the	DET
concept-2276	34	23	posterior	posterior	ADJ
concept-2276	34	24	probability	probability	NOUN
concept-2276	34	25	.	.	PUNCT
concept-2276	35	1	in	in	ADP
concept-2276	35	2	this	this	DET
concept-2276	35	3	case	case	NOUN
concept-2276	35	4	,	,	PUNCT
concept-2276	35	5	we	we	PRON
concept-2276	35	6	will	will	AUX
concept-2276	35	7	use	use	VERB
concept-2276	35	8	plate	plate	NOUN
concept-2276	35	9	appearances	appearance	NOUN
concept-2276	35	10	,	,	PUNCT
concept-2276	35	11	times	time	NOUN
concept-2276	35	12	on	on	ADP
concept-2276	35	13	base	base	NOUN
concept-2276	35	14	,	,	PUNCT
concept-2276	35	15	and	and	CCONJ
concept-2276	35	16	on	on	ADP
concept-2276	35	17	-	-	PUNCT
concept-2276	35	18	base	base	NOUN
concept-2276	35	19	percentage	percentage	NOUN
concept-2276	35	20	as	as	ADP
concept-2276	35	21	the	the	DET
concept-2276	35	22	relevant	relevant	ADJ
concept-2276	35	23	information	information	NOUN
concept-2276	35	24	and	and	CCONJ
concept-2276	35	25	we	we	PRON
concept-2276	35	26	will	will	AUX
concept-2276	35	27	use	use	VERB
concept-2276	35	28	true	true	ADJ
concept-2276	35	29	ability	ability	NOUN
concept-2276	35	30	as	as	ADP
concept-2276	35	31	the	the	DET
concept-2276	35	32	prior	prior	ADJ
concept-2276	35	33	/	/	SYM
concept-2276	35	34	posterior	posterior	ADJ
concept-2276	35	35	probability	probability	NOUN
concept-2276	35	36	.	.	PUNCT
concept-2276	36	1	we	we	PRON
concept-2276	36	2	will	will	AUX
concept-2276	36	3	use	use	VERB
concept-2276	36	4	true	true	ADJ
concept-2276	36	5	ability	ability	NOUN
concept-2276	36	6	for	for	ADP
concept-2276	36	7	as	as	ADP
concept-2276	36	8	a	a	DET
concept-2276	36	9	prior	prior	ADJ
concept-2276	36	10	probability	probability	NOUN
concept-2276	36	11	for	for	ADP
concept-2276	36	12	building	build	VERB
concept-2276	36	13	the	the	DET
concept-2276	36	14	model	model	NOUN
concept-2276	36	15	and	and	CCONJ
concept-2276	36	16	we	we	PRON
concept-2276	36	17	will	will	AUX
concept-2276	36	18	use	use	VERB
concept-2276	36	19	true	true	ADJ
concept-2276	36	20	ability	ability	NOUN
concept-2276	36	21	as	as	ADP
concept-2276	36	22	a	a	DET
concept-2276	36	23	posterior	posterior	ADJ
concept-2276	36	24	probability	probability	NOUN
concept-2276	36	25	for	for	ADP
concept-2276	36	26	determining	determine	VERB
concept-2276	36	27	which	which	PRON
concept-2276	36	28	on	on	ADP
concept-2276	36	29	-	-	PUNCT
concept-2276	36	30	base	base	NOUN
concept-2276	36	31	percentages	percentage	NOUN
concept-2276	36	32	measure	measure	VERB
concept-2276	36	33	the	the	DET
concept-2276	36	34	better	well	ADJ
concept-2276	36	35	players	player	NOUN
concept-2276	36	36	’	'	PUNCT
concept-2276	36	37	offensive	offensive	ADJ
concept-2276	36	38	skill	skill	NOUN
concept-2276	36	39	.	.	PUNCT
concept-2276	37	1	we	we	PRON
concept-2276	37	2	will	will	AUX
concept-2276	37	3	aggregate	aggregate	VERB
concept-2276	37	4	the	the	DET
concept-2276	37	5	obp	obp	NOUN
concept-2276	37	6	formula	formula	NOUN
concept-2276	37	7	to	to	ADP
concept-2276	37	8	obp	obp	PROPN
concept-2276	37	9	=	=	SYM
concept-2276	37	10	times	time	NOUN
concept-2276	37	11	on	on	ADP
concept-2276	37	12	base	base	NOUN
concept-2276	37	13	plate	plate	NOUN
concept-2276	37	14	appearances	appearance	VERB
concept-2276	37	15	where	where	SCONJ
concept-2276	37	16	times	time	NOUN
concept-2276	37	17	-	-	PUNCT
concept-2276	37	18	on	on	ADP
concept-2276	37	19	-	-	PUNCT
concept-2276	37	20	base	base	NOUN
concept-2276	37	21	=	=	NOUN
concept-2276	37	22	h	h	NOUN
concept-2276	38	1	+	+	CCONJ
concept-2276	38	2	bb	bb	PROPN
concept-2276	38	3	+	+	CCONJ
concept-2276	38	4	hbp	hbp	PROPN
concept-2276	38	5	and	and	CCONJ
concept-2276	38	6	plate	plate	NOUN
concept-2276	38	7	appearances	appearance	NOUN
concept-2276	38	8	=	=	PUNCT
concept-2276	38	9	ab	ab	PROPN
concept-2276	39	1	+	+	CCONJ
concept-2276	39	2	bb	bb	PROPN
concept-2276	40	1	+	+	CCONJ
concept-2276	40	2	hbp	hbp	PROPN
concept-2276	40	3	+	+	CCONJ
concept-2276	40	4	sf	sf	NOUN
concept-2276	41	1	and	and	CCONJ
concept-2276	41	2	find	find	VERB
concept-2276	41	3	the	the	DET
concept-2276	41	4	joint	joint	ADJ
concept-2276	41	5	distribution	distribution	NOUN
concept-2276	41	6	of	of	ADP
concept-2276	41	7	the	the	DET
concept-2276	41	8	random	random	ADJ
concept-2276	41	9	variables	variable	NOUN
concept-2276	41	10	tob	tob	PROPN
concept-2276	41	11	(	(	PUNCT
concept-2276	41	12	times	time	NOUN
concept-2276	41	13	-	-	PUNCT
concept-2276	41	14	on	on	ADP
concept-2276	41	15	-	-	PUNCT
concept-2276	41	16	base	base	NOUN
concept-2276	41	17	)	)	PUNCT
concept-2276	41	18	,	,	PUNCT
concept-2276	41	19	p	p	X
concept-2276	41	20	(	(	PUNCT
concept-2276	41	21	prior	prior	ADJ
concept-2276	41	22	true	true	ADJ
concept-2276	41	23	ability	ability	NOUN
concept-2276	41	24	)	)	PUNCT
concept-2276	41	25	,	,	PUNCT
concept-2276	41	26	and	and	CCONJ
concept-2276	41	27	pa	pa	PROPN
concept-2276	41	28	(	(	PUNCT
concept-2276	41	29	plate	plate	NOUN
concept-2276	41	30	appearances	appearance	NOUN
concept-2276	41	31	)	)	PUNCT
concept-2276	41	32	.	.	PUNCT
concept-2276	42	1	we	we	PRON
concept-2276	42	2	first	first	ADV
concept-2276	42	3	find	find	VERB
concept-2276	42	4	the	the	DET
concept-2276	42	5	marginal	marginal	ADJ
concept-2276	42	6	distribution	distribution	NOUN
concept-2276	42	7	of	of	ADP
concept-2276	42	8	pa	pa	PROPN
concept-2276	42	9	.	.	PUNCT
concept-2276	43	1	then	then	ADV
concept-2276	43	2	we	we	PRON
concept-2276	43	3	model	model	VERB
concept-2276	43	4	the	the	DET
concept-2276	43	5	conditional	conditional	ADJ
concept-2276	43	6	distribution	distribution	NOUN
concept-2276	43	7	of	of	ADP
concept-2276	43	8	p	p	NOUN
concept-2276	43	9	given	give	VERB
concept-2276	43	10	pa	pa	PROPN
concept-2276	43	11	.	.	PUNCT
concept-2276	44	1	after	after	ADP
concept-2276	44	2	that	that	PRON
concept-2276	44	3	,	,	PUNCT
concept-2276	44	4	we	we	PRON
concept-2276	44	5	model	model	VERB
concept-2276	44	6	the	the	DET
concept-2276	44	7	conditional	conditional	ADJ
concept-2276	44	8	distribution	distribution	NOUN
concept-2276	44	9	of	of	ADP
concept-2276	44	10	tob	tob	NOUN
concept-2276	44	11	given	give	VERB
concept-2276	44	12	p	p	PROPN
concept-2276	44	13	and	and	CCONJ
concept-2276	44	14	pa	pa	PROPN
concept-2276	44	15	.	.	PROPN
concept-2276	44	16	i.	i.	PROPN
concept-2276	44	17	plate	plate	PROPN
concept-2276	44	18	appearances	appearance	VERB
concept-2276	44	19	to	to	PART
concept-2276	44	20	model	model	VERB
concept-2276	44	21	the	the	DET
concept-2276	44	22	marginal	marginal	ADJ
concept-2276	44	23	distribution	distribution	NOUN
concept-2276	44	24	of	of	ADP
concept-2276	44	25	pa	pa	PROPN
concept-2276	44	26	,	,	PUNCT
concept-2276	44	27	we	we	PRON
concept-2276	44	28	first	first	ADV
concept-2276	44	29	made	make	VERB
concept-2276	44	30	histograms	histogram	NOUN
concept-2276	44	31	of	of	ADP
concept-2276	44	32	the	the	DET
concept-2276	44	33	player	player	NOUN
concept-2276	44	34	plate	plate	NOUN
concept-2276	44	35	appearances	appearance	VERB
concept-2276	44	36	totals	total	NOUN
concept-2276	44	37	for	for	ADP
concept-2276	44	38	the	the	DET
concept-2276	44	39	2015	2015	NUM
concept-2276	44	40	and	and	CCONJ
concept-2276	44	41	2016	2016	NUM
concept-2276	44	42	seasons	season	NOUN
concept-2276	44	43	.	.	PUNCT
concept-2276	45	1	figure	figure	VERB
concept-2276	45	2	1	1	NUM
concept-2276	45	3	presents	present	VERB
concept-2276	45	4	the	the	DET
concept-2276	45	5	histograms	histogram	NOUN
concept-2276	45	6	of	of	ADP
concept-2276	45	7	the	the	DET
concept-2276	45	8	plate	plate	NOUN
concept-2276	45	9	appearances	appearance	VERB
concept-2276	45	10	for	for	ADP
concept-2276	45	11	the	the	DET
concept-2276	45	12	2015	2015	NUM
concept-2276	45	13	season	season	NOUN
concept-2276	45	14	,	,	PUNCT
concept-2276	45	15	2016	2016	NUM
concept-2276	45	16	season	season	NOUN
concept-2276	45	17	,	,	PUNCT
concept-2276	45	18	and	and	CCONJ
concept-2276	45	19	the	the	DET
concept-2276	45	20	two	two	NUM
concept-2276	45	21	seasons	season	NOUN
concept-2276	45	22	combined	combine	VERB
concept-2276	45	23	.	.	PUNCT
concept-2276	46	1	by	by	ADP
concept-2276	46	2	approximating	approximate	VERB
concept-2276	46	3	the	the	DET
concept-2276	46	4	histograms	histogram	NOUN
concept-2276	46	5	with	with	ADP
concept-2276	46	6	a	a	DET
concept-2276	46	7	combination	combination	NOUN
concept-2276	46	8	of	of	ADP
concept-2276	46	9	lines	line	NOUN
concept-2276	46	10	and	and	CCONJ
concept-2276	46	11	curves	curve	NOUN
concept-2276	46	12	,	,	PUNCT
concept-2276	46	13	we	we	PRON
concept-2276	46	14	created	create	VERB
concept-2276	46	15	a	a	DET
concept-2276	46	16	probability	probability	NOUN
concept-2276	46	17	density	density	NOUN
concept-2276	46	18	function	function	NOUN
concept-2276	46	19	for	for	ADP
concept-2276	46	20	the	the	DET
concept-2276	46	21	plate	plate	NOUN
concept-2276	46	22	appearances	appearance	NOUN
concept-2276	46	23	.	.	PUNCT
concept-2276	47	1	the	the	DET
concept-2276	47	2	reason	reason	NOUN
concept-2276	47	3	that	that	PRON
concept-2276	47	4	we	we	PRON
concept-2276	47	5	do	do	VERB
concept-2276	47	6	this	this	DET
concept-2276	47	7	task	task	NOUN
concept-2276	47	8	is	be	AUX
concept-2276	47	9	to	to	PART
concept-2276	47	10	convert	convert	VERB
concept-2276	47	11	the	the	DET
concept-2276	47	12	plate	plate	NOUN
concept-2276	47	13	appearances	appearance	VERB
concept-2276	47	14	data	datum	NOUN
concept-2276	47	15	from	from	ADP
concept-2276	47	16	a	a	DET
concept-2276	47	17	practical	practical	ADJ
concept-2276	47	18	histogram	histogram	NOUN
concept-2276	47	19	model	model	NOUN
concept-2276	47	20	to	to	ADP
concept-2276	47	21	a	a	DET
concept-2276	47	22	theoretical	theoretical	ADJ
concept-2276	47	23	probability	probability	NOUN
concept-2276	47	24	density	density	NOUN
concept-2276	47	25	function	function	NOUN
concept-2276	47	26	model	model	NOUN
concept-2276	47	27	.	.	PUNCT
concept-2276	48	1	the	the	DET
concept-2276	48	2	probability	probability	NOUN
concept-2276	48	3	density	density	NOUN
concept-2276	48	4	function	function	NOUN
concept-2276	48	5	will	will	AUX
concept-2276	48	6	allow	allow	VERB
concept-2276	48	7	us	we	PRON
concept-2276	48	8	to	to	PART
concept-2276	48	9	make	make	VERB
concept-2276	48	10	calculations	calculation	NOUN
concept-2276	48	11	when	when	SCONJ
concept-2276	48	12	3	3	NUM
concept-2276	48	13	2015	2015	NUM
concept-2276	48	14	season	season	NOUN
concept-2276	48	15	plate	plate	NOUN
concept-2276	48	16	appearances	appearance	VERB
concept-2276	48	17	f	f	PROPN
concept-2276	48	18	re	re	NOUN
concept-2276	48	19	q	q	X
concept-2276	48	20	u	u	X
concept-2276	48	21	e	e	X
concept-2276	48	22	n	n	PROPN
concept-2276	48	23	c	c	PROPN
concept-2276	48	24	y	y	PROPN
concept-2276	48	25	0	0	NUM
concept-2276	48	26	200	200	NUM
concept-2276	48	27	400	400	NUM
concept-2276	48	28	600	600	NUM
concept-2276	48	29	800	800	NUM
concept-2276	48	30	0	0	NUM
concept-2276	48	31	2	2	NUM
concept-2276	48	32	0	0	NUM
concept-2276	48	33	4	4	NUM
concept-2276	48	34	0	0	NUM
concept-2276	48	35	6	6	NUM
concept-2276	48	36	0	0	NUM
concept-2276	48	37	8	8	NUM
concept-2276	48	38	0	0	NUM
concept-2276	48	39	2016	2016	NUM
concept-2276	48	40	season	season	NOUN
concept-2276	48	41	plate	plate	NOUN
concept-2276	48	42	appearances	appearance	VERB
concept-2276	48	43	f	f	PROPN
concept-2276	48	44	re	re	NOUN
concept-2276	48	45	q	q	X
concept-2276	48	46	u	u	X
concept-2276	48	47	e	e	X
concept-2276	48	48	n	n	PROPN
concept-2276	48	49	c	c	PROPN
concept-2276	48	50	y	y	PROPN
concept-2276	48	51	0	0	NUM
concept-2276	48	52	200	200	NUM
concept-2276	48	53	400	400	NUM
concept-2276	48	54	600	600	NUM
concept-2276	48	55	800	800	NUM
concept-2276	48	56	0	0	NUM
concept-2276	48	57	2	2	NUM
concept-2276	48	58	0	0	NUM
concept-2276	48	59	4	4	NUM
concept-2276	48	60	0	0	NUM
concept-2276	48	61	6	6	NUM
concept-2276	48	62	0	0	NUM
concept-2276	48	63	8	8	NUM
concept-2276	48	64	0	0	NUM
concept-2276	48	65	combined	combine	VERB
concept-2276	48	66	data	datum	NOUN
concept-2276	48	67	plate	plate	NOUN
concept-2276	48	68	appearances	appearance	VERB
concept-2276	48	69	f	f	PROPN
concept-2276	48	70	re	re	NOUN
concept-2276	48	71	q	q	X
concept-2276	48	72	u	u	X
concept-2276	48	73	e	e	X
concept-2276	48	74	n	n	PROPN
concept-2276	48	75	c	c	PROPN
concept-2276	48	76	y	y	PROPN
concept-2276	48	77	0	0	NUM
concept-2276	48	78	200	200	NUM
concept-2276	48	79	400	400	NUM
concept-2276	48	80	600	600	NUM
concept-2276	48	81	800	800	NUM
concept-2276	48	82	0	0	NUM
concept-2276	48	83	5	5	NUM
concept-2276	48	84	0	0	NUM
concept-2276	48	85	1	1	NUM
concept-2276	48	86	0	0	NUM
concept-2276	48	87	0	0	NUM
concept-2276	48	88	1	1	NUM
concept-2276	48	89	5	5	NUM
concept-2276	48	90	0	0	NUM
concept-2276	48	91	figure	figure	NOUN
concept-2276	48	92	1	1	NUM
concept-2276	48	93	:	:	PUNCT
concept-2276	48	94	histogram	histogram	NOUN
concept-2276	48	95	of	of	ADP
concept-2276	48	96	plate	plate	NOUN
concept-2276	48	97	appearances	appearance	NOUN
concept-2276	48	98	for	for	ADP
concept-2276	48	99	the	the	DET
concept-2276	48	100	2015	2015	NUM
concept-2276	48	101	,	,	PUNCT
concept-2276	48	102	2016	2016	NUM
concept-2276	48	103	,	,	PUNCT
concept-2276	48	104	and	and	CCONJ
concept-2276	48	105	combined	combined	ADJ
concept-2276	48	106	seasons	season	NOUN
concept-2276	48	107	respectively	respectively	ADV
concept-2276	48	108	this	this	DET
concept-2276	48	109	distribution	distribution	NOUN
concept-2276	48	110	is	be	AUX
concept-2276	48	111	combined	combine	VERB
concept-2276	48	112	with	with	ADP
concept-2276	48	113	the	the	DET
concept-2276	48	114	other	other	ADJ
concept-2276	48	115	distributions	distribution	NOUN
concept-2276	48	116	in	in	ADP
concept-2276	48	117	the	the	DET
concept-2276	48	118	model	model	NOUN
concept-2276	48	119	.	.	PUNCT
concept-2276	49	1	notice	notice	VERB
concept-2276	49	2	that	that	SCONJ
concept-2276	49	3	all	all	DET
concept-2276	49	4	three	three	NUM
concept-2276	49	5	histograms	histogram	NOUN
concept-2276	49	6	were	be	AUX
concept-2276	49	7	relatively	relatively	ADV
concept-2276	49	8	similar	similar	ADJ
concept-2276	49	9	,	,	PUNCT
concept-2276	49	10	which	which	PRON
concept-2276	49	11	allows	allow	VERB
concept-2276	49	12	us	we	PRON
concept-2276	49	13	to	to	PART
concept-2276	49	14	form	form	VERB
concept-2276	49	15	a	a	DET
concept-2276	49	16	density	density	NOUN
concept-2276	49	17	function	function	NOUN
concept-2276	49	18	that	that	PRON
concept-2276	49	19	will	will	AUX
concept-2276	49	20	capture	capture	VERB
concept-2276	49	21	the	the	DET
concept-2276	49	22	main	main	ADJ
concept-2276	49	23	properties	property	NOUN
concept-2276	49	24	of	of	ADP
concept-2276	49	25	each	each	PRON
concept-2276	49	26	of	of	ADP
concept-2276	49	27	the	the	DET
concept-2276	49	28	histograms	histogram	NOUN
concept-2276	49	29	.	.	PUNCT
concept-2276	50	1	the	the	DET
concept-2276	50	2	goal	goal	NOUN
concept-2276	50	3	of	of	ADP
concept-2276	50	4	the	the	DET
concept-2276	50	5	density	density	NOUN
concept-2276	50	6	function	function	NOUN
concept-2276	50	7	is	be	AUX
concept-2276	50	8	to	to	PART
concept-2276	50	9	create	create	VERB
concept-2276	50	10	a	a	DET
concept-2276	50	11	function	function	NOUN
concept-2276	50	12	that	that	PRON
concept-2276	50	13	will	will	AUX
concept-2276	50	14	approximate	approximate	VERB
concept-2276	50	15	the	the	DET
concept-2276	50	16	probability	probability	NOUN
concept-2276	50	17	of	of	ADP
concept-2276	50	18	each	each	DET
concept-2276	50	19	plate	plate	NOUN
concept-2276	50	20	appearance	appearance	NOUN
concept-2276	50	21	occurring	occur	VERB
concept-2276	50	22	.	.	PUNCT
concept-2276	51	1	while	while	SCONJ
concept-2276	51	2	one	one	PRON
concept-2276	51	3	could	could	AUX
concept-2276	51	4	do	do	VERB
concept-2276	51	5	this	this	PRON
concept-2276	51	6	by	by	ADP
concept-2276	51	7	simply	simply	ADV
concept-2276	51	8	counting	count	VERB
concept-2276	51	9	the	the	DET
concept-2276	51	10	frequencies	frequency	NOUN
concept-2276	51	11	of	of	ADP
concept-2276	51	12	a	a	DET
concept-2276	51	13	plate	plate	NOUN
concept-2276	51	14	appearance	appearance	NOUN
concept-2276	51	15	occurring	occur	VERB
concept-2276	51	16	and	and	CCONJ
concept-2276	51	17	dividing	divide	VERB
concept-2276	51	18	by	by	ADP
concept-2276	51	19	the	the	DET
concept-2276	51	20	number	number	NOUN
concept-2276	51	21	of	of	ADP
concept-2276	51	22	players	player	NOUN
concept-2276	51	23	,	,	PUNCT
concept-2276	51	24	there	there	PRON
concept-2276	51	25	are	be	VERB
concept-2276	51	26	a	a	DET
concept-2276	51	27	lot	lot	NOUN
concept-2276	51	28	of	of	ADP
concept-2276	51	29	variance	variance	NOUN
concept-2276	51	30	with	with	ADP
concept-2276	51	31	each	each	PRON
concept-2276	51	32	of	of	ADP
concept-2276	51	33	the	the	DET
concept-2276	51	34	probabilities	probability	NOUN
concept-2276	51	35	since	since	SCONJ
concept-2276	51	36	the	the	DET
concept-2276	51	37	probabilities	probability	NOUN
concept-2276	51	38	would	would	AUX
concept-2276	51	39	vary	vary	VERB
concept-2276	51	40	a	a	DET
concept-2276	51	41	lot	lot	NOUN
concept-2276	51	42	from	from	ADP
concept-2276	51	43	year	year	NOUN
concept-2276	51	44	to	to	ADP
concept-2276	51	45	year	year	NOUN
concept-2276	51	46	,	,	PUNCT
concept-2276	51	47	thus	thus	ADV
concept-2276	51	48	making	make	VERB
concept-2276	51	49	for	for	ADP
concept-2276	51	50	an	an	DET
concept-2276	51	51	unreliable	unreliable	ADJ
concept-2276	51	52	model	model	NOUN
concept-2276	51	53	.	.	PUNCT
concept-2276	52	1	making	make	VERB
concept-2276	52	2	a	a	DET
concept-2276	52	3	probability	probability	NOUN
concept-2276	52	4	density	density	NOUN
concept-2276	52	5	function	function	NOUN
concept-2276	52	6	using	use	VERB
concept-2276	52	7	lines	line	NOUN
concept-2276	52	8	and	and	CCONJ
concept-2276	52	9	curves	curve	NOUN
concept-2276	52	10	will	will	AUX
concept-2276	52	11	allow	allow	VERB
concept-2276	52	12	us	we	PRON
concept-2276	52	13	to	to	PART
concept-2276	52	14	retain	retain	VERB
concept-2276	52	15	the	the	DET
concept-2276	52	16	general	general	ADJ
concept-2276	52	17	pattern	pattern	NOUN
concept-2276	52	18	that	that	PRON
concept-2276	52	19	is	be	AUX
concept-2276	52	20	observed	observe	VERB
concept-2276	52	21	with	with	ADP
concept-2276	52	22	the	the	DET
concept-2276	52	23	baseball	baseball	NOUN
concept-2276	52	24	data	datum	NOUN
concept-2276	52	25	over	over	ADP
concept-2276	52	26	the	the	DET
concept-2276	52	27	course	course	NOUN
concept-2276	52	28	of	of	ADP
concept-2276	52	29	multiple	multiple	ADJ
concept-2276	52	30	seasons	season	NOUN
concept-2276	52	31	,	,	PUNCT
concept-2276	52	32	rather	rather	ADV
concept-2276	52	33	than	than	ADP
concept-2276	52	34	baseball	baseball	NOUN
concept-2276	52	35	data	datum	NOUN
concept-2276	52	36	just	just	ADV
concept-2276	52	37	for	for	ADP
concept-2276	52	38	a	a	DET
concept-2276	52	39	particular	particular	ADJ
concept-2276	52	40	year	year	NOUN
concept-2276	52	41	.	.	PUNCT
concept-2276	53	1	with	with	ADP
concept-2276	53	2	turning	turn	VERB
concept-2276	53	3	a	a	DET
concept-2276	53	4	probability	probability	NOUN
concept-2276	53	5	distribution	distribution	NOUN
concept-2276	53	6	function	function	NOUN
concept-2276	53	7	into	into	ADP
concept-2276	53	8	a	a	DET
concept-2276	53	9	function	function	NOUN
concept-2276	53	10	that	that	PRON
concept-2276	53	11	approximates	approximate	VERB
concept-2276	53	12	the	the	DET
concept-2276	53	13	probabilities	probability	NOUN
concept-2276	53	14	of	of	ADP
concept-2276	53	15	individual	individual	ADJ
concept-2276	53	16	plate	plate	NOUN
concept-2276	53	17	appearances	appearance	NOUN
concept-2276	53	18	occurring	occur	VERB
concept-2276	53	19	,	,	PUNCT
concept-2276	53	20	we	we	PRON
concept-2276	53	21	will	will	AUX
concept-2276	53	22	use	use	VERB
concept-2276	53	23	the	the	DET
concept-2276	53	24	fact	fact	NOUN
concept-2276	53	25	that	that	SCONJ
concept-2276	53	26	p(pa	p(pa	PROPN
concept-2276	53	27	=	=	SYM
concept-2276	53	28	pa	pa	PROPN
concept-2276	53	29	)	)	PUNCT
concept-2276	53	30	=	=	PROPN
concept-2276	53	31	p(pa	p(pa	NOUN
concept-2276	53	32	≤	≤	NUM
concept-2276	53	33	pa	pa	PROPN
concept-2276	53	34	<	<	X
concept-2276	53	35	pa	pa	PROPN
concept-2276	53	36	+	+	PROPN
concept-2276	53	37	1	1	NUM
concept-2276	53	38	)	)	PUNCT
concept-2276	53	39	.	.	PUNCT
concept-2276	54	1	this	this	PRON
concept-2276	54	2	is	be	AUX
concept-2276	54	3	reasonable	reasonable	ADJ
concept-2276	54	4	to	to	PART
concept-2276	54	5	do	do	VERB
concept-2276	54	6	since	since	SCONJ
concept-2276	54	7	plate	plate	NOUN
concept-2276	54	8	appearances	appearance	NOUN
concept-2276	54	9	are	be	AUX
concept-2276	54	10	only	only	ADV
concept-2276	54	11	integers	integer	NOUN
concept-2276	54	12	and	and	CCONJ
concept-2276	54	13	partitioning	partition	VERB
concept-2276	54	14	the	the	DET
concept-2276	54	15	domain	domain	NOUN
concept-2276	54	16	of	of	ADP
concept-2276	54	17	f(x	f(x	PROPN
concept-2276	54	18	)	)	PUNCT
concept-2276	54	19	,	,	PUNCT
concept-2276	54	20	which	which	PRON
concept-2276	54	21	is	be	AUX
concept-2276	54	22	the	the	DET
concept-2276	54	23	real	real	ADJ
concept-2276	54	24	line	line	NOUN
concept-2276	54	25	,	,	PUNCT
concept-2276	54	26	into	into	ADP
concept-2276	54	27	discrete	discrete	ADJ
concept-2276	54	28	parts	part	NOUN
concept-2276	54	29	allows	allow	VERB
concept-2276	54	30	us	we	PRON
concept-2276	54	31	to	to	PART
concept-2276	54	32	have	have	VERB
concept-2276	54	33	the	the	DET
concept-2276	54	34	distribution	distribution	NOUN
concept-2276	54	35	d(pa	d(pa	NOUN
concept-2276	54	36	)	)	PUNCT
concept-2276	54	37	to	to	PART
concept-2276	54	38	have	have	VERB
concept-2276	54	39	the	the	DET
concept-2276	54	40	domain	domain	NOUN
concept-2276	54	41	consisting	consist	VERB
concept-2276	54	42	of	of	ADP
concept-2276	54	43	integers	integer	NOUN
concept-2276	54	44	.	.	PUNCT
concept-2276	55	1	d(pa	d(pa	NOUN
concept-2276	55	2	)	)	PUNCT
concept-2276	55	3	≡	≡	PROPN
concept-2276	55	4	∫	∫	PROPN
concept-2276	56	1	pa+1	pa+1	INTJ
concept-2276	56	2	pa	pa	PROPN
concept-2276	56	3	f	f	PROPN
concept-2276	56	4	(	(	PUNCT
concept-2276	56	5	t)dt	t)dt	PROPN
concept-2276	56	6	(	(	PUNCT
concept-2276	56	7	1	1	NUM
concept-2276	56	8	)	)	PUNCT
concept-2276	56	9	where	where	SCONJ
concept-2276	56	10	f	f	PROPN
concept-2276	56	11	is	be	AUX
concept-2276	56	12	the	the	DET
concept-2276	56	13	density	density	NOUN
concept-2276	56	14	function	function	VERB
concept-2276	56	15	4	4	NUM
concept-2276	56	16	f	f	NOUN
concept-2276	56	17	(	(	PUNCT
concept-2276	56	18	x	x	NOUN
concept-2276	56	19	)	)	PUNCT
concept-2276	56	20	=	=	SYM
concept-2276	56	21			NUM
concept-2276	56	22	0.004779146e−.014285714x	0.004779146e−.014285714x	NOUN
concept-2276	57	1	+	+	NUM
concept-2276	57	2	.001013758	.001013758	PROPN
concept-2276	58	1	if	if	SCONJ
concept-2276	58	2	0	0	NUM
concept-2276	58	3	≤	≤	NUM
concept-2276	58	4	x	x	X
concept-2276	58	5	<	<	X
concept-2276	58	6	280	280	NUM
concept-2276	58	7	0.00083273	0.00083273	NUM
concept-2276	58	8	if	if	SCONJ
concept-2276	58	9	280	280	NUM
concept-2276	58	10	≤	≤	NUM
concept-2276	58	11	x	x	PUNCT
concept-2276	58	12	<	<	X
concept-2276	58	13	600	600	NUM
concept-2276	58	14	0.001122375	0.001122375	NUM
concept-2276	58	15	if	if	SCONJ
concept-2276	58	16	600	600	NUM
concept-2276	58	17	≤	≤	NUM
concept-2276	58	18	x	x	PUNCT
concept-2276	58	19	<	<	X
concept-2276	58	20	700	700	NUM
concept-2276	58	21	−0.00000501319544x	−0.00000501319544x	NOUN
concept-2276	58	22	+	+	NUM
concept-2276	58	23	0.0038100285	0.0038100285	NUM
concept-2276	58	24	if	if	SCONJ
concept-2276	58	25	700	700	NUM
concept-2276	58	26	≤	≤	NUM
concept-2276	58	27	x	x	X
concept-2276	58	28	<	<	X
concept-2276	58	29	760	760	NUM
concept-2276	58	30	even	even	ADV
concept-2276	58	31	though	though	SCONJ
concept-2276	58	32	one	one	PRON
concept-2276	58	33	could	could	AUX
concept-2276	58	34	theoretically	theoretically	ADV
concept-2276	58	35	have	have	VERB
concept-2276	58	36	an	an	DET
concept-2276	58	37	unlimited	unlimited	ADJ
concept-2276	58	38	number	number	NOUN
concept-2276	58	39	of	of	ADP
concept-2276	58	40	plate	plate	NOUN
concept-2276	58	41	appearances	appearance	NOUN
concept-2276	58	42	in	in	ADP
concept-2276	58	43	a	a	DET
concept-2276	58	44	season	season	NOUN
concept-2276	58	45	,	,	PUNCT
concept-2276	58	46	in	in	ADP
concept-2276	58	47	practice	practice	NOUN
concept-2276	58	48	,	,	PUNCT
concept-2276	58	49	none	none	NOUN
concept-2276	58	50	of	of	ADP
concept-2276	58	51	the	the	DET
concept-2276	58	52	plate	plate	NOUN
concept-2276	58	53	appearances	appearance	NOUN
concept-2276	58	54	have	have	AUX
concept-2276	58	55	surpassed	surpass	VERB
concept-2276	58	56	760	760	NUM
concept-2276	58	57	,	,	PUNCT
concept-2276	58	58	so	so	ADV
concept-2276	58	59	for	for	ADP
concept-2276	58	60	the	the	DET
concept-2276	58	61	sake	sake	NOUN
concept-2276	58	62	of	of	ADP
concept-2276	58	63	this	this	DET
concept-2276	58	64	model	model	NOUN
concept-2276	58	65	,	,	PUNCT
concept-2276	58	66	we	we	PRON
concept-2276	58	67	assume	assume	VERB
concept-2276	58	68	that	that	SCONJ
concept-2276	58	69	x	x	PUNCT
concept-2276	58	70	<	<	X
concept-2276	58	71	760	760	NUM
concept-2276	58	72	.	.	PUNCT
concept-2276	58	73	ii	ii	PROPN
concept-2276	58	74	.	.	PUNCT
concept-2276	59	1	true	true	ADJ
concept-2276	59	2	ability	ability	NOUN
concept-2276	59	3	to	to	PART
concept-2276	59	4	model	model	VERB
concept-2276	59	5	the	the	DET
concept-2276	59	6	conditional	conditional	ADJ
concept-2276	59	7	distribution	distribution	NOUN
concept-2276	59	8	of	of	ADP
concept-2276	59	9	prior	prior	ADJ
concept-2276	59	10	true	true	ADJ
concept-2276	59	11	ability	ability	NOUN
concept-2276	59	12	p	p	NOUN
concept-2276	59	13	of	of	ADP
concept-2276	59	14	a	a	DET
concept-2276	59	15	player	player	NOUN
concept-2276	59	16	getting	get	VERB
concept-2276	59	17	on	on	ADP
concept-2276	59	18	-	-	PUNCT
concept-2276	59	19	base	base	NOUN
concept-2276	59	20	given	give	VERB
concept-2276	59	21	only	only	ADV
concept-2276	59	22	pa	pa	PROPN
concept-2276	59	23	and	and	CCONJ
concept-2276	59	24	nothing	nothing	PRON
concept-2276	59	25	else	else	ADV
concept-2276	59	26	,	,	PUNCT
concept-2276	59	27	we	we	PRON
concept-2276	59	28	turned	turn	VERB
concept-2276	59	29	to	to	ADP
concept-2276	59	30	the	the	DET
concept-2276	59	31	beta	beta	ADJ
concept-2276	59	32	family	family	NOUN
concept-2276	59	33	of	of	ADP
concept-2276	59	34	distributions	distribution	NOUN
concept-2276	59	35	.	.	PUNCT
concept-2276	60	1	the	the	DET
concept-2276	60	2	beta	beta	ADJ
concept-2276	60	3	distribution	distribution	NOUN
concept-2276	60	4	is	be	AUX
concept-2276	60	5	a	a	DET
concept-2276	60	6	probability	probability	NOUN
concept-2276	60	7	density	density	NOUN
concept-2276	60	8	function	function	VERB
concept-2276	60	9	such	such	ADJ
concept-2276	60	10	that	that	SCONJ
concept-2276	60	11	x	x	PRON
concept-2276	60	12	is	be	AUX
concept-2276	60	13	between	between	ADP
concept-2276	60	14	0	0	NUM
concept-2276	60	15	and	and	CCONJ
concept-2276	60	16	1	1	NUM
concept-2276	60	17	and	and	CCONJ
concept-2276	60	18	α	α	NOUN
concept-2276	60	19	and	and	CCONJ
concept-2276	60	20	β	β	X
concept-2276	60	21	are	be	AUX
concept-2276	60	22	greater	great	ADJ
concept-2276	60	23	than	than	ADP
concept-2276	60	24	0	0	NUM
concept-2276	60	25	.	.	PUNCT
concept-2276	61	1	with	with	ADP
concept-2276	61	2	this	this	DET
concept-2276	61	3	distribution	distribution	NOUN
concept-2276	61	4	,	,	PUNCT
concept-2276	61	5	fx(x	fx(x	PUNCT
concept-2276	61	6	)	)	PUNCT
concept-2276	61	7	=	=	PUNCT
concept-2276	61	8	xα−1(1−x)β−1	xα−1(1−x)β−1	PROPN
concept-2276	61	9	b(α	b(α	PROPN
concept-2276	61	10	,	,	PUNCT
concept-2276	61	11	β	β	NOUN
concept-2276	61	12	)	)	PUNCT
concept-2276	61	13	where	where	SCONJ
concept-2276	61	14	b(α	b(α	PROPN
concept-2276	61	15	,	,	PUNCT
concept-2276	61	16	β	β	NOUN
concept-2276	61	17	)	)	PUNCT
concept-2276	61	18	=	=	SYM
concept-2276	61	19	γ(α)γ(β	γ(α)γ(β	NOUN
concept-2276	61	20	)	)	PUNCT
concept-2276	61	21	γ(α+β	γ(α+β	NUM
concept-2276	61	22	)	)	PUNCT
concept-2276	61	23	and	and	CCONJ
concept-2276	61	24	γ(α	γ(α	NOUN
concept-2276	61	25	)	)	PUNCT
concept-2276	62	1	=	=	PRON
concept-2276	62	2	(	(	PUNCT
concept-2276	62	3	α−	α−	ADP
concept-2276	62	4	1	1	NUM
concept-2276	62	5	)	)	PUNCT
concept-2276	62	6	!	!	PUNCT
concept-2276	63	1	=	=	PUNCT
concept-2276	64	1	∫	∫	PROPN
concept-2276	65	1	∞	∞	PROPN
concept-2276	65	2	0	0	NUM
concept-2276	65	3	xα−1e−xdx	xα−1e−xdx	PROPN
concept-2276	65	4	.	.	PUNCT
concept-2276	66	1	frey	frey	PROPN
concept-2276	66	2	(	(	PUNCT
concept-2276	66	3	2007	2007	NUM
concept-2276	66	4	)	)	PUNCT
concept-2276	66	5	found	find	VERB
concept-2276	66	6	that	that	SCONJ
concept-2276	66	7	one	one	PRON
concept-2276	66	8	can	can	AUX
concept-2276	66	9	find	find	VERB
concept-2276	66	10	the	the	DET
concept-2276	66	11	true	true	ADJ
concept-2276	66	12	ability	ability	NOUN
concept-2276	66	13	for	for	ADP
concept-2276	66	14	batting	batting	NOUN
concept-2276	66	15	average	average	NOUN
concept-2276	66	16	by	by	ADP
concept-2276	66	17	modeling	model	VERB
concept-2276	66	18	the	the	DET
concept-2276	66	19	mean	mean	NOUN
concept-2276	66	20	of	of	ADP
concept-2276	66	21	ability	ability	NOUN
concept-2276	66	22	(	(	PUNCT
concept-2276	66	23	µ(a	µ(a	PROPN
concept-2276	66	24	)	)	PUNCT
concept-2276	66	25	)	)	PUNCT
concept-2276	66	26	given	give	VERB
concept-2276	66	27	at	at	ADP
concept-2276	66	28	bats	bat	NOUN
concept-2276	66	29	and	and	CCONJ
concept-2276	66	30	the	the	DET
concept-2276	66	31	one	one	NUM
concept-2276	66	32	of	of	ADP
concept-2276	66	33	the	the	DET
concept-2276	66	34	parameters	parameter	NOUN
concept-2276	66	35	of	of	ADP
concept-2276	66	36	variability	variability	NOUN
concept-2276	66	37	of	of	ADP
concept-2276	66	38	ability	ability	NOUN
concept-2276	66	39	(	(	PUNCT
concept-2276	66	40	c	c	NOUN
concept-2276	66	41	)	)	PUNCT
concept-2276	66	42	given	give	VERB
concept-2276	66	43	at	at	ADP
concept-2276	66	44	bats	bat	NOUN
concept-2276	66	45	.	.	PUNCT
concept-2276	67	1	then	then	ADV
concept-2276	67	2	one	one	PRON
concept-2276	67	3	can	can	AUX
concept-2276	67	4	set	set	VERB
concept-2276	67	5	µ	µ	NOUN
concept-2276	67	6	=	=	SYM
concept-2276	67	7	α	α	PRON
concept-2276	67	8	α+β	α+β	PROPN
concept-2276	67	9	and	and	CCONJ
concept-2276	67	10	c	c	NOUN
concept-2276	67	11	=	=	SYM
concept-2276	67	12	α	α	PROPN
concept-2276	68	1	+	+	X
concept-2276	68	2	β	β	NOUN
concept-2276	68	3	since	since	SCONJ
concept-2276	68	4	these	these	DET
concept-2276	68	5	two	two	NUM
concept-2276	68	6	parameters	parameter	NOUN
concept-2276	68	7	are	be	AUX
concept-2276	68	8	sufficient	sufficient	ADJ
concept-2276	68	9	to	to	PART
concept-2276	68	10	create	create	VERB
concept-2276	68	11	a	a	DET
concept-2276	68	12	beta	beta	ADJ
concept-2276	68	13	distribution	distribution	NOUN
concept-2276	68	14	model	model	NOUN
concept-2276	68	15	.	.	PUNCT
concept-2276	69	1	we	we	PRON
concept-2276	69	2	can	can	AUX
concept-2276	69	3	do	do	VERB
concept-2276	69	4	likewise	likewise	ADV
concept-2276	69	5	for	for	ADP
concept-2276	69	6	obp	obp	PROPN
concept-2276	69	7	by	by	ADP
concept-2276	69	8	substituting	substitute	VERB
concept-2276	69	9	at	at	ADP
concept-2276	69	10	bats	bat	NOUN
concept-2276	69	11	with	with	ADP
concept-2276	69	12	plate	plate	NOUN
concept-2276	69	13	appearances	appearance	NOUN
concept-2276	69	14	.	.	PUNCT
concept-2276	70	1	one	one	PRON
concept-2276	70	2	can	can	AUX
concept-2276	70	3	find	find	VERB
concept-2276	70	4	µ	µ	NOUN
concept-2276	70	5	by	by	ADP
concept-2276	70	6	doing	do	VERB
concept-2276	70	7	a	a	DET
concept-2276	70	8	lowess	lowess	ADJ
concept-2276	70	9	fit	fit	NOUN
concept-2276	70	10	of	of	ADP
concept-2276	70	11	a	a	DET
concept-2276	70	12	plot	plot	NOUN
concept-2276	70	13	of	of	ADP
concept-2276	70	14	on	on	ADP
concept-2276	70	15	-	-	PUNCT
concept-2276	70	16	base	base	NOUN
concept-2276	70	17	percentages	percentage	NOUN
concept-2276	70	18	versus	versus	ADP
concept-2276	70	19	plate	plate	NOUN
concept-2276	70	20	appearances	appearance	NOUN
concept-2276	70	21	and	and	CCONJ
concept-2276	70	22	creating	create	VERB
concept-2276	70	23	the	the	DET
concept-2276	70	24	equation	equation	NOUN
concept-2276	70	25	of	of	ADP
concept-2276	70	26	the	the	DET
concept-2276	70	27	lowess	lowess	ADJ
concept-2276	70	28	fit	fit	ADJ
concept-2276	70	29	line	line	NOUN
concept-2276	70	30	similar	similar	ADJ
concept-2276	70	31	to	to	ADP
concept-2276	70	32	what	what	PRON
concept-2276	70	33	we	we	PRON
concept-2276	70	34	did	do	AUX
concept-2276	70	35	with	with	ADP
concept-2276	70	36	the	the	DET
concept-2276	70	37	plate	plate	NOUN
concept-2276	70	38	appearances	appearance	NOUN
concept-2276	70	39	model	model	NOUN
concept-2276	70	40	.	.	PUNCT
concept-2276	71	1	figure	figure	NOUN
concept-2276	71	2	2	2	NUM
concept-2276	71	3	contains	contain	VERB
concept-2276	71	4	the	the	DET
concept-2276	71	5	lowess	lowess	ADJ
concept-2276	71	6	fit	fit	ADJ
concept-2276	71	7	plot	plot	NOUN
concept-2276	71	8	.	.	PUNCT
concept-2276	72	1	this	this	DET
concept-2276	72	2	equation	equation	NOUN
concept-2276	72	3	is	be	AUX
concept-2276	72	4	meant	mean	VERB
concept-2276	72	5	to	to	PART
concept-2276	72	6	be	be	AUX
concept-2276	72	7	an	an	DET
concept-2276	72	8	approximation	approximation	NOUN
concept-2276	72	9	of	of	ADP
concept-2276	72	10	the	the	DET
concept-2276	72	11	lowess	lowess	ADJ
concept-2276	72	12	fit	fit	NOUN
concept-2276	72	13	in	in	ADP
concept-2276	72	14	figure	figure	NOUN
concept-2276	72	15	2	2	NUM
concept-2276	72	16	.	.	PUNCT
concept-2276	72	17	from	from	ADP
concept-2276	72	18	this	this	DET
concept-2276	72	19	process	process	NOUN
concept-2276	72	20	it	it	PRON
concept-2276	72	21	follows	follow	VERB
concept-2276	72	22	that	that	SCONJ
concept-2276	72	23	µ(pa	µ(pa	NOUN
concept-2276	72	24	)	)	PUNCT
concept-2276	72	25	=	=	PUNCT
concept-2276	73	1			PUNCT
concept-2276	74	1	0.000261494x	0.000261494x	NOUN
concept-2276	75	1	+	+	NUM
concept-2276	75	2	.253448276	.253448276	NOUN
concept-2276	75	3	if	if	SCONJ
concept-2276	75	4	pa	pa	PROPN
concept-2276	75	5	≤	≤	PROPN
concept-2276	75	6	194	194	NUM
concept-2276	75	7	0.000078736x	0.000078736x	NOUN
concept-2276	76	1	+	+	X
concept-2276	76	2	.288965517	.288965517	INTJ
concept-2276	77	1	if	if	SCONJ
concept-2276	77	2	pa	pa	PROPN
concept-2276	77	3	>	>	X
concept-2276	77	4	194	194	NUM
concept-2276	77	5	with	with	ADP
concept-2276	77	6	finding	find	VERB
concept-2276	77	7	c	c	NOUN
concept-2276	77	8	,	,	PUNCT
concept-2276	77	9	we	we	PRON
concept-2276	77	10	have	have	VERB
concept-2276	77	11	to	to	PART
concept-2276	77	12	account	account	VERB
concept-2276	77	13	for	for	ADP
concept-2276	77	14	the	the	DET
concept-2276	77	15	fact	fact	NOUN
concept-2276	77	16	that	that	SCONJ
concept-2276	77	17	better	well	ADJ
concept-2276	77	18	players	player	NOUN
concept-2276	77	19	play	play	VERB
concept-2276	77	20	more	more	ADJ
concept-2276	77	21	.	.	PUNCT
concept-2276	78	1	as	as	ADP
concept-2276	78	2	a	a	DET
concept-2276	78	3	result	result	NOUN
concept-2276	78	4	of	of	ADP
concept-2276	78	5	this	this	DET
concept-2276	78	6	fact	fact	NOUN
concept-2276	78	7	,	,	PUNCT
concept-2276	78	8	the	the	DET
concept-2276	78	9	distribution	distribution	NOUN
concept-2276	78	10	of	of	ADP
concept-2276	78	11	p	p	NOUN
concept-2276	78	12	for	for	ADP
concept-2276	78	13	players	player	NOUN
concept-2276	78	14	with	with	ADP
concept-2276	78	15	a	a	DET
concept-2276	78	16	higher	high	ADJ
concept-2276	78	17	number	number	NOUN
concept-2276	78	18	plate	plate	NOUN
concept-2276	78	19	appearances	appearance	NOUN
concept-2276	78	20	will	will	AUX
concept-2276	78	21	be	be	AUX
concept-2276	78	22	stochastically	stochastically	ADV
concept-2276	78	23	larger	large	ADJ
concept-2276	78	24	than	than	ADP
concept-2276	78	25	those	those	PRON
concept-2276	78	26	with	with	ADP
concept-2276	78	27	a	a	DET
concept-2276	78	28	lower	low	ADJ
concept-2276	78	29	number	number	NOUN
concept-2276	78	30	of	of	ADP
concept-2276	78	31	plate	plate	NOUN
concept-2276	78	32	appearances	appearance	NOUN
concept-2276	78	33	.	.	PUNCT
concept-2276	79	1	what	what	PRON
concept-2276	79	2	frey	frey	NOUN
concept-2276	79	3	(	(	PUNCT
concept-2276	79	4	2007	2007	NUM
concept-2276	79	5	)	)	PUNCT
concept-2276	79	6	did	do	VERB
concept-2276	79	7	for	for	ADP
concept-2276	79	8	finding	find	VERB
concept-2276	79	9	5	5	NUM
concept-2276	79	10	0	0	NUM
concept-2276	79	11	200	200	NUM
concept-2276	79	12	400	400	NUM
concept-2276	80	1	600	600	NUM
concept-2276	80	2	0	0	NUM
concept-2276	80	3	.0	.0	NUM
concept-2276	80	4	0	0	NUM
concept-2276	81	1	.2	.2	NUM
concept-2276	81	2	0	0	NUM
concept-2276	82	1	.4	.4	NUM
concept-2276	82	2	0	0	NUM
concept-2276	83	1	.6	.6	NUM
concept-2276	83	2	0	0	NUM
concept-2276	83	3	.8	.8	NUM
concept-2276	83	4	1	1	NUM
concept-2276	83	5	.0	.0	NUM
concept-2276	83	6	plate	plate	NOUN
concept-2276	83	7	appearances	appearance	VERB
concept-2276	83	8	o	o	NOUN
concept-2276	83	9	b	b	X
concept-2276	83	10	p	p	NOUN
concept-2276	83	11	figure	figure	NOUN
concept-2276	83	12	2	2	NUM
concept-2276	83	13	:	:	PUNCT
concept-2276	83	14	plot	plot	NOUN
concept-2276	83	15	of	of	ADP
concept-2276	83	16	plate	plate	NOUN
concept-2276	83	17	appearances	appearance	NOUN
concept-2276	83	18	vs	vs	ADP
concept-2276	83	19	obp	obp	PROPN
concept-2276	83	20	’s	’s	PART
concept-2276	83	21	for	for	ADP
concept-2276	83	22	the	the	DET
concept-2276	83	23	2016	2016	NUM
concept-2276	83	24	season	season	NOUN
concept-2276	83	25	.	.	PUNCT
concept-2276	84	1	the	the	DET
concept-2276	84	2	extra	extra	ADJ
concept-2276	84	3	line	line	NOUN
concept-2276	84	4	is	be	AUX
concept-2276	84	5	a	a	DET
concept-2276	84	6	lowess	lowess	ADJ
concept-2276	84	7	fit	fit	NOUN
concept-2276	84	8	.	.	PUNCT
concept-2276	85	1	the	the	DET
concept-2276	85	2	variability	variability	NOUN
concept-2276	85	3	of	of	ADP
concept-2276	85	4	batting	batting	NOUN
concept-2276	85	5	average	average	NOUN
concept-2276	85	6	was	be	AUX
concept-2276	85	7	to	to	PART
concept-2276	85	8	first	first	ADJ
concept-2276	85	9	plot	plot	VERB
concept-2276	85	10	the	the	DET
concept-2276	85	11	variability	variability	NOUN
concept-2276	85	12	of	of	ADP
concept-2276	85	13	batting	batting	NOUN
concept-2276	85	14	average	average	NOUN
concept-2276	85	15	as	as	ADP
concept-2276	85	16	a	a	DET
concept-2276	85	17	function	function	NOUN
concept-2276	85	18	of	of	ADP
concept-2276	85	19	at	at	ADP
concept-2276	85	20	bats	bat	NOUN
concept-2276	85	21	.	.	PUNCT
concept-2276	86	1	for	for	ADP
concept-2276	86	2	at	at	ADP
concept-2276	86	3	bat	bat	NOUN
concept-2276	86	4	bins	bin	NOUN
concept-2276	86	5	[	[	X
concept-2276	86	6	290,310	290,310	NUM
concept-2276	86	7	)	)	PUNCT
concept-2276	86	8	,	,	PUNCT
concept-2276	86	9	[	[	X
concept-2276	86	10	310,330),	310,330),	NUM
concept-2276	86	11	...	...	PUNCT
concept-2276	86	12	[690,710	[690,710	X
concept-2276	86	13	)	)	PUNCT
concept-2276	86	14	,	,	PUNCT
concept-2276	86	15	he	he	PRON
concept-2276	86	16	computed	compute	VERB
concept-2276	86	17	the	the	DET
concept-2276	86	18	within	within	ADP
concept-2276	86	19	-	-	PUNCT
concept-2276	86	20	bin	bin	NOUN
concept-2276	86	21	standard	standard	ADJ
concept-2276	86	22	deviations	deviation	NOUN
concept-2276	86	23	and	and	CCONJ
concept-2276	86	24	plotted	plot	VERB
concept-2276	86	25	them	they	PRON
concept-2276	86	26	as	as	ADP
concept-2276	86	27	a	a	DET
concept-2276	86	28	function	function	NOUN
concept-2276	86	29	of	of	ADP
concept-2276	86	30	at	at	ADP
concept-2276	86	31	bats	bat	NOUN
concept-2276	86	32	,	,	PUNCT
concept-2276	86	33	thus	thus	ADV
concept-2276	86	34	creating	create	VERB
concept-2276	86	35	a	a	DET
concept-2276	86	36	scatter	scatter	NOUN
concept-2276	86	37	plot	plot	NOUN
concept-2276	86	38	of	of	ADP
concept-2276	86	39	points	point	NOUN
concept-2276	86	40	.	.	PUNCT
concept-2276	87	1	we	we	PRON
concept-2276	87	2	can	can	AUX
concept-2276	87	3	do	do	VERB
concept-2276	87	4	likewise	likewise	ADV
concept-2276	87	5	for	for	ADP
concept-2276	87	6	finding	find	VERB
concept-2276	87	7	the	the	DET
concept-2276	87	8	true	true	ADJ
concept-2276	87	9	ability	ability	NOUN
concept-2276	87	10	for	for	ADP
concept-2276	87	11	obp	obp	PROPN
concept-2276	87	12	.	.	PUNCT
concept-2276	88	1	once	once	SCONJ
concept-2276	88	2	one	one	PRON
concept-2276	88	3	has	have	AUX
concept-2276	88	4	made	make	VERB
concept-2276	88	5	the	the	DET
concept-2276	88	6	plot	plot	NOUN
concept-2276	88	7	,	,	PUNCT
concept-2276	88	8	one	one	PRON
concept-2276	88	9	can	can	AUX
concept-2276	88	10	find	find	VERB
concept-2276	88	11	c	c	NOUN
concept-2276	88	12	by	by	ADP
concept-2276	88	13	using	use	VERB
concept-2276	88	14	the	the	DET
concept-2276	88	15	function	function	NOUN
concept-2276	88	16	var	var	NOUN
concept-2276	88	17	(	(	PUNCT
concept-2276	88	18	tob	tob	VERB
concept-2276	88	19	pa	pa	PROPN
concept-2276	88	20	)	)	PUNCT
concept-2276	88	21	=	=	SYM
concept-2276	88	22	1	1	NUM
concept-2276	88	23	pa	pa	PROPN
concept-2276	88	24	µ(pa	µ(pa	NUM
concept-2276	88	25	)	)	PUNCT
concept-2276	88	26	+	+	CCONJ
concept-2276	88	27	(	(	PUNCT
concept-2276	88	28	1−	1−	NUM
concept-2276	88	29	1	1	NUM
concept-2276	88	30	pa	pa	PROPN
concept-2276	88	31	)	)	PUNCT
concept-2276	88	32	(	(	PUNCT
concept-2276	88	33	cµ(pa)2	cµ(pa)2	NOUN
concept-2276	88	34	+	+	CCONJ
concept-2276	88	35	µ(pa	µ(pa	NOUN
concept-2276	88	36	)	)	PUNCT
concept-2276	88	37	c	c	NOUN
concept-2276	89	1	+	+	NOUN
concept-2276	89	2	1	1	NUM
concept-2276	89	3	)	)	PUNCT
concept-2276	89	4	−	−	PROPN
concept-2276	89	5	µ(pa)2	µ(pa)2	PROPN
concept-2276	89	6	.	.	PUNCT
concept-2276	90	1	this	this	DET
concept-2276	90	2	variance	variance	NOUN
concept-2276	90	3	function	function	NOUN
concept-2276	90	4	will	will	AUX
concept-2276	90	5	act	act	VERB
concept-2276	90	6	as	as	ADP
concept-2276	90	7	contours	contours	NOUN
concept-2276	90	8	on	on	ADP
concept-2276	90	9	the	the	DET
concept-2276	90	10	graph	graph	NOUN
concept-2276	90	11	of	of	ADP
concept-2276	90	12	standard	standard	ADJ
concept-2276	90	13	deviations	deviation	NOUN
concept-2276	90	14	with	with	ADP
concept-2276	90	15	varying	vary	VERB
concept-2276	90	16	curves	curve	NOUN
concept-2276	90	17	such	such	ADJ
concept-2276	90	18	that	that	SCONJ
concept-2276	90	19	every	every	DET
concept-2276	90	20	point	point	NOUN
concept-2276	90	21	on	on	ADP
concept-2276	90	22	a	a	DET
concept-2276	90	23	curve	curve	NOUN
concept-2276	90	24	will	will	AUX
concept-2276	90	25	have	have	VERB
concept-2276	90	26	the	the	DET
concept-2276	90	27	same	same	ADJ
concept-2276	90	28	value	value	NOUN
concept-2276	90	29	of	of	ADP
concept-2276	90	30	c	c	PROPN
concept-2276	90	31	with	with	ADP
concept-2276	90	32	the	the	DET
concept-2276	90	33	locations	location	NOUN
concept-2276	90	34	of	of	ADP
concept-2276	90	35	the	the	DET
concept-2276	90	36	curves	curve	NOUN
concept-2276	90	37	changing	change	VERB
concept-2276	90	38	as	as	ADP
concept-2276	90	39	a	a	DET
concept-2276	90	40	function	function	NOUN
concept-2276	90	41	of	of	ADP
concept-2276	90	42	c	c	PROPN
concept-2276	90	43	(	(	PUNCT
concept-2276	90	44	i.e.	i.e.	X
concept-2276	90	45	,	,	PUNCT
concept-2276	90	46	with	with	ADP
concept-2276	90	47	this	this	DET
concept-2276	90	48	function	function	NOUN
concept-2276	90	49	,	,	PUNCT
concept-2276	90	50	as	as	SCONJ
concept-2276	90	51	c	c	NOUN
concept-2276	90	52	increases	increase	NOUN
concept-2276	90	53	or	or	CCONJ
concept-2276	90	54	decreases	decrease	VERB
concept-2276	90	55	the	the	DET
concept-2276	90	56	curve	curve	NOUN
concept-2276	90	57	will	will	AUX
concept-2276	90	58	go	go	VERB
concept-2276	90	59	down	down	ADV
concept-2276	90	60	or	or	CCONJ
concept-2276	90	61	up	up	ADV
concept-2276	90	62	relative	relative	ADJ
concept-2276	90	63	to	to	ADP
concept-2276	90	64	the	the	DET
concept-2276	90	65	points	point	NOUN
concept-2276	90	66	on	on	ADP
concept-2276	90	67	the	the	DET
concept-2276	90	68	graph	graph	NOUN
concept-2276	90	69	respectively	respectively	ADV
concept-2276	90	70	)	)	PUNCT
concept-2276	90	71	.	.	PUNCT
concept-2276	91	1	all	all	PRON
concept-2276	91	2	we	we	PRON
concept-2276	91	3	need	need	VERB
concept-2276	91	4	to	to	PART
concept-2276	91	5	do	do	VERB
concept-2276	91	6	is	be	AUX
concept-2276	91	7	to	to	PART
concept-2276	91	8	find	find	VERB
concept-2276	91	9	the	the	DET
concept-2276	91	10	curve	curve	NOUN
concept-2276	91	11	such	such	ADJ
concept-2276	91	12	that	that	SCONJ
concept-2276	91	13	half	half	NOUN
concept-2276	91	14	of	of	ADP
concept-2276	91	15	the	the	DET
concept-2276	91	16	points	point	NOUN
concept-2276	91	17	fall	fall	VERB
concept-2276	91	18	above	above	ADP
concept-2276	91	19	the	the	DET
concept-2276	91	20	curve	curve	NOUN
concept-2276	91	21	and	and	CCONJ
concept-2276	91	22	half	half	DET
concept-2276	91	23	the	the	DET
concept-2276	91	24	points	point	NOUN
concept-2276	91	25	fall	fall	VERB
concept-2276	91	26	below	below	ADP
concept-2276	91	27	it	it	PRON
concept-2276	91	28	and	and	CCONJ
concept-2276	91	29	mark	mark	VERB
concept-2276	91	30	the	the	DET
concept-2276	91	31	curve	curve	NOUN
concept-2276	91	32	’s	’s	PART
concept-2276	91	33	corresponding	correspond	VERB
concept-2276	91	34	c	c	PROPN
concept-2276	91	35	value	value	NOUN
concept-2276	91	36	.	.	PUNCT
concept-2276	92	1	after	after	ADP
concept-2276	92	2	doing	do	VERB
concept-2276	92	3	this	this	DET
concept-2276	92	4	procedure	procedure	NOUN
concept-2276	92	5	,	,	PUNCT
concept-2276	92	6	we	we	PRON
concept-2276	92	7	end	end	VERB
concept-2276	92	8	up	up	ADP
concept-2276	92	9	having	have	VERB
concept-2276	92	10	c	c	NOUN
concept-2276	92	11	being	be	AUX
concept-2276	92	12	equal	equal	ADJ
concept-2276	92	13	to	to	ADP
concept-2276	92	14	625	625	NUM
concept-2276	92	15	.	.	PUNCT
concept-2276	93	1	figure	figure	NOUN
concept-2276	93	2	3	3	NUM
concept-2276	93	3	shows	show	VERB
concept-2276	93	4	the	the	DET
concept-2276	93	5	standard	standard	ADJ
concept-2276	93	6	deviation	deviation	NOUN
concept-2276	93	7	versus	versus	ADP
concept-2276	93	8	plate	plate	NOUN
concept-2276	93	9	appearances	appearance	NOUN
concept-2276	93	10	plot	plot	NOUN
concept-2276	93	11	with	with	ADP
concept-2276	93	12	the	the	DET
concept-2276	93	13	middle	middle	ADJ
concept-2276	93	14	curve	curve	NOUN
concept-2276	93	15	being	be	AUX
concept-2276	93	16	best	good	ADJ
concept-2276	93	17	representation	representation	NOUN
concept-2276	93	18	the	the	DET
concept-2276	93	19	variability	variability	NOUN
concept-2276	93	20	in	in	ADP
concept-2276	93	21	the	the	DET
concept-2276	93	22	true	true	ADJ
concept-2276	93	23	ability	ability	NOUN
concept-2276	93	24	.	.	PUNCT
concept-2276	94	1	at	at	ADP
concept-2276	94	2	this	this	DET
concept-2276	94	3	point	point	NOUN
concept-2276	94	4	,	,	PUNCT
concept-2276	94	5	we	we	PRON
concept-2276	94	6	have	have	AUX
concept-2276	94	7	established	establish	VERB
concept-2276	94	8	a	a	DET
concept-2276	94	9	relationship	relationship	NOUN
concept-2276	94	10	between	between	ADP
concept-2276	94	11	the	the	DET
concept-2276	94	12	prior	prior	ADJ
concept-2276	94	13	true	true	ADJ
concept-2276	94	14	ability	ability	NOUN
concept-2276	94	15	and	and	CCONJ
concept-2276	94	16	plate	plate	NOUN
concept-2276	94	17	appearances	appearance	NOUN
concept-2276	94	18	.	.	PUNCT
concept-2276	95	1	6	6	NUM
concept-2276	95	2	300	300	NUM
concept-2276	95	3	400	400	NUM
concept-2276	95	4	500	500	NUM
concept-2276	95	5	600	600	NUM
concept-2276	95	6	700	700	NUM
concept-2276	95	7	0	0	NUM
concept-2276	95	8	.0	.0	NUM
concept-2276	95	9	0	0	NUM
concept-2276	95	10	5	5	NUM
concept-2276	95	11	0	0	NUM
concept-2276	95	12	.0	.0	NUM
concept-2276	95	13	1	1	NUM
concept-2276	95	14	5	5	NUM
concept-2276	95	15	0	0	NUM
concept-2276	95	16	.0	.0	NUM
concept-2276	95	17	2	2	NUM
concept-2276	95	18	5	5	NUM
concept-2276	95	19	0	0	NUM
concept-2276	95	20	.0	.0	NUM
concept-2276	95	21	3	3	NUM
concept-2276	95	22	5	5	NUM
concept-2276	95	23	plate	plate	NOUN
concept-2276	95	24	appearances	appearance	NOUN
concept-2276	95	25	s	s	PART
concept-2276	95	26	d	d	NOUN
concept-2276	95	27	(	(	PUNCT
concept-2276	95	28	o	o	NOUN
concept-2276	95	29	b	b	PROPN
concept-2276	95	30	p	p	NOUN
concept-2276	95	31	)	)	PUNCT
concept-2276	95	32	figure	figure	NOUN
concept-2276	95	33	3	3	NUM
concept-2276	95	34	:	:	PUNCT
concept-2276	95	35	empirical	empirical	ADJ
concept-2276	95	36	bin	bin	NOUN
concept-2276	95	37	-	-	PUNCT
concept-2276	95	38	by	by	ADP
concept-2276	95	39	-	-	PUNCT
concept-2276	95	40	bin	bin	NOUN
concept-2276	95	41	standard	standard	ADJ
concept-2276	95	42	deviations	deviation	NOUN
concept-2276	95	43	for	for	ADP
concept-2276	95	44	obp	obp	PROPN
concept-2276	95	45	.	.	PUNCT
concept-2276	96	1	in	in	ADP
concept-2276	96	2	the	the	DET
concept-2276	96	3	top	top	ADJ
concept-2276	96	4	,	,	PUNCT
concept-2276	96	5	middle	middle	ADJ
concept-2276	96	6	,	,	PUNCT
concept-2276	96	7	and	and	CCONJ
concept-2276	96	8	bottom	bottom	ADJ
concept-2276	96	9	curve	curve	NOUN
concept-2276	96	10	,	,	PUNCT
concept-2276	96	11	c=400	c=400	PROPN
concept-2276	96	12	,	,	PUNCT
concept-2276	96	13	625	625	NUM
concept-2276	96	14	and	and	CCONJ
concept-2276	96	15	900	900	NUM
concept-2276	96	16	respectively	respectively	ADV
concept-2276	96	17	.	.	PUNCT
concept-2276	97	1	we	we	PRON
concept-2276	97	2	will	will	AUX
concept-2276	97	3	use	use	VERB
concept-2276	97	4	c=625	c=625	PROPN
concept-2276	97	5	for	for	ADP
concept-2276	97	6	our	our	PRON
concept-2276	97	7	model	model	NOUN
concept-2276	97	8	.	.	PUNCT
concept-2276	98	1	iii	iii	PROPN
concept-2276	98	2	.	.	PROPN
concept-2276	98	3	times	time	NOUN
concept-2276	98	4	on	on	ADP
concept-2276	98	5	base	base	NOUN
concept-2276	98	6	finally	finally	ADV
concept-2276	98	7	,	,	PUNCT
concept-2276	98	8	we	we	PRON
concept-2276	98	9	need	need	VERB
concept-2276	98	10	to	to	PART
concept-2276	98	11	model	model	VERB
concept-2276	98	12	the	the	DET
concept-2276	98	13	distribution	distribution	NOUN
concept-2276	98	14	of	of	ADP
concept-2276	98	15	tob	tob	NOUN
concept-2276	98	16	given	give	VERB
concept-2276	98	17	pa	pa	PROPN
concept-2276	98	18	and	and	CCONJ
concept-2276	98	19	p.	p.	NOUN
concept-2276	98	20	the	the	DET
concept-2276	98	21	most	most	ADV
concept-2276	98	22	natural	natural	ADJ
concept-2276	98	23	model	model	NOUN
concept-2276	98	24	for	for	ADP
concept-2276	98	25	this	this	PRON
concept-2276	98	26	would	would	AUX
concept-2276	98	27	be	be	AUX
concept-2276	98	28	to	to	PART
concept-2276	98	29	see	see	VERB
concept-2276	98	30	if	if	SCONJ
concept-2276	98	31	tob	tob	PROPN
concept-2276	98	32	were	be	AUX
concept-2276	98	33	distributed	distribute	VERB
concept-2276	98	34	as	as	ADP
concept-2276	98	35	binomial(pa	binomial(pa	NOUN
concept-2276	98	36	,	,	PUNCT
concept-2276	98	37	p	p	NOUN
concept-2276	98	38	)	)	PUNCT
concept-2276	98	39	.	.	PUNCT
concept-2276	99	1	the	the	DET
concept-2276	99	2	binomial	binomial	ADJ
concept-2276	99	3	distribution	distribution	NOUN
concept-2276	99	4	b(n	b(n	NOUN
concept-2276	99	5	,	,	PUNCT
concept-2276	99	6	p	p	NOUN
concept-2276	99	7	)	)	PUNCT
concept-2276	99	8	is	be	AUX
concept-2276	99	9	a	a	DET
concept-2276	99	10	probability	probability	NOUN
concept-2276	99	11	mass	mass	NOUN
concept-2276	99	12	function	function	NOUN
concept-2276	99	13	(	(	PUNCT
concept-2276	99	14	probability	probability	NOUN
concept-2276	99	15	distribution	distribution	NOUN
concept-2276	99	16	function	function	NOUN
concept-2276	99	17	for	for	ADP
concept-2276	99	18	discrete	discrete	ADJ
concept-2276	99	19	random	random	ADJ
concept-2276	99	20	variables	variable	NOUN
concept-2276	99	21	)	)	PUNCT
concept-2276	99	22	that	that	PRON
concept-2276	99	23	models	model	VERB
concept-2276	99	24	the	the	DET
concept-2276	99	25	number	number	NOUN
concept-2276	99	26	of	of	ADP
concept-2276	99	27	successes	success	NOUN
concept-2276	99	28	or	or	CCONJ
concept-2276	99	29	failures	failure	NOUN
concept-2276	99	30	of	of	ADP
concept-2276	99	31	n	n	CCONJ
concept-2276	99	32	independent	independent	ADJ
concept-2276	99	33	identical	identical	ADJ
concept-2276	99	34	trials	trial	NOUN
concept-2276	99	35	where	where	SCONJ
concept-2276	99	36	each	each	DET
concept-2276	99	37	trial	trial	NOUN
concept-2276	99	38	only	only	ADV
concept-2276	99	39	has	have	VERB
concept-2276	99	40	an	an	DET
concept-2276	99	41	outcome	outcome	NOUN
concept-2276	99	42	of	of	ADP
concept-2276	99	43	a	a	DET
concept-2276	99	44	success	success	NOUN
concept-2276	99	45	with	with	ADP
concept-2276	99	46	probability	probability	NOUN
concept-2276	99	47	p	p	NOUN
concept-2276	99	48	or	or	CCONJ
concept-2276	99	49	failure	failure	NOUN
concept-2276	99	50	with	with	ADP
concept-2276	99	51	probability	probability	NOUN
concept-2276	100	1	1−	1−	NUM
concept-2276	101	1	p.	p.	NOUN
concept-2276	102	1	the	the	DET
concept-2276	102	2	probability	probability	NOUN
concept-2276	102	3	mass	mass	NOUN
concept-2276	102	4	function	function	NOUN
concept-2276	102	5	for	for	ADP
concept-2276	102	6	this	this	DET
concept-2276	102	7	distribution	distribution	NOUN
concept-2276	102	8	is	be	AUX
concept-2276	102	9	fx(x	fx(x	ADJ
concept-2276	102	10	)	)	PUNCT
concept-2276	103	1	=	=	SYM
concept-2276	103	2	(	(	PUNCT
concept-2276	103	3	n	n	X
concept-2276	103	4	x)px(1−	x)px(1−	PROPN
concept-2276	103	5	p)n−x	p)n−x	PROPN
concept-2276	103	6	where	where	SCONJ
concept-2276	103	7	(	(	PUNCT
concept-2276	103	8	n	n	X
concept-2276	103	9	x	x	NOUN
concept-2276	103	10	)	)	PUNCT
concept-2276	103	11	=	=	SYM
concept-2276	103	12	n	n	X
concept-2276	103	13	!	!	PUNCT
concept-2276	103	14	x!(n−x	x!(n−x	NUM
concept-2276	103	15	)	)	PUNCT
concept-2276	103	16	!	!	PUNCT
concept-2276	104	1	and	and	CCONJ
concept-2276	104	2	n	n	PRON
concept-2276	104	3	is	be	AUX
concept-2276	104	4	an	an	DET
concept-2276	104	5	integer	integer	NOUN
concept-2276	104	6	between	between	ADP
concept-2276	104	7	0	0	NUM
concept-2276	104	8	and	and	CCONJ
concept-2276	104	9	n	n	PRON
concept-2276	104	10	inclusively	inclusively	ADV
concept-2276	104	11	.	.	PUNCT
concept-2276	105	1	in	in	ADP
concept-2276	105	2	this	this	DET
concept-2276	105	3	model	model	NOUN
concept-2276	105	4	,	,	PUNCT
concept-2276	105	5	we	we	PRON
concept-2276	105	6	are	be	AUX
concept-2276	105	7	trying	try	VERB
concept-2276	105	8	to	to	PART
concept-2276	105	9	see	see	VERB
concept-2276	105	10	if	if	SCONJ
concept-2276	105	11	we	we	PRON
concept-2276	105	12	are	be	AUX
concept-2276	105	13	use	use	VERB
concept-2276	105	14	each	each	DET
concept-2276	105	15	plate	plate	NOUN
concept-2276	105	16	appearance	appearance	NOUN
concept-2276	105	17	as	as	ADP
concept-2276	105	18	a	a	DET
concept-2276	105	19	trial	trial	NOUN
concept-2276	105	20	and	and	CCONJ
concept-2276	105	21	the	the	DET
concept-2276	105	22	prior	prior	ADJ
concept-2276	105	23	true	true	ADJ
concept-2276	105	24	ability	ability	NOUN
concept-2276	105	25	as	as	ADP
concept-2276	105	26	the	the	DET
concept-2276	105	27	probability	probability	NOUN
concept-2276	105	28	of	of	ADP
concept-2276	105	29	getting	get	VERB
concept-2276	105	30	on	on	ADP
concept-2276	105	31	-	-	PUNCT
concept-2276	105	32	base	base	NOUN
concept-2276	105	33	since	since	SCONJ
concept-2276	105	34	we	we	PRON
concept-2276	105	35	have	have	AUX
concept-2276	105	36	found	find	VERB
concept-2276	105	37	a	a	DET
concept-2276	105	38	model	model	NOUN
concept-2276	105	39	for	for	ADP
concept-2276	105	40	plate	plate	NOUN
concept-2276	105	41	appearances	appearance	NOUN
concept-2276	105	42	and	and	CCONJ
concept-2276	105	43	prior	prior	ADJ
concept-2276	105	44	true	true	ADJ
concept-2276	105	45	ability	ability	NOUN
concept-2276	105	46	in	in	ADP
concept-2276	105	47	the	the	DET
concept-2276	105	48	earlier	early	ADJ
concept-2276	105	49	sections	section	NOUN
concept-2276	105	50	.	.	PUNCT
concept-2276	106	1	frey	frey	NOUN
concept-2276	106	2	(	(	PUNCT
concept-2276	106	3	2007	2007	NUM
concept-2276	106	4	)	)	PUNCT
concept-2276	106	5	showed	show	VERB
concept-2276	106	6	that	that	SCONJ
concept-2276	106	7	one	one	PRON
concept-2276	106	8	can	can	AUX
concept-2276	106	9	see	see	VERB
concept-2276	106	10	if	if	SCONJ
concept-2276	106	11	hits	hit	NOUN
concept-2276	106	12	(	(	PUNCT
concept-2276	106	13	h	h	NOUN
concept-2276	106	14	)	)	PUNCT
concept-2276	106	15	were	be	AUX
concept-2276	106	16	binomial(at	binomial(at	PROPN
concept-2276	106	17	bats(a	bats(a	PROPN
concept-2276	106	18	)	)	PUNCT
concept-2276	106	19	,	,	PUNCT
concept-2276	106	20	prior	prior	ADJ
concept-2276	106	21	true	true	ADJ
concept-2276	106	22	ability(p	ability(p	NOUN
concept-2276	106	23	)	)	PUNCT
concept-2276	106	24	)	)	PUNCT
concept-2276	106	25	by	by	ADP
concept-2276	106	26	selecting	select	VERB
concept-2276	106	27	players	player	NOUN
concept-2276	106	28	with	with	ADP
concept-2276	106	29	at	at	ADV
concept-2276	106	30	least	least	ADV
concept-2276	106	31	300	300	NUM
concept-2276	106	32	at	at	ADP
concept-2276	106	33	bats	bat	NOUN
concept-2276	106	34	for	for	ADP
concept-2276	106	35	the	the	DET
concept-2276	106	36	same	same	ADJ
concept-2276	106	37	team	team	NOUN
concept-2276	106	38	for	for	ADP
concept-2276	106	39	two	two	NUM
concept-2276	106	40	consecutive	consecutive	ADJ
concept-2276	106	41	years	year	NOUN
concept-2276	106	42	and	and	CCONJ
concept-2276	106	43	seeing	see	VERB
concept-2276	106	44	if	if	SCONJ
concept-2276	106	45	(	(	PUNCT
concept-2276	106	46	h1	h1	VERB
concept-2276	106	47	a1	a1	PROPN
concept-2276	106	48	−	−	PROPN
concept-2276	106	49	h2	h2	NOUN
concept-2276	106	50	a2	a2	PROPN
concept-2276	106	51	)	)	PUNCT
concept-2276	106	52	√	√	PROPN
concept-2276	106	53	p̂(1−	p̂(1−	ADJ
concept-2276	106	54	p̂)(a−1	p̂)(a−1	NOUN
concept-2276	106	55	1	1	NUM
concept-2276	107	1	+	+	CCONJ
concept-2276	107	2	a−1	a−1	PROPN
concept-2276	107	3	2	2	NUM
concept-2276	107	4	)	)	PUNCT
concept-2276	107	5	∼	∼	NOUN
concept-2276	107	6	n(0	n(0	PROPN
concept-2276	107	7	,	,	PUNCT
concept-2276	107	8	1	1	NUM
concept-2276	107	9	)	)	PUNCT
concept-2276	107	10	where	where	SCONJ
concept-2276	107	11	h1	h1	PROPN
concept-2276	107	12	,	,	PUNCT
concept-2276	107	13	h2	h2	PROPN
concept-2276	107	14	,	,	PUNCT
concept-2276	107	15	a1	a1	PROPN
concept-2276	107	16	,	,	PUNCT
concept-2276	107	17	a2	a2	PROPN
concept-2276	107	18	are	be	AUX
concept-2276	107	19	the	the	DET
concept-2276	107	20	hits	hit	NOUN
concept-2276	107	21	and	and	CCONJ
concept-2276	107	22	at	at	ADP
concept-2276	107	23	bats	bat	NOUN
concept-2276	107	24	of	of	ADP
concept-2276	107	25	two	two	NUM
concept-2276	107	26	consecutive	consecutive	ADJ
concept-2276	107	27	seasons	season	NOUN
concept-2276	107	28	respectively	respectively	ADV
concept-2276	107	29	and	and	CCONJ
concept-2276	107	30	p̂	p̂	X
concept-2276	107	31	=	=	PUNCT
concept-2276	108	1	h1+h2	h1+h2	PROPN
concept-2276	108	2	a1+a2	a1+a2	PROPN
concept-2276	108	3	.	.	PUNCT
concept-2276	109	1	the	the	DET
concept-2276	109	2	premise	premise	NOUN
concept-2276	109	3	behind	behind	ADP
concept-2276	109	4	picking	pick	VERB
concept-2276	109	5	players	player	NOUN
concept-2276	109	6	’	’	PART
concept-2276	109	7	data	datum	NOUN
concept-2276	109	8	from	from	ADP
concept-2276	109	9	two	two	NUM
concept-2276	109	10	consecutive	consecutive	ADJ
concept-2276	109	11	seasons	season	NOUN
concept-2276	109	12	is	be	AUX
concept-2276	109	13	the	the	DET
concept-2276	109	14	fact	fact	NOUN
concept-2276	109	15	that	that	SCONJ
concept-2276	109	16	a	a	DET
concept-2276	109	17	7	7	NUM
concept-2276	109	18	player	player	NOUN
concept-2276	109	19	’s	’s	PART
concept-2276	109	20	skill	skill	NOUN
concept-2276	109	21	is	be	AUX
concept-2276	109	22	n’t	not	PART
concept-2276	109	23	going	go	VERB
concept-2276	109	24	to	to	PART
concept-2276	109	25	change	change	VERB
concept-2276	109	26	very	very	ADV
concept-2276	109	27	much	much	ADV
concept-2276	109	28	over	over	ADP
concept-2276	109	29	this	this	DET
concept-2276	109	30	time	time	NOUN
concept-2276	109	31	frame	frame	NOUN
concept-2276	109	32	which	which	PRON
concept-2276	109	33	makes	make	VERB
concept-2276	109	34	the	the	DET
concept-2276	109	35	trials	trial	NOUN
concept-2276	109	36	more	more	ADJ
concept-2276	109	37	"	"	PUNCT
concept-2276	109	38	independent	independent	ADJ
concept-2276	109	39	"	"	PUNCT
concept-2276	109	40	and	and	CCONJ
concept-2276	109	41	"	"	PUNCT
concept-2276	109	42	identical	identical	ADJ
concept-2276	109	43	"	"	PUNCT
concept-2276	109	44	.	.	PUNCT
concept-2276	110	1	we	we	PRON
concept-2276	110	2	can	can	AUX
concept-2276	110	3	do	do	VERB
concept-2276	110	4	likewise	likewise	ADV
concept-2276	110	5	for	for	ADP
concept-2276	110	6	obp	obp	PROPN
concept-2276	110	7	by	by	ADP
concept-2276	110	8	substituting	substitute	VERB
concept-2276	110	9	a	a	PRON
concept-2276	110	10	with	with	ADP
concept-2276	110	11	pa	pa	PROPN
concept-2276	110	12	and	and	CCONJ
concept-2276	110	13	h	h	NOUN
concept-2276	110	14	with	with	ADP
concept-2276	110	15	tob	tob	NOUN
concept-2276	110	16	.	.	PUNCT
concept-2276	111	1	after	after	ADP
concept-2276	111	2	carrying	carry	VERB
concept-2276	111	3	out	out	ADP
concept-2276	111	4	this	this	DET
concept-2276	111	5	process	process	NOUN
concept-2276	111	6	by	by	ADP
concept-2276	111	7	looking	look	VERB
concept-2276	111	8	at	at	ADP
concept-2276	111	9	a	a	DET
concept-2276	111	10	histogram	histogram	NOUN
concept-2276	111	11	and	and	CCONJ
concept-2276	111	12	calculating	calculate	VERB
concept-2276	111	13	the	the	DET
concept-2276	111	14	mean	mean	ADJ
concept-2276	111	15	and	and	CCONJ
concept-2276	111	16	standard	standard	ADJ
concept-2276	111	17	deviation	deviation	NOUN
concept-2276	111	18	,	,	PUNCT
concept-2276	111	19	it	it	PRON
concept-2276	111	20	turns	turn	VERB
concept-2276	111	21	out	out	ADP
concept-2276	111	22	that	that	SCONJ
concept-2276	111	23	the	the	DET
concept-2276	111	24	times	time	NOUN
concept-2276	111	25	on	on	ADP
concept-2276	111	26	base	base	NOUN
concept-2276	111	27	does	do	AUX
concept-2276	111	28	follow	follow	VERB
concept-2276	111	29	a	a	DET
concept-2276	111	30	binomial	binomial	ADJ
concept-2276	111	31	distribution	distribution	NOUN
concept-2276	111	32	.	.	PUNCT
concept-2276	112	1	at	at	ADP
concept-2276	112	2	this	this	DET
concept-2276	112	3	point	point	NOUN
concept-2276	112	4	,	,	PUNCT
concept-2276	112	5	we	we	PRON
concept-2276	112	6	have	have	AUX
concept-2276	112	7	established	establish	VERB
concept-2276	112	8	a	a	DET
concept-2276	112	9	relationship	relationship	NOUN
concept-2276	112	10	between	between	ADP
concept-2276	112	11	tob	tob	NOUN
concept-2276	112	12	with	with	ADP
concept-2276	112	13	p	p	NOUN
concept-2276	112	14	and	and	CCONJ
concept-2276	112	15	pa	pa	PROPN
concept-2276	112	16	.	.	PROPN
concept-2276	112	17	iv	iv	PROPN
concept-2276	112	18	.	.	PUNCT
concept-2276	113	1	checking	check	VERB
concept-2276	113	2	the	the	DET
concept-2276	113	3	model	model	NOUN
concept-2276	113	4	after	after	ADP
concept-2276	113	5	completing	complete	VERB
concept-2276	113	6	our	our	PRON
concept-2276	113	7	model	model	NOUN
concept-2276	113	8	,	,	PUNCT
concept-2276	113	9	we	we	PRON
concept-2276	113	10	decided	decide	VERB
concept-2276	113	11	to	to	PART
concept-2276	113	12	create	create	VERB
concept-2276	113	13	a	a	DET
concept-2276	113	14	simulation	simulation	NOUN
concept-2276	113	15	of	of	ADP
concept-2276	113	16	700	700	NUM
concept-2276	113	17	players	player	NOUN
concept-2276	113	18	using	use	VERB
concept-2276	113	19	the	the	DET
concept-2276	113	20	model	model	NOUN
concept-2276	113	21	and	and	CCONJ
concept-2276	113	22	compare	compare	VERB
concept-2276	113	23	its	its	PRON
concept-2276	113	24	scatter	scatter	NOUN
concept-2276	113	25	plot	plot	NOUN
concept-2276	113	26	of	of	ADP
concept-2276	113	27	obp	obp	PROPN
concept-2276	113	28	to	to	PART
concept-2276	113	29	plate	plate	VERB
concept-2276	113	30	appearances	appearance	NOUN
concept-2276	113	31	to	to	ADP
concept-2276	113	32	that	that	PRON
concept-2276	113	33	of	of	ADP
concept-2276	113	34	the	the	DET
concept-2276	113	35	real	real	ADJ
concept-2276	113	36	data	datum	NOUN
concept-2276	113	37	.	.	PUNCT
concept-2276	114	1	for	for	ADP
concept-2276	114	2	each	each	DET
concept-2276	114	3	player	player	NOUN
concept-2276	114	4	,	,	PUNCT
concept-2276	114	5	we	we	PRON
concept-2276	114	6	first	first	ADV
concept-2276	114	7	found	find	VERB
concept-2276	114	8	a	a	DET
concept-2276	114	9	random	random	ADJ
concept-2276	114	10	value	value	NOUN
concept-2276	114	11	of	of	ADP
concept-2276	114	12	pa	pa	PROPN
concept-2276	114	13	subject	subject	NOUN
concept-2276	114	14	to	to	ADP
concept-2276	114	15	its	its	PRON
concept-2276	114	16	probability	probability	NOUN
concept-2276	114	17	density	density	NOUN
concept-2276	114	18	function	function	NOUN
concept-2276	114	19	,	,	PUNCT
concept-2276	114	20	then	then	ADV
concept-2276	114	21	found	find	VERB
concept-2276	114	22	a	a	DET
concept-2276	114	23	random	random	ADJ
concept-2276	114	24	value	value	NOUN
concept-2276	114	25	of	of	ADP
concept-2276	114	26	p	p	NOUN
concept-2276	114	27	using	use	VERB
concept-2276	114	28	its	its	PRON
concept-2276	114	29	conditional	conditional	ADJ
concept-2276	114	30	beta	beta	ADJ
concept-2276	114	31	distribution	distribution	NOUN
concept-2276	114	32	with	with	ADP
concept-2276	114	33	the	the	DET
concept-2276	114	34	random	random	ADJ
concept-2276	114	35	value	value	NOUN
concept-2276	114	36	of	of	ADP
concept-2276	114	37	pa	pa	PROPN
concept-2276	114	38	,	,	PUNCT
concept-2276	114	39	and	and	CCONJ
concept-2276	114	40	then	then	ADV
concept-2276	114	41	found	find	VERB
concept-2276	114	42	a	a	DET
concept-2276	114	43	random	random	ADJ
concept-2276	114	44	number	number	NOUN
concept-2276	114	45	of	of	ADP
concept-2276	114	46	tob	tob	NOUN
concept-2276	114	47	by	by	ADP
concept-2276	114	48	picking	pick	VERB
concept-2276	114	49	a	a	DET
concept-2276	114	50	random	random	ADJ
concept-2276	114	51	number	number	NOUN
concept-2276	114	52	from	from	ADP
concept-2276	114	53	it	it	PRON
concept-2276	114	54	’s	’	VERB
concept-2276	114	55	corresponding	correspond	VERB
concept-2276	114	56	binomial	binomial	ADJ
concept-2276	114	57	distribution	distribution	NOUN
concept-2276	114	58	with	with	ADP
concept-2276	114	59	the	the	DET
concept-2276	114	60	random	random	ADJ
concept-2276	114	61	value	value	NOUN
concept-2276	114	62	of	of	ADP
concept-2276	114	63	pa	pa	PROPN
concept-2276	114	64	and	and	CCONJ
concept-2276	114	65	p.	p.	NOUN
concept-2276	114	66	then	then	ADV
concept-2276	114	67	we	we	PRON
concept-2276	114	68	computed	compute	VERB
concept-2276	114	69	the	the	DET
concept-2276	114	70	obp	obp	NOUN
concept-2276	114	71	for	for	ADP
concept-2276	114	72	each	each	DET
concept-2276	114	73	simulated	simulate	VERB
concept-2276	114	74	player	player	NOUN
concept-2276	114	75	using	use	VERB
concept-2276	114	76	the	the	DET
concept-2276	114	77	random	random	ADJ
concept-2276	114	78	values	value	NOUN
concept-2276	114	79	of	of	ADP
concept-2276	114	80	pa	pa	PROPN
concept-2276	114	81	and	and	CCONJ
concept-2276	114	82	tob	tob	PROPN
concept-2276	114	83	.	.	PUNCT
concept-2276	115	1	then	then	ADV
concept-2276	115	2	we	we	PRON
concept-2276	115	3	made	make	VERB
concept-2276	115	4	a	a	DET
concept-2276	115	5	scatter	scatter	NOUN
concept-2276	115	6	plot	plot	NOUN
concept-2276	115	7	with	with	ADP
concept-2276	115	8	the	the	DET
concept-2276	115	9	players	player	NOUN
concept-2276	115	10	’	’	PART
concept-2276	115	11	obp	obp	PROPN
concept-2276	115	12	and	and	CCONJ
concept-2276	115	13	plate	plate	NOUN
concept-2276	115	14	appearances	appearance	NOUN
concept-2276	115	15	to	to	PART
concept-2276	115	16	compare	compare	VERB
concept-2276	115	17	it	it	PRON
concept-2276	115	18	to	to	ADP
concept-2276	115	19	the	the	DET
concept-2276	115	20	scatter	scatter	NOUN
concept-2276	115	21	plot	plot	NOUN
concept-2276	115	22	of	of	ADP
concept-2276	115	23	the	the	DET
concept-2276	115	24	original	original	ADJ
concept-2276	115	25	data	datum	NOUN
concept-2276	115	26	.	.	PUNCT
concept-2276	116	1	figure	figure	NOUN
concept-2276	116	2	4	4	NUM
concept-2276	116	3	shows	show	VERB
concept-2276	116	4	the	the	DET
concept-2276	116	5	scatter	scatter	NOUN
concept-2276	116	6	plots	plot	NOUN
concept-2276	116	7	of	of	ADP
concept-2276	116	8	the	the	DET
concept-2276	116	9	data	datum	NOUN
concept-2276	116	10	alongside	alongside	ADV
concept-2276	116	11	with	with	ADP
concept-2276	116	12	the	the	DET
concept-2276	116	13	original	original	ADJ
concept-2276	116	14	data	datum	NOUN
concept-2276	116	15	.	.	PUNCT
concept-2276	117	1	notice	notice	VERB
concept-2276	117	2	that	that	SCONJ
concept-2276	117	3	the	the	DET
concept-2276	117	4	simulated	simulate	VERB
concept-2276	117	5	data	data	NOUN
concept-2276	117	6	plot	plot	NOUN
concept-2276	117	7	is	be	AUX
concept-2276	117	8	very	very	ADV
concept-2276	117	9	similar	similar	ADJ
concept-2276	117	10	to	to	ADP
concept-2276	117	11	that	that	PRON
concept-2276	117	12	of	of	ADP
concept-2276	117	13	the	the	DET
concept-2276	117	14	real	real	ADJ
concept-2276	117	15	data	datum	NOUN
concept-2276	117	16	so	so	SCONJ
concept-2276	117	17	this	this	DET
concept-2276	117	18	model	model	NOUN
concept-2276	117	19	captures	capture	VERB
concept-2276	117	20	the	the	DET
concept-2276	117	21	essence	essence	NOUN
concept-2276	117	22	of	of	ADP
concept-2276	117	23	the	the	DET
concept-2276	117	24	baseball	baseball	NOUN
concept-2276	117	25	data	datum	NOUN
concept-2276	117	26	.	.	PUNCT
concept-2276	118	1	0	0	NUM
concept-2276	119	1	200	200	NUM
concept-2276	119	2	400	400	NUM
concept-2276	119	3	600	600	NUM
concept-2276	119	4	0	0	NUM
concept-2276	120	1	.0	.0	NUM
concept-2276	120	2	0	0	NUM
concept-2276	121	1	.2	.2	NUM
concept-2276	121	2	0	0	NUM
concept-2276	122	1	.4	.4	NUM
concept-2276	122	2	0	0	NUM
concept-2276	123	1	.6	.6	NUM
concept-2276	123	2	0	0	NUM
concept-2276	123	3	.8	.8	NUM
concept-2276	123	4	1	1	NUM
concept-2276	123	5	.0	.0	NUM
concept-2276	123	6	plate	plate	NOUN
concept-2276	123	7	appearances	appearance	VERB
concept-2276	123	8	o	o	NOUN
concept-2276	123	9	b	b	NOUN
concept-2276	123	10	p	p	NOUN
concept-2276	123	11	0	0	NUM
concept-2276	123	12	200	200	NUM
concept-2276	123	13	400	400	NUM
concept-2276	124	1	600	600	NUM
concept-2276	124	2	0	0	NUM
concept-2276	124	3	.0	.0	NUM
concept-2276	124	4	0	0	NUM
concept-2276	125	1	.2	.2	NUM
concept-2276	125	2	0	0	NUM
concept-2276	126	1	.4	.4	NUM
concept-2276	126	2	0	0	NUM
concept-2276	127	1	.6	.6	NUM
concept-2276	127	2	0	0	NUM
concept-2276	127	3	.8	.8	NUM
concept-2276	127	4	1	1	NUM
concept-2276	127	5	.0	.0	NUM
concept-2276	127	6	plate	plate	NOUN
concept-2276	127	7	appearances	appearance	VERB
concept-2276	127	8	o	o	NOUN
concept-2276	127	9	b	b	NOUN
concept-2276	127	10	p	p	NOUN
concept-2276	127	11	0	0	NUM
concept-2276	127	12	200	200	NUM
concept-2276	127	13	400	400	NUM
concept-2276	128	1	600	600	NUM
concept-2276	128	2	0	0	NUM
concept-2276	128	3	.0	.0	NUM
concept-2276	128	4	0	0	NUM
concept-2276	129	1	.2	.2	NUM
concept-2276	129	2	0	0	NUM
concept-2276	130	1	.4	.4	NUM
concept-2276	130	2	0	0	NUM
concept-2276	131	1	.6	.6	NUM
concept-2276	131	2	0	0	NUM
concept-2276	131	3	.8	.8	NUM
concept-2276	131	4	1	1	NUM
concept-2276	131	5	.0	.0	NUM
concept-2276	131	6	plate	plate	NOUN
concept-2276	131	7	appearances	appearance	VERB
concept-2276	131	8	o	o	NOUN
concept-2276	131	9	b	b	X
concept-2276	131	10	p	p	NOUN
concept-2276	131	11	figure	figure	NOUN
concept-2276	131	12	4	4	NUM
concept-2276	131	13	:	:	PUNCT
concept-2276	131	14	plate	plate	NOUN
concept-2276	131	15	appearances	appearance	NOUN
concept-2276	131	16	by	by	ADP
concept-2276	131	17	obp	obp	NOUN
concept-2276	131	18	plots	plot	NOUN
concept-2276	131	19	.	.	PUNCT
concept-2276	132	1	the	the	DET
concept-2276	132	2	left	left	ADV
concept-2276	132	3	-	-	PUNCT
concept-2276	132	4	most	most	ADJ
concept-2276	132	5	one	one	NOUN
concept-2276	132	6	is	be	AUX
concept-2276	132	7	with	with	ADP
concept-2276	132	8	the	the	DET
concept-2276	132	9	2016	2016	NUM
concept-2276	132	10	data	datum	NOUN
concept-2276	132	11	and	and	CCONJ
concept-2276	132	12	the	the	DET
concept-2276	132	13	other	other	ADJ
concept-2276	132	14	two	two	NUM
concept-2276	132	15	are	be	AUX
concept-2276	132	16	created	create	VERB
concept-2276	132	17	by	by	ADP
concept-2276	132	18	simulation	simulation	NOUN
concept-2276	132	19	with	with	ADP
concept-2276	132	20	the	the	DET
concept-2276	132	21	first	first	ADJ
concept-2276	132	22	model	model	NOUN
concept-2276	132	23	.	.	PUNCT
concept-2276	133	1	8	8	NUM
concept-2276	133	2	iii	iii	NOUN
concept-2276	133	3	.	.	PUNCT
concept-2276	134	1	the	the	DET
concept-2276	134	2	second	second	ADJ
concept-2276	134	3	proposed	propose	VERB
concept-2276	134	4	model	model	NOUN
concept-2276	134	5	the	the	DET
concept-2276	134	6	second	second	ADJ
concept-2276	134	7	model	model	NOUN
concept-2276	134	8	will	will	AUX
concept-2276	134	9	use	use	VERB
concept-2276	134	10	a	a	DET
concept-2276	134	11	more	more	ADV
concept-2276	134	12	specific	specific	ADJ
concept-2276	134	13	model	model	NOUN
concept-2276	134	14	to	to	PART
concept-2276	134	15	better	well	ADV
concept-2276	134	16	fit	fit	VERB
concept-2276	134	17	the	the	DET
concept-2276	134	18	obp	obp	NOUN
concept-2276	134	19	data	datum	NOUN
concept-2276	134	20	and	and	CCONJ
concept-2276	134	21	will	will	AUX
concept-2276	134	22	use	use	VERB
concept-2276	134	23	a	a	DET
concept-2276	134	24	simulation	simulation	NOUN
concept-2276	134	25	to	to	PART
concept-2276	134	26	find	find	VERB
concept-2276	134	27	the	the	DET
concept-2276	134	28	true	true	ADJ
concept-2276	134	29	ability	ability	NOUN
concept-2276	134	30	given	give	VERB
concept-2276	134	31	the	the	DET
concept-2276	134	32	information	information	NOUN
concept-2276	134	33	presented	present	VERB
concept-2276	134	34	in	in	ADP
concept-2276	134	35	the	the	DET
concept-2276	134	36	model	model	NOUN
concept-2276	134	37	.	.	PUNCT
concept-2276	135	1	we	we	PRON
concept-2276	135	2	will	will	AUX
concept-2276	135	3	look	look	VERB
concept-2276	135	4	at	at	ADP
concept-2276	135	5	each	each	PRON
concept-2276	135	6	of	of	ADP
concept-2276	135	7	the	the	DET
concept-2276	135	8	numerator	numerator	NOUN
concept-2276	135	9	components	component	NOUN
concept-2276	135	10	of	of	ADP
concept-2276	135	11	obp	obp	PROPN
concept-2276	135	12	and	and	CCONJ
concept-2276	135	13	find	find	VERB
concept-2276	135	14	the	the	DET
concept-2276	135	15	joint	joint	ADJ
concept-2276	135	16	distribution	distribution	NOUN
concept-2276	135	17	of	of	ADP
concept-2276	135	18	the	the	DET
concept-2276	135	19	variables	variable	NOUN
concept-2276	135	20	h	h	NOUN
concept-2276	135	21	,	,	PUNCT
concept-2276	135	22	bb	bb	PROPN
concept-2276	135	23	,	,	PUNCT
concept-2276	135	24	hbp	hbp	PROPN
concept-2276	135	25	,	,	PUNCT
concept-2276	135	26	p	p	X
concept-2276	135	27	,	,	PUNCT
concept-2276	135	28	and	and	CCONJ
concept-2276	135	29	pa	pa	PROPN
concept-2276	135	30	.	.	PUNCT
concept-2276	136	1	we	we	PRON
concept-2276	136	2	try	try	VERB
concept-2276	136	3	to	to	PART
concept-2276	136	4	find	find	VERB
concept-2276	136	5	the	the	DET
concept-2276	136	6	marginal	marginal	ADJ
concept-2276	136	7	distribution	distribution	NOUN
concept-2276	136	8	of	of	ADP
concept-2276	136	9	pa	pa	PROPN
concept-2276	136	10	,	,	PUNCT
concept-2276	136	11	conditional	conditional	ADJ
concept-2276	136	12	distributions	distribution	NOUN
concept-2276	136	13	of	of	ADP
concept-2276	136	14	ph	ph	NOUN
concept-2276	136	15	,	,	PUNCT
concept-2276	136	16	pbb	pbb	ADJ
concept-2276	136	17	,	,	PUNCT
concept-2276	136	18	and	and	CCONJ
concept-2276	136	19	phbp	phbp	NOUN
concept-2276	136	20	given	give	VERB
concept-2276	136	21	pa	pa	PROPN
concept-2276	137	1	and	and	CCONJ
concept-2276	137	2	then	then	ADV
concept-2276	137	3	the	the	DET
concept-2276	137	4	conditional	conditional	ADJ
concept-2276	137	5	distribution	distribution	NOUN
concept-2276	137	6	of	of	ADP
concept-2276	137	7	h	h	NOUN
concept-2276	137	8	,	,	PUNCT
concept-2276	137	9	bb	bb	PROPN
concept-2276	137	10	,	,	PUNCT
concept-2276	137	11	and	and	CCONJ
concept-2276	137	12	hbp	hbp	PROPN
concept-2276	137	13	given	give	VERB
concept-2276	137	14	ph	ph	PROPN
concept-2276	137	15	,	,	PUNCT
concept-2276	137	16	pbb	pbb	NOUN
concept-2276	137	17	,	,	PUNCT
concept-2276	137	18	phbp	phbp	NOUN
concept-2276	137	19	and	and	CCONJ
concept-2276	137	20	pa	pa	PROPN
concept-2276	137	21	.	.	PROPN
concept-2276	137	22	i.	i.	PROPN
concept-2276	137	23	plate	plate	PROPN
concept-2276	137	24	appearances	appearance	VERB
concept-2276	137	25	in	in	ADP
concept-2276	137	26	this	this	DET
concept-2276	137	27	model	model	NOUN
concept-2276	137	28	,	,	PUNCT
concept-2276	137	29	the	the	DET
concept-2276	137	30	model	model	NOUN
concept-2276	137	31	for	for	ADP
concept-2276	137	32	pa	pa	PROPN
concept-2276	137	33	is	be	AUX
concept-2276	137	34	the	the	DET
concept-2276	137	35	exact	exact	ADJ
concept-2276	137	36	same	same	ADJ
concept-2276	137	37	model	model	NOUN
concept-2276	137	38	as	as	ADP
concept-2276	137	39	the	the	DET
concept-2276	137	40	model	model	NOUN
concept-2276	137	41	used	use	VERB
concept-2276	137	42	for	for	ADP
concept-2276	137	43	pa	pa	PROPN
concept-2276	137	44	in	in	ADP
concept-2276	137	45	section	section	NOUN
concept-2276	137	46	2.1	2.1	NUM
concept-2276	137	47	so	so	SCONJ
concept-2276	137	48	we	we	PRON
concept-2276	137	49	omit	omit	VERB
concept-2276	137	50	the	the	DET
concept-2276	137	51	details	detail	NOUN
concept-2276	137	52	.	.	PUNCT
concept-2276	138	1	ii	ii	X
concept-2276	138	2	.	.	PUNCT
concept-2276	139	1	true	true	ADJ
concept-2276	139	2	ability	ability	NOUN
concept-2276	139	3	unlike	unlike	ADP
concept-2276	139	4	section	section	NOUN
concept-2276	139	5	2.2	2.2	NUM
concept-2276	139	6	where	where	SCONJ
concept-2276	139	7	we	we	PRON
concept-2276	139	8	only	only	ADV
concept-2276	139	9	needed	need	VERB
concept-2276	139	10	to	to	PART
concept-2276	139	11	find	find	VERB
concept-2276	139	12	the	the	DET
concept-2276	139	13	prior	prior	ADJ
concept-2276	139	14	true	true	ADJ
concept-2276	139	15	ability	ability	NOUN
concept-2276	139	16	of	of	ADP
concept-2276	139	17	a	a	DET
concept-2276	139	18	player	player	NOUN
concept-2276	139	19	getting	get	VERB
concept-2276	139	20	on	on	ADP
concept-2276	139	21	-	-	PUNCT
concept-2276	139	22	base	base	NOUN
concept-2276	139	23	given	give	VERB
concept-2276	139	24	only	only	ADV
concept-2276	139	25	pa	pa	PROPN
concept-2276	139	26	,	,	PUNCT
concept-2276	139	27	in	in	ADP
concept-2276	139	28	this	this	DET
concept-2276	139	29	model	model	NOUN
concept-2276	139	30	,	,	PUNCT
concept-2276	139	31	we	we	PRON
concept-2276	139	32	need	need	VERB
concept-2276	139	33	to	to	PART
concept-2276	139	34	find	find	VERB
concept-2276	139	35	the	the	DET
concept-2276	139	36	prior	prior	ADJ
concept-2276	139	37	true	true	ADJ
concept-2276	139	38	abilities	ability	NOUN
concept-2276	139	39	for	for	ADP
concept-2276	139	40	a	a	DET
concept-2276	139	41	player	player	NOUN
concept-2276	139	42	to	to	PART
concept-2276	139	43	get	get	VERB
concept-2276	139	44	a	a	DET
concept-2276	139	45	hit	hit	NOUN
concept-2276	139	46	(	(	PUNCT
concept-2276	139	47	ph	ph	NOUN
concept-2276	139	48	)	)	PUNCT
concept-2276	139	49	,	,	PUNCT
concept-2276	139	50	walk	walk	NOUN
concept-2276	139	51	(	(	PUNCT
concept-2276	139	52	pbb	pbb	NOUN
concept-2276	139	53	)	)	PUNCT
concept-2276	139	54	,	,	PUNCT
concept-2276	139	55	hit	hit	VERB
concept-2276	139	56	-	-	PUNCT
concept-2276	139	57	by	by	ADP
concept-2276	139	58	-	-	PUNCT
concept-2276	139	59	pitch	pitch	NOUN
concept-2276	139	60	(	(	PUNCT
concept-2276	139	61	phbp	phbp	NOUN
concept-2276	139	62	)	)	PUNCT
concept-2276	139	63	,	,	PUNCT
concept-2276	139	64	and	and	CCONJ
concept-2276	139	65	out	out	ADV
concept-2276	139	66	(	(	PUNCT
concept-2276	139	67	1−	1−	NUM
concept-2276	139	68	ph	ph	NOUN
concept-2276	139	69	−	−	PROPN
concept-2276	139	70	pbb	pbb	NOUN
concept-2276	139	71	−	−	PROPN
concept-2276	139	72	phbp	phbp	NOUN
concept-2276	139	73	)	)	PUNCT
concept-2276	139	74	given	give	VERB
concept-2276	139	75	only	only	ADV
concept-2276	139	76	pa	pa	PROPN
concept-2276	139	77	.	.	PUNCT
concept-2276	140	1	since	since	SCONJ
concept-2276	140	2	we	we	PRON
concept-2276	140	3	are	be	AUX
concept-2276	140	4	looking	look	VERB
concept-2276	140	5	at	at	ADP
concept-2276	140	6	probabilities	probability	NOUN
concept-2276	140	7	such	such	ADJ
concept-2276	140	8	that	that	SCONJ
concept-2276	140	9	the	the	DET
concept-2276	140	10	sum	sum	NOUN
concept-2276	140	11	of	of	ADP
concept-2276	140	12	probabilities	probability	NOUN
concept-2276	140	13	of	of	ADP
concept-2276	140	14	the	the	DET
concept-2276	140	15	four	four	NUM
concept-2276	140	16	components	component	NOUN
concept-2276	140	17	adds	add	VERB
concept-2276	140	18	up	up	ADP
concept-2276	140	19	to	to	ADP
concept-2276	140	20	1	1	NUM
concept-2276	140	21	(	(	PUNCT
concept-2276	140	22	reaching	reach	VERB
concept-2276	140	23	on	on	ADP
concept-2276	140	24	-	-	PUNCT
concept-2276	140	25	base	base	NOUN
concept-2276	140	26	by	by	ADP
concept-2276	140	27	fielders	fielder	NOUN
concept-2276	140	28	’	'	PUNCT
concept-2276	140	29	choice	choice	NOUN
concept-2276	140	30	or	or	CCONJ
concept-2276	140	31	by	by	ADP
concept-2276	140	32	an	an	DET
concept-2276	140	33	error	error	NOUN
concept-2276	140	34	is	be	AUX
concept-2276	140	35	counted	count	VERB
concept-2276	140	36	as	as	ADP
concept-2276	140	37	an	an	DET
concept-2276	140	38	out	out	NOUN
concept-2276	140	39	according	accord	VERB
concept-2276	140	40	to	to	ADP
concept-2276	140	41	the	the	DET
concept-2276	140	42	definition	definition	NOUN
concept-2276	140	43	of	of	ADP
concept-2276	140	44	on	on	ADP
concept-2276	140	45	-	-	PUNCT
concept-2276	140	46	base	base	NOUN
concept-2276	140	47	percentage	percentage	NOUN
concept-2276	140	48	)	)	PUNCT
concept-2276	140	49	,	,	PUNCT
concept-2276	140	50	the	the	DET
concept-2276	140	51	most	most	ADV
concept-2276	140	52	natural	natural	ADJ
concept-2276	140	53	distribution	distribution	NOUN
concept-2276	140	54	to	to	PART
concept-2276	140	55	turn	turn	VERB
concept-2276	140	56	to	to	PART
concept-2276	140	57	would	would	AUX
concept-2276	140	58	be	be	AUX
concept-2276	140	59	the	the	DET
concept-2276	140	60	dirichlet	dirichlet	NOUN
concept-2276	140	61	distribution	distribution	NOUN
concept-2276	140	62	.	.	PUNCT
concept-2276	141	1	the	the	DET
concept-2276	141	2	dirichlet	dirichlet	PROPN
concept-2276	141	3	distribution	distribution	NOUN
concept-2276	141	4	is	be	AUX
concept-2276	141	5	the	the	DET
concept-2276	141	6	multi	multi	ADJ
concept-2276	141	7	-	-	ADJ
concept-2276	141	8	variable	variable	ADJ
concept-2276	141	9	equivalent	equivalent	NOUN
concept-2276	141	10	of	of	ADP
concept-2276	141	11	the	the	DET
concept-2276	141	12	beta	beta	ADJ
concept-2276	141	13	distribution	distribution	NOUN
concept-2276	141	14	where	where	SCONJ
concept-2276	141	15	n	n	NOUN
concept-2276	141	16	=	=	SYM
concept-2276	141	17	2	2	NUM
concept-2276	141	18	of	of	ADP
concept-2276	141	19	the	the	DET
concept-2276	141	20	dirichlet	dirichlet	NOUN
concept-2276	141	21	distribution	distribution	NOUN
concept-2276	141	22	is	be	AUX
concept-2276	141	23	the	the	DET
concept-2276	141	24	beta	beta	ADJ
concept-2276	141	25	distribution	distribution	NOUN
concept-2276	141	26	.	.	PUNCT
concept-2276	142	1	the	the	DET
concept-2276	142	2	probability	probability	NOUN
concept-2276	142	3	density	density	NOUN
concept-2276	142	4	function	function	NOUN
concept-2276	142	5	of	of	ADP
concept-2276	142	6	the	the	DET
concept-2276	142	7	dirichlet	dirichlet	NOUN
concept-2276	142	8	distribution	distribution	NOUN
concept-2276	142	9	is	be	AUX
concept-2276	142	10	fx1,x2,	fx1,x2,	NOUN
concept-2276	142	11	...	...	PUNCT
concept-2276	142	12	,xn(x1	,xn(x1	PUNCT
concept-2276	142	13	,	,	PUNCT
concept-2276	142	14	x2	x2	PROPN
concept-2276	142	15	,	,	PUNCT
concept-2276	142	16	...	...	PUNCT
concept-2276	142	17	,	,	PUNCT
concept-2276	142	18	xn	xn	X
concept-2276	142	19	)	)	PUNCT
concept-2276	142	20	=	=	SYM
concept-2276	143	1	1	1	NUM
concept-2276	143	2	b(α1,α2,	b(α1,α2,	NUM
concept-2276	143	3	...	...	PUNCT
concept-2276	143	4	,αn	,αn	PUNCT
concept-2276	143	5	)	)	PUNCT
concept-2276	143	6	πn	πn	VERB
concept-2276	143	7	i=1xαi−1	i=1xαi−1	PROPN
concept-2276	143	8	i	i	PRON
concept-2276	143	9	where	where	SCONJ
concept-2276	143	10	b(α1	b(α1	NOUN
concept-2276	143	11	,	,	PUNCT
concept-2276	143	12	α2	α2	ADJ
concept-2276	143	13	,	,	PUNCT
concept-2276	143	14	...	...	PUNCT
concept-2276	143	15	,	,	PUNCT
concept-2276	143	16	αn	αn	NOUN
concept-2276	143	17	)	)	PUNCT
concept-2276	143	18	=	=	PUNCT
concept-2276	143	19	πn	πn	X
concept-2276	143	20	i=1γ(αi	i=1γ(αi	PROPN
concept-2276	143	21	)	)	PUNCT
concept-2276	143	22	γ(σn	γ(σn	NUM
concept-2276	143	23	i=1αi	i=1αi	NOUN
concept-2276	143	24	)	)	PUNCT
concept-2276	143	25	we	we	PRON
concept-2276	143	26	can	can	AUX
concept-2276	143	27	use	use	VERB
concept-2276	143	28	the	the	DET
concept-2276	143	29	same	same	ADJ
concept-2276	143	30	process	process	NOUN
concept-2276	143	31	of	of	ADP
concept-2276	143	32	finding	find	VERB
concept-2276	143	33	the	the	DET
concept-2276	143	34	distribution	distribution	NOUN
concept-2276	143	35	as	as	ADP
concept-2276	143	36	in	in	ADP
concept-2276	143	37	section	section	NOUN
concept-2276	143	38	2.2	2.2	NUM
concept-2276	143	39	by	by	ADP
concept-2276	143	40	finding	find	VERB
concept-2276	143	41	the	the	DET
concept-2276	143	42	means	mean	NOUN
concept-2276	143	43	of	of	ADP
concept-2276	143	44	the	the	DET
concept-2276	143	45	different	different	ADJ
concept-2276	143	46	abilities	ability	NOUN
concept-2276	143	47	and	and	CCONJ
concept-2276	143	48	the	the	DET
concept-2276	143	49	variability	variability	NOUN
concept-2276	143	50	of	of	ADP
concept-2276	143	51	the	the	DET
concept-2276	143	52	abilities	ability	NOUN
concept-2276	143	53	.	.	PUNCT
concept-2276	144	1	in	in	ADP
concept-2276	144	2	this	this	DET
concept-2276	144	3	case	case	NOUN
concept-2276	144	4	,	,	PUNCT
concept-2276	144	5	we	we	PRON
concept-2276	144	6	set	set	VERB
concept-2276	144	7	µ1	µ1	PROPN
concept-2276	144	8	=	=	SYM
concept-2276	144	9	α1	α1	PROPN
concept-2276	144	10	α1+α2+α3+α4	α1+α2+α3+α4	NOUN
concept-2276	144	11	,	,	PUNCT
concept-2276	144	12	µ2	µ2	PROPN
concept-2276	144	13	=	=	SYM
concept-2276	144	14	α2	α2	PROPN
concept-2276	144	15	α1+α2+α3+α4	α1+α2+α3+α4	NOUN
concept-2276	144	16	,	,	PUNCT
concept-2276	144	17	µ3	µ3	PROPN
concept-2276	144	18	=	=	SYM
concept-2276	144	19	α3	α3	NOUN
concept-2276	144	20	α1+α2+α3+α4	α1+α2+α3+α4	NOUN
concept-2276	144	21	,	,	PUNCT
concept-2276	144	22	and	and	CCONJ
concept-2276	144	23	µ4	µ4	PROPN
concept-2276	144	24	=	=	SYM
concept-2276	144	25	1−	1−	NUM
concept-2276	144	26	µ1	µ1	NOUN
concept-2276	144	27	−	−	PROPN
concept-2276	144	28	µ2	µ2	PROPN
concept-2276	144	29	−	−	PROPN
concept-2276	144	30	µ3	µ3	PROPN
concept-2276	144	31	where	where	SCONJ
concept-2276	144	32	µ1,µ2,µ3	µ1,µ2,µ3	NOUN
concept-2276	144	33	,	,	PUNCT
concept-2276	144	34	and	and	CCONJ
concept-2276	144	35	µ4	µ4	PROPN
concept-2276	144	36	are	be	AUX
concept-2276	144	37	the	the	DET
concept-2276	144	38	means	mean	NOUN
concept-2276	144	39	corresponding	correspond	VERB
concept-2276	144	40	to	to	ADP
concept-2276	144	41	hits	hit	NOUN
concept-2276	144	42	,	,	PUNCT
concept-2276	144	43	walks	walk	NOUN
concept-2276	144	44	,	,	PUNCT
concept-2276	144	45	hit	hit	NOUN
concept-2276	144	46	-	-	PUNCT
concept-2276	144	47	by	by	ADP
concept-2276	144	48	-	-	PUNCT
concept-2276	144	49	pitches	pitch	NOUN
concept-2276	144	50	and	and	CCONJ
concept-2276	144	51	outs	out	NOUN
concept-2276	144	52	respectively	respectively	ADV
concept-2276	144	53	.	.	PUNCT
concept-2276	145	1	in	in	ADP
concept-2276	145	2	this	this	DET
concept-2276	145	3	case	case	NOUN
concept-2276	145	4	,	,	PUNCT
concept-2276	145	5	c	c	PROPN
concept-2276	145	6	will	will	AUX
concept-2276	145	7	be	be	AUX
concept-2276	145	8	equal	equal	ADJ
concept-2276	145	9	to	to	ADP
concept-2276	145	10	α1	α1	PROPN
concept-2276	145	11	+	+	CCONJ
concept-2276	145	12	α2	α2	ADJ
concept-2276	145	13	+	+	CCONJ
concept-2276	145	14	α3	α3	ADJ
concept-2276	145	15	+	+	NUM
concept-2276	145	16	α4	α4	NOUN
concept-2276	145	17	.	.	PUNCT
concept-2276	146	1	using	use	VERB
concept-2276	146	2	the	the	DET
concept-2276	146	3	same	same	ADJ
concept-2276	146	4	process	process	NOUN
concept-2276	146	5	as	as	ADP
concept-2276	146	6	what	what	PRON
concept-2276	146	7	we	we	PRON
concept-2276	146	8	used	use	VERB
concept-2276	146	9	in	in	ADP
concept-2276	146	10	section	section	NOUN
concept-2276	146	11	2.2	2.2	NUM
concept-2276	146	12	,	,	PUNCT
concept-2276	146	13	it	it	PRON
concept-2276	146	14	follows	follow	VERB
concept-2276	146	15	that	that	SCONJ
concept-2276	146	16	9	9	NUM
concept-2276	146	17	µ1(pa	µ1(pa	NUM
concept-2276	146	18	)	)	PUNCT
concept-2276	146	19	=	=	PUNCT
concept-2276	147	1			X
concept-2276	147	2	0.000125969x	0.000125969x	PROPN
concept-2276	148	1	+	+	CCONJ
concept-2276	148	2	.187209302	.187209302	NOUN
concept-2276	148	3	if	if	SCONJ
concept-2276	148	4	pa	pa	PROPN
concept-2276	148	5	≤	≤	ADV
concept-2276	148	6	230	230	NUM
concept-2276	148	7	0.000070543x	0.000070543x	PROPN
concept-2276	149	1	+	+	CCONJ
concept-2276	149	2	.2	.2	NUM
concept-2276	149	3	if	if	SCONJ
concept-2276	149	4	pa	pa	PROPN
concept-2276	149	5	>	>	X
concept-2276	149	6	230	230	NUM
concept-2276	149	7	µ2(pa	µ2(pa	NUM
concept-2276	149	8	)	)	PUNCT
concept-2276	149	9	=	=	SYM
concept-2276	150	1			NUM
concept-2276	150	2	0.000217241x	0.000217241x	NOUN
concept-2276	150	3	+	+	CCONJ
concept-2276	150	4	.04137931	.04137931	NOUN
concept-2276	150	5	if	if	SCONJ
concept-2276	150	6	pa	pa	PROPN
concept-2276	150	7	≤	≤	PROPN
concept-2276	150	8	167	167	NUM
concept-2276	150	9	0.000015517x	0.000015517x	NOUN
concept-2276	151	1	+	+	CCONJ
concept-2276	151	2	.075172414	.075172414	NOUN
concept-2276	152	1	if	if	SCONJ
concept-2276	152	2	pa	pa	PROPN
concept-2276	152	3	>	>	X
concept-2276	152	4	167	167	NUM
concept-2276	152	5	µ3(pa	µ3(pa	NUM
concept-2276	152	6	)	)	PUNCT
concept-2276	152	7	=	=	PUNCT
concept-2276	152	8			X
concept-2276	152	9	0.000030864x	0.000030864x	ADJ
concept-2276	152	10	if	if	SCONJ
concept-2276	152	11	pa	pa	PROPN
concept-2276	152	12	≤	≤	PROPN
concept-2276	152	13	232	232	NUM
concept-2276	152	14	0.000003292x	0.000003292x	PUNCT
concept-2276	153	1	+	+	CCONJ
concept-2276	153	2	.006419753	.006419753	VERB
concept-2276	153	3	if	if	SCONJ
concept-2276	153	4	pa	pa	PROPN
concept-2276	153	5	>	>	X
concept-2276	153	6	232	232	NUM
concept-2276	153	7	in	in	ADP
concept-2276	153	8	this	this	DET
concept-2276	153	9	case	case	NOUN
concept-2276	153	10	,	,	PUNCT
concept-2276	153	11	µ4	µ4	PROPN
concept-2276	153	12	is	be	AUX
concept-2276	153	13	omitted	omit	VERB
concept-2276	153	14	since	since	SCONJ
concept-2276	153	15	it	it	PRON
concept-2276	153	16	is	be	AUX
concept-2276	153	17	just	just	ADV
concept-2276	153	18	a	a	DET
concept-2276	153	19	function	function	NOUN
concept-2276	153	20	of	of	ADP
concept-2276	153	21	the	the	DET
concept-2276	153	22	other	other	ADJ
concept-2276	153	23	3	3	NUM
concept-2276	153	24	functions	function	NOUN
concept-2276	153	25	and	and	CCONJ
concept-2276	153	26	carries	carry	VERB
concept-2276	153	27	little	little	ADJ
concept-2276	153	28	benefit	benefit	NOUN
concept-2276	153	29	in	in	ADP
concept-2276	153	30	the	the	DET
concept-2276	153	31	model	model	NOUN
concept-2276	153	32	.	.	PUNCT
concept-2276	154	1	since	since	SCONJ
concept-2276	154	2	the	the	DET
concept-2276	154	3	process	process	NOUN
concept-2276	154	4	of	of	ADP
concept-2276	154	5	finding	find	VERB
concept-2276	154	6	c	c	NOUN
concept-2276	154	7	is	be	AUX
concept-2276	154	8	the	the	DET
concept-2276	154	9	exact	exact	ADJ
concept-2276	154	10	same	same	ADJ
concept-2276	154	11	process	process	NOUN
concept-2276	154	12	as	as	ADP
concept-2276	154	13	in	in	ADP
concept-2276	154	14	section	section	NOUN
concept-2276	154	15	2.2	2.2	NUM
concept-2276	154	16	,	,	PUNCT
concept-2276	154	17	we	we	PRON
concept-2276	154	18	omit	omit	VERB
concept-2276	154	19	the	the	DET
concept-2276	154	20	details	detail	NOUN
concept-2276	154	21	with	with	ADP
concept-2276	154	22	the	the	DET
concept-2276	154	23	process	process	NOUN
concept-2276	154	24	and	and	CCONJ
concept-2276	154	25	say	say	VERB
concept-2276	154	26	that	that	SCONJ
concept-2276	154	27	we	we	PRON
concept-2276	154	28	will	will	AUX
concept-2276	154	29	use	use	VERB
concept-2276	154	30	c	c	NOUN
concept-2276	154	31	=	=	SYM
concept-2276	154	32	625	625	NUM
concept-2276	154	33	as	as	SCONJ
concept-2276	154	34	was	be	AUX
concept-2276	154	35	used	use	VERB
concept-2276	154	36	in	in	ADP
concept-2276	154	37	the	the	DET
concept-2276	154	38	previous	previous	ADJ
concept-2276	154	39	model	model	NOUN
concept-2276	154	40	.	.	PUNCT
concept-2276	155	1	now	now	ADV
concept-2276	155	2	we	we	PRON
concept-2276	155	3	have	have	VERB
concept-2276	155	4	a	a	DET
concept-2276	155	5	connection	connection	NOUN
concept-2276	155	6	between	between	ADP
concept-2276	155	7	the	the	DET
concept-2276	155	8	prior	prior	ADJ
concept-2276	155	9	true	true	ADJ
concept-2276	155	10	ability	ability	NOUN
concept-2276	155	11	with	with	ADP
concept-2276	155	12	plate	plate	NOUN
concept-2276	155	13	appearances	appearance	NOUN
concept-2276	155	14	.	.	PUNCT
concept-2276	156	1	iii	iii	X
concept-2276	156	2	.	.	PROPN
concept-2276	156	3	hits	hit	NOUN
concept-2276	156	4	,	,	PUNCT
concept-2276	156	5	walks	walk	NOUN
concept-2276	156	6	,	,	PUNCT
concept-2276	156	7	hit	hit	NOUN
concept-2276	156	8	-	-	PUNCT
concept-2276	156	9	by	by	ADP
concept-2276	156	10	-	-	PUNCT
concept-2276	156	11	pitches	pitch	NOUN
concept-2276	156	12	finally	finally	ADV
concept-2276	156	13	,	,	PUNCT
concept-2276	156	14	we	we	PRON
concept-2276	156	15	need	need	VERB
concept-2276	156	16	to	to	PART
concept-2276	156	17	model	model	VERB
concept-2276	156	18	the	the	DET
concept-2276	156	19	distribution	distribution	NOUN
concept-2276	156	20	of	of	ADP
concept-2276	156	21	hits	hit	NOUN
concept-2276	156	22	(	(	PUNCT
concept-2276	156	23	h	h	NOUN
concept-2276	156	24	)	)	PUNCT
concept-2276	156	25	,	,	PUNCT
concept-2276	156	26	walks	walk	VERB
concept-2276	156	27	(	(	PUNCT
concept-2276	156	28	bb	bb	NOUN
concept-2276	156	29	)	)	PUNCT
concept-2276	156	30	,	,	PUNCT
concept-2276	156	31	and	and	CCONJ
concept-2276	156	32	hit	hit	VERB
concept-2276	156	33	-	-	PUNCT
concept-2276	156	34	by	by	ADP
concept-2276	156	35	-	-	PUNCT
concept-2276	156	36	pitches	pitch	NOUN
concept-2276	156	37	(	(	PUNCT
concept-2276	156	38	hbp	hbp	NOUN
concept-2276	156	39	)	)	PUNCT
concept-2276	156	40	given	give	VERB
concept-2276	156	41	pa	pa	PROPN
concept-2276	156	42	,	,	PUNCT
concept-2276	156	43	ph	ph	PROPN
concept-2276	156	44	,	,	PUNCT
concept-2276	156	45	pbb	pbb	ADJ
concept-2276	156	46	,	,	PUNCT
concept-2276	156	47	and	and	CCONJ
concept-2276	156	48	phbp	phbp	NOUN
concept-2276	156	49	.	.	PUNCT
concept-2276	157	1	since	since	SCONJ
concept-2276	157	2	we	we	PRON
concept-2276	157	3	are	be	AUX
concept-2276	157	4	modeling	model	VERB
concept-2276	157	5	plate	plate	NOUN
concept-2276	157	6	appearances	appearance	NOUN
concept-2276	157	7	as	as	ADP
concept-2276	157	8	independent	independent	ADJ
concept-2276	157	9	events	event	NOUN
concept-2276	157	10	that	that	PRON
concept-2276	157	11	only	only	ADV
concept-2276	157	12	lead	lead	VERB
concept-2276	157	13	to	to	ADP
concept-2276	157	14	outcomes	outcome	NOUN
concept-2276	157	15	h	h	NOUN
concept-2276	157	16	,	,	PUNCT
concept-2276	157	17	bb	bb	PROPN
concept-2276	157	18	,	,	PUNCT
concept-2276	157	19	hbp	hbp	PROPN
concept-2276	157	20	,	,	PUNCT
concept-2276	157	21	and	and	CCONJ
concept-2276	157	22	outs	out	NOUN
concept-2276	157	23	,	,	PUNCT
concept-2276	157	24	the	the	DET
concept-2276	157	25	most	most	ADV
concept-2276	157	26	natural	natural	ADJ
concept-2276	157	27	distribution	distribution	NOUN
concept-2276	157	28	to	to	PART
concept-2276	157	29	turn	turn	VERB
concept-2276	157	30	to	to	PART
concept-2276	157	31	would	would	AUX
concept-2276	157	32	be	be	AUX
concept-2276	157	33	the	the	DET
concept-2276	157	34	multinomial	multinomial	ADJ
concept-2276	157	35	distribution	distribution	NOUN
concept-2276	157	36	.	.	PUNCT
concept-2276	158	1	the	the	DET
concept-2276	158	2	multinomial	multinomial	ADJ
concept-2276	158	3	distribution	distribution	NOUN
concept-2276	158	4	is	be	AUX
concept-2276	158	5	the	the	DET
concept-2276	158	6	multi	multi	ADJ
concept-2276	158	7	-	-	ADJ
concept-2276	158	8	variable	variable	ADJ
concept-2276	158	9	analogue	analogue	NOUN
concept-2276	158	10	of	of	ADP
concept-2276	158	11	the	the	DET
concept-2276	158	12	binomial	binomial	ADJ
concept-2276	158	13	distribution	distribution	NOUN
concept-2276	158	14	.	.	PUNCT
concept-2276	159	1	like	like	ADP
concept-2276	159	2	the	the	DET
concept-2276	159	3	binomial	binomial	ADJ
concept-2276	159	4	distribution	distribution	NOUN
concept-2276	159	5	,	,	PUNCT
concept-2276	159	6	the	the	DET
concept-2276	159	7	multinomial	multinomial	ADJ
concept-2276	159	8	distribution	distribution	NOUN
concept-2276	159	9	measures	measure	VERB
concept-2276	159	10	the	the	DET
concept-2276	159	11	outcomes	outcome	NOUN
concept-2276	159	12	of	of	ADP
concept-2276	159	13	n	n	CCONJ
concept-2276	159	14	identical	identical	ADJ
concept-2276	159	15	,	,	PUNCT
concept-2276	159	16	independent	independent	ADJ
concept-2276	159	17	trials	trial	NOUN
concept-2276	159	18	.	.	PUNCT
concept-2276	160	1	however	however	ADV
concept-2276	160	2	,	,	PUNCT
concept-2276	160	3	unlike	unlike	ADP
concept-2276	160	4	the	the	DET
concept-2276	160	5	binomial	binomial	ADJ
concept-2276	160	6	distribution	distribution	NOUN
concept-2276	160	7	where	where	SCONJ
concept-2276	160	8	each	each	DET
concept-2276	160	9	trial	trial	NOUN
concept-2276	160	10	only	only	ADV
concept-2276	160	11	has	have	VERB
concept-2276	160	12	outcomes	outcome	NOUN
concept-2276	160	13	success	success	NOUN
concept-2276	160	14	and	and	CCONJ
concept-2276	160	15	failure	failure	NOUN
concept-2276	160	16	with	with	ADP
concept-2276	160	17	probabilities	probability	NOUN
concept-2276	160	18	p	p	NOUN
concept-2276	160	19	and	and	CCONJ
concept-2276	160	20	1−	1−	NUM
concept-2276	160	21	p	p	NOUN
concept-2276	160	22	respectively	respectively	ADV
concept-2276	160	23	,	,	PUNCT
concept-2276	160	24	the	the	DET
concept-2276	160	25	multinomial	multinomial	ADJ
concept-2276	160	26	distribution	distribution	NOUN
concept-2276	160	27	trials	trial	NOUN
concept-2276	160	28	have	have	VERB
concept-2276	160	29	outcomes	outcome	NOUN
concept-2276	160	30	x1	x1	NUM
concept-2276	160	31	with	with	ADP
concept-2276	160	32	probability	probability	NOUN
concept-2276	160	33	p1	p1	NOUN
concept-2276	160	34	,	,	PUNCT
concept-2276	160	35	x2	x2	PROPN
concept-2276	160	36	with	with	ADP
concept-2276	160	37	probability	probability	NOUN
concept-2276	160	38	p2,	p2,	X
concept-2276	160	39	...	...	PUNCT
concept-2276	160	40	,xk	,xk	PUNCT
concept-2276	160	41	with	with	ADP
concept-2276	160	42	probability	probability	NOUN
concept-2276	160	43	pk	pk	NOUN
concept-2276	160	44	where	where	SCONJ
concept-2276	160	45	xi	xi	PROPN
concept-2276	160	46	’s	’s	PART
concept-2276	160	47	are	be	AUX
concept-2276	160	48	integers	integer	NOUN
concept-2276	160	49	with	with	ADP
concept-2276	160	50	σk	σk	PROPN
concept-2276	160	51	i=1xi	i=1xi	PROPN
concept-2276	160	52	=	=	SYM
concept-2276	160	53	n	n	PROPN
concept-2276	160	54	and	and	CCONJ
concept-2276	160	55	pi	pi	NOUN
concept-2276	160	56	’s	’s	PART
concept-2276	160	57	are	be	AUX
concept-2276	160	58	probabilities	probability	NOUN
concept-2276	161	1	such	such	ADJ
concept-2276	161	2	that	that	PRON
concept-2276	161	3	σk	σk	VERB
concept-2276	161	4	i=1	i=1	PROPN
concept-2276	161	5	pi	pi	NOUN
concept-2276	161	6	=	=	NOUN
concept-2276	161	7	1	1	X
concept-2276	161	8	.	.	PUNCT
concept-2276	162	1	the	the	DET
concept-2276	162	2	probability	probability	NOUN
concept-2276	162	3	mass	mass	NOUN
concept-2276	162	4	function	function	NOUN
concept-2276	162	5	for	for	ADP
concept-2276	162	6	this	this	DET
concept-2276	162	7	distribution	distribution	NOUN
concept-2276	162	8	is	be	AUX
concept-2276	162	9	n	n	PRON
concept-2276	162	10	!	!	PUNCT
concept-2276	162	11	x1!x2!	x1!x2!	PUNCT
concept-2276	162	12	...	...	PUNCT
concept-2276	163	1	xk	xk	PROPN
concept-2276	163	2	!	!	PUNCT
concept-2276	164	1	px1	px1	PROPN
concept-2276	164	2	1	1	NUM
concept-2276	164	3	p2x2	p2x2	NOUN
concept-2276	164	4	...	...	PUNCT
concept-2276	164	5	pxk	pxk	PROPN
concept-2276	165	1	k	k	PROPN
concept-2276	165	2	.	.	PUNCT
concept-2276	166	1	notice	notice	VERB
concept-2276	166	2	that	that	SCONJ
concept-2276	166	3	for	for	ADP
concept-2276	166	4	k	k	PROPN
concept-2276	166	5	=	=	SYM
concept-2276	166	6	2	2	NUM
concept-2276	166	7	,	,	PUNCT
concept-2276	166	8	the	the	DET
concept-2276	166	9	multinomial	multinomial	ADJ
concept-2276	166	10	distribution	distribution	NOUN
concept-2276	166	11	is	be	AUX
concept-2276	166	12	the	the	DET
concept-2276	166	13	binomial	binomial	ADJ
concept-2276	166	14	distribution	distribution	NOUN
concept-2276	166	15	.	.	PUNCT
concept-2276	167	1	however	however	ADV
concept-2276	167	2	,	,	PUNCT
concept-2276	167	3	in	in	ADP
concept-2276	167	4	order	order	NOUN
concept-2276	167	5	for	for	SCONJ
concept-2276	167	6	h	h	NOUN
concept-2276	167	7	,	,	PUNCT
concept-2276	167	8	bb	bb	PROPN
concept-2276	167	9	and	and	CCONJ
concept-2276	167	10	hbp	hbp	PROPN
concept-2276	167	11	to	to	PART
concept-2276	167	12	be	be	AUX
concept-2276	167	13	modeled	model	VERB
concept-2276	167	14	this	this	DET
concept-2276	167	15	way	way	NOUN
concept-2276	167	16	,	,	PUNCT
concept-2276	167	17	we	we	PRON
concept-2276	167	18	need	need	VERB
concept-2276	167	19	to	to	PART
concept-2276	167	20	have	have	VERB
concept-2276	167	21	hits	hit	NOUN
concept-2276	167	22	to	to	PART
concept-2276	167	23	be	be	AUX
concept-2276	167	24	modeled	model	VERB
concept-2276	167	25	as	as	ADP
concept-2276	167	26	(	(	PUNCT
concept-2276	167	27	h1	h1	PROPN
concept-2276	167	28	pa1	pa1	PROPN
concept-2276	167	29	−	−	PROPN
concept-2276	167	30	h2	h2	PROPN
concept-2276	167	31	pa2	pa2	PROPN
concept-2276	167	32	)	)	PUNCT
concept-2276	167	33	√	√	PROPN
concept-2276	168	1	p̂h(1−	p̂h(1−	PROPN
concept-2276	168	2	p̂h)(pa−1	p̂h)(pa−1	NOUN
concept-2276	168	3	1	1	NUM
concept-2276	169	1	+	+	CCONJ
concept-2276	169	2	pa−1	pa−1	NOUN
concept-2276	169	3	2	2	X
concept-2276	169	4	)	)	PUNCT
concept-2276	169	5	∼	∼	NOUN
concept-2276	169	6	n(0	n(0	PROPN
concept-2276	169	7	,	,	PUNCT
concept-2276	169	8	1	1	NUM
concept-2276	169	9	)	)	PUNCT
concept-2276	169	10	10	10	NUM
concept-2276	169	11	where	where	SCONJ
concept-2276	169	12	p̂h	p̂h	ADV
concept-2276	169	13	=	=	SYM
concept-2276	170	1	h1+h2	h1+h2	PROPN
concept-2276	170	2	pa1+pa2	pa1+pa2	NOUN
concept-2276	170	3	.	.	PUNCT
concept-2276	171	1	notice	notice	VERB
concept-2276	171	2	that	that	SCONJ
concept-2276	171	3	this	this	DET
concept-2276	171	4	modeled	model	VERB
concept-2276	171	5	function	function	NOUN
concept-2276	171	6	is	be	AUX
concept-2276	171	7	analogous	analogous	ADJ
concept-2276	171	8	to	to	ADP
concept-2276	171	9	the	the	DET
concept-2276	171	10	one	one	NUM
concept-2276	171	11	in	in	ADP
concept-2276	171	12	section	section	NOUN
concept-2276	171	13	2.3	2.3	NUM
concept-2276	171	14	.	.	PUNCT
concept-2276	172	1	we	we	PRON
concept-2276	172	2	would	would	AUX
concept-2276	172	3	also	also	ADV
concept-2276	172	4	need	need	VERB
concept-2276	172	5	walks	walk	NOUN
concept-2276	172	6	and	and	CCONJ
concept-2276	172	7	hit	hit	VERB
concept-2276	172	8	-	-	PUNCT
concept-2276	172	9	by	by	ADP
concept-2276	172	10	-	-	PUNCT
concept-2276	172	11	pitches	pitch	NOUN
concept-2276	172	12	to	to	PART
concept-2276	172	13	be	be	AUX
concept-2276	172	14	verified	verify	VERB
concept-2276	172	15	in	in	ADP
concept-2276	172	16	a	a	DET
concept-2276	172	17	similar	similar	ADJ
concept-2276	172	18	fashion	fashion	NOUN
concept-2276	172	19	.	.	PUNCT
concept-2276	173	1	the	the	DET
concept-2276	173	2	way	way	NOUN
concept-2276	173	3	that	that	PRON
concept-2276	173	4	one	one	NUM
concept-2276	173	5	verifies	verifie	NOUN
concept-2276	173	6	this	this	PRON
concept-2276	173	7	is	be	AUX
concept-2276	173	8	the	the	DET
concept-2276	173	9	same	same	ADJ
concept-2276	173	10	as	as	ADP
concept-2276	173	11	the	the	DET
concept-2276	173	12	technique	technique	NOUN
concept-2276	173	13	used	use	VERB
concept-2276	173	14	in	in	ADP
concept-2276	173	15	the	the	DET
concept-2276	173	16	first	first	ADJ
concept-2276	173	17	model	model	NOUN
concept-2276	173	18	so	so	SCONJ
concept-2276	173	19	we	we	PRON
concept-2276	173	20	omit	omit	VERB
concept-2276	173	21	the	the	DET
concept-2276	173	22	details	detail	NOUN
concept-2276	173	23	.	.	PUNCT
concept-2276	174	1	after	after	ADP
concept-2276	174	2	carrying	carry	VERB
concept-2276	174	3	out	out	ADP
concept-2276	174	4	this	this	DET
concept-2276	174	5	process	process	NOUN
concept-2276	174	6	by	by	ADP
concept-2276	174	7	looking	look	VERB
concept-2276	174	8	at	at	ADP
concept-2276	174	9	the	the	DET
concept-2276	174	10	histograms	histogram	NOUN
concept-2276	174	11	of	of	ADP
concept-2276	174	12	h	h	NOUN
concept-2276	174	13	,	,	PUNCT
concept-2276	174	14	bb	bb	NOUN
concept-2276	174	15	,	,	PUNCT
concept-2276	174	16	and	and	CCONJ
concept-2276	174	17	hbp	hbp	PROPN
concept-2276	174	18	and	and	CCONJ
concept-2276	174	19	calculating	calculate	VERB
concept-2276	174	20	their	their	PRON
concept-2276	174	21	means	mean	NOUN
concept-2276	174	22	and	and	CCONJ
concept-2276	174	23	standard	standard	ADJ
concept-2276	174	24	deviations	deviation	NOUN
concept-2276	174	25	,	,	PUNCT
concept-2276	174	26	it	it	PRON
concept-2276	174	27	turns	turn	VERB
concept-2276	174	28	out	out	ADP
concept-2276	174	29	that	that	SCONJ
concept-2276	174	30	each	each	PRON
concept-2276	174	31	of	of	ADP
concept-2276	174	32	the	the	DET
concept-2276	174	33	formulas	formula	NOUN
concept-2276	174	34	are	be	AUX
concept-2276	174	35	normal	normal	ADJ
concept-2276	174	36	,	,	PUNCT
concept-2276	174	37	which	which	PRON
concept-2276	174	38	means	mean	VERB
concept-2276	174	39	that	that	SCONJ
concept-2276	174	40	hits	hit	VERB
concept-2276	174	41	,	,	PUNCT
concept-2276	174	42	walks	walk	VERB
concept-2276	174	43	and	and	CCONJ
concept-2276	174	44	hit	hit	VERB
concept-2276	174	45	-	-	PUNCT
concept-2276	174	46	by	by	ADP
concept-2276	174	47	-	-	PUNCT
concept-2276	174	48	pitches	pitch	NOUN
concept-2276	174	49	follows	follow	VERB
concept-2276	174	50	as	as	ADP
concept-2276	174	51	a	a	DET
concept-2276	174	52	multinomial	multinomial	ADJ
concept-2276	174	53	distribution	distribution	NOUN
concept-2276	174	54	.	.	PUNCT
concept-2276	175	1	iv	iv	X
concept-2276	175	2	.	.	PUNCT
concept-2276	175	3	checking	check	VERB
concept-2276	175	4	the	the	DET
concept-2276	175	5	model	model	NOUN
concept-2276	175	6	after	after	ADP
concept-2276	175	7	completing	complete	VERB
concept-2276	175	8	our	our	PRON
concept-2276	175	9	model	model	NOUN
concept-2276	175	10	,	,	PUNCT
concept-2276	175	11	we	we	PRON
concept-2276	175	12	decided	decide	VERB
concept-2276	175	13	to	to	PART
concept-2276	175	14	create	create	VERB
concept-2276	175	15	a	a	DET
concept-2276	175	16	simulation	simulation	NOUN
concept-2276	175	17	of	of	ADP
concept-2276	175	18	700	700	NUM
concept-2276	175	19	players	player	NOUN
concept-2276	175	20	using	use	VERB
concept-2276	175	21	the	the	DET
concept-2276	175	22	model	model	NOUN
concept-2276	175	23	and	and	CCONJ
concept-2276	175	24	compare	compare	VERB
concept-2276	175	25	its	its	PRON
concept-2276	175	26	scatter	scatter	NOUN
concept-2276	175	27	plot	plot	NOUN
concept-2276	175	28	of	of	ADP
concept-2276	175	29	obp	obp	PROPN
concept-2276	175	30	to	to	PART
concept-2276	175	31	plate	plate	VERB
concept-2276	175	32	appearances	appearance	NOUN
concept-2276	175	33	to	to	ADP
concept-2276	175	34	that	that	PRON
concept-2276	175	35	of	of	ADP
concept-2276	175	36	the	the	DET
concept-2276	175	37	real	real	ADJ
concept-2276	175	38	data	datum	NOUN
concept-2276	175	39	.	.	PUNCT
concept-2276	176	1	for	for	ADP
concept-2276	176	2	each	each	DET
concept-2276	176	3	player	player	NOUN
concept-2276	176	4	,	,	PUNCT
concept-2276	176	5	we	we	PRON
concept-2276	176	6	first	first	ADV
concept-2276	176	7	found	find	VERB
concept-2276	176	8	pa	pa	PROPN
concept-2276	176	9	using	use	VERB
concept-2276	176	10	its	its	PRON
concept-2276	176	11	probability	probability	NOUN
concept-2276	176	12	density	density	NOUN
concept-2276	176	13	function	function	NOUN
concept-2276	176	14	,	,	PUNCT
concept-2276	176	15	then	then	ADV
concept-2276	176	16	found	find	VERB
concept-2276	176	17	a	a	DET
concept-2276	176	18	random	random	ADJ
concept-2276	176	19	value	value	NOUN
concept-2276	176	20	of	of	ADP
concept-2276	176	21	ph	ph	NOUN
concept-2276	176	22	,	,	PUNCT
concept-2276	176	23	pbb	pbb	NOUN
concept-2276	176	24	,	,	PUNCT
concept-2276	176	25	phbp	phbp	NOUN
concept-2276	176	26	,	,	PUNCT
concept-2276	176	27	and	and	CCONJ
concept-2276	176	28	pout	pout	VERB
concept-2276	176	29	using	use	VERB
concept-2276	176	30	the	the	DET
concept-2276	176	31	dirichlet	dirichlet	NOUN
concept-2276	176	32	distribution	distribution	NOUN
concept-2276	176	33	,	,	PUNCT
concept-2276	176	34	and	and	CCONJ
concept-2276	176	35	then	then	ADV
concept-2276	176	36	found	find	VERB
concept-2276	176	37	the	the	DET
concept-2276	176	38	number	number	NOUN
concept-2276	176	39	of	of	ADP
concept-2276	176	40	hits	hit	NOUN
concept-2276	176	41	,	,	PUNCT
concept-2276	176	42	walks	walk	NOUN
concept-2276	176	43	,	,	PUNCT
concept-2276	176	44	hit	hit	NOUN
concept-2276	176	45	-	-	PUNCT
concept-2276	176	46	by	by	ADP
concept-2276	176	47	-	-	PUNCT
concept-2276	176	48	pitches	pitch	NOUN
concept-2276	176	49	and	and	CCONJ
concept-2276	176	50	outs	out	NOUN
concept-2276	176	51	by	by	ADP
concept-2276	176	52	picking	pick	VERB
concept-2276	176	53	a	a	DET
concept-2276	176	54	random	random	ADJ
concept-2276	176	55	number	number	NOUN
concept-2276	176	56	from	from	ADP
concept-2276	176	57	it	it	PRON
concept-2276	176	58	’s	’	VERB
concept-2276	176	59	corresponding	correspond	VERB
concept-2276	176	60	multinomial	multinomial	ADJ
concept-2276	176	61	distribution	distribution	NOUN
concept-2276	176	62	.	.	PUNCT
concept-2276	177	1	we	we	PRON
concept-2276	177	2	then	then	ADV
concept-2276	177	3	computed	compute	VERB
concept-2276	177	4	each	each	DET
concept-2276	177	5	simulated	simulated	ADJ
concept-2276	177	6	player	player	NOUN
concept-2276	177	7	’s	’s	PART
concept-2276	177	8	obp	obp	NOUN
concept-2276	177	9	by	by	ADP
concept-2276	177	10	the	the	DET
concept-2276	177	11	formula	formula	NOUN
concept-2276	177	12	hits+walks+hit	hits+walks+hit	PROPN
concept-2276	177	13	-	-	PUNCT
concept-2276	177	14	by	by	ADP
concept-2276	177	15	-	-	PUNCT
concept-2276	177	16	pitches	pitches	NOUN
concept-2276	177	17	plate	plate	NOUN
concept-2276	177	18	appearances	appearance	NOUN
concept-2276	177	19	and	and	CCONJ
concept-2276	177	20	made	make	VERB
concept-2276	177	21	a	a	DET
concept-2276	177	22	scatter	scatter	NOUN
concept-2276	177	23	plot	plot	NOUN
concept-2276	177	24	similar	similar	ADJ
concept-2276	177	25	to	to	ADP
concept-2276	177	26	that	that	PRON
concept-2276	177	27	in	in	ADP
concept-2276	177	28	the	the	DET
concept-2276	177	29	first	first	ADJ
concept-2276	177	30	model	model	NOUN
concept-2276	177	31	.	.	PUNCT
concept-2276	178	1	figure	figure	NOUN
concept-2276	178	2	5	5	NUM
concept-2276	178	3	shows	show	VERB
concept-2276	178	4	the	the	DET
concept-2276	178	5	scatter	scatter	NOUN
concept-2276	178	6	plots	plot	NOUN
concept-2276	178	7	of	of	ADP
concept-2276	178	8	the	the	DET
concept-2276	178	9	data	datum	NOUN
concept-2276	178	10	alongside	alongside	ADV
concept-2276	178	11	with	with	ADP
concept-2276	178	12	the	the	DET
concept-2276	178	13	real	real	ADJ
concept-2276	178	14	data	datum	NOUN
concept-2276	178	15	.	.	PUNCT
concept-2276	179	1	notice	notice	VERB
concept-2276	179	2	again	again	ADV
concept-2276	179	3	that	that	SCONJ
concept-2276	179	4	the	the	DET
concept-2276	179	5	simulated	simulate	VERB
concept-2276	179	6	data	data	NOUN
concept-2276	179	7	plot	plot	NOUN
concept-2276	179	8	is	be	AUX
concept-2276	179	9	very	very	ADV
concept-2276	179	10	similar	similar	ADJ
concept-2276	179	11	to	to	ADP
concept-2276	179	12	that	that	PRON
concept-2276	179	13	of	of	ADP
concept-2276	179	14	the	the	DET
concept-2276	179	15	real	real	ADJ
concept-2276	179	16	data	datum	NOUN
concept-2276	179	17	so	so	SCONJ
concept-2276	179	18	this	this	DET
concept-2276	179	19	model	model	NOUN
concept-2276	179	20	captures	capture	VERB
concept-2276	179	21	the	the	DET
concept-2276	179	22	essence	essence	NOUN
concept-2276	179	23	of	of	ADP
concept-2276	179	24	the	the	DET
concept-2276	179	25	baseball	baseball	NOUN
concept-2276	179	26	data	datum	NOUN
concept-2276	179	27	.	.	PUNCT
concept-2276	180	1	0	0	NUM
concept-2276	181	1	200	200	NUM
concept-2276	181	2	400	400	NUM
concept-2276	181	3	600	600	NUM
concept-2276	181	4	0	0	NUM
concept-2276	182	1	.0	.0	NUM
concept-2276	182	2	0	0	NUM
concept-2276	183	1	.2	.2	NUM
concept-2276	183	2	0	0	NUM
concept-2276	184	1	.4	.4	NUM
concept-2276	184	2	0	0	NUM
concept-2276	185	1	.6	.6	NUM
concept-2276	185	2	0	0	NUM
concept-2276	185	3	.8	.8	NUM
concept-2276	185	4	1	1	NUM
concept-2276	185	5	.0	.0	NUM
concept-2276	185	6	plate	plate	NOUN
concept-2276	185	7	appearances	appearance	VERB
concept-2276	185	8	o	o	NOUN
concept-2276	185	9	b	b	NOUN
concept-2276	185	10	p	p	NOUN
concept-2276	185	11	0	0	NUM
concept-2276	185	12	200	200	NUM
concept-2276	185	13	400	400	NUM
concept-2276	186	1	600	600	NUM
concept-2276	186	2	0	0	NUM
concept-2276	186	3	.0	.0	NUM
concept-2276	186	4	0	0	NUM
concept-2276	187	1	.2	.2	NUM
concept-2276	187	2	0	0	NUM
concept-2276	188	1	.4	.4	NUM
concept-2276	188	2	0	0	NUM
concept-2276	189	1	.6	.6	NUM
concept-2276	189	2	0	0	NUM
concept-2276	189	3	.8	.8	NUM
concept-2276	189	4	1	1	NUM
concept-2276	189	5	.0	.0	NUM
concept-2276	189	6	plate	plate	NOUN
concept-2276	189	7	appearances	appearance	VERB
concept-2276	189	8	o	o	NOUN
concept-2276	189	9	b	b	NOUN
concept-2276	189	10	p	p	NOUN
concept-2276	189	11	0	0	NUM
concept-2276	189	12	200	200	NUM
concept-2276	189	13	400	400	NUM
concept-2276	190	1	600	600	NUM
concept-2276	190	2	0	0	NUM
concept-2276	190	3	.0	.0	NUM
concept-2276	190	4	0	0	NUM
concept-2276	191	1	.2	.2	NUM
concept-2276	191	2	0	0	NUM
concept-2276	192	1	.4	.4	NUM
concept-2276	192	2	0	0	NUM
concept-2276	193	1	.6	.6	NUM
concept-2276	193	2	0	0	NUM
concept-2276	193	3	.8	.8	NUM
concept-2276	193	4	1	1	NUM
concept-2276	193	5	.0	.0	NUM
concept-2276	193	6	plate	plate	NOUN
concept-2276	193	7	appearances	appearance	VERB
concept-2276	193	8	o	o	NOUN
concept-2276	193	9	b	b	X
concept-2276	193	10	p	p	NOUN
concept-2276	193	11	figure	figure	NOUN
concept-2276	193	12	5	5	NUM
concept-2276	193	13	:	:	PUNCT
concept-2276	193	14	plate	plate	NOUN
concept-2276	193	15	appearances	appearance	NOUN
concept-2276	193	16	by	by	ADP
concept-2276	193	17	obp	obp	NOUN
concept-2276	193	18	plots	plot	NOUN
concept-2276	193	19	.	.	PUNCT
concept-2276	194	1	the	the	DET
concept-2276	194	2	left	left	ADV
concept-2276	194	3	-	-	PUNCT
concept-2276	194	4	most	most	ADJ
concept-2276	194	5	one	one	NOUN
concept-2276	194	6	is	be	AUX
concept-2276	194	7	with	with	ADP
concept-2276	194	8	the	the	DET
concept-2276	194	9	2016	2016	NUM
concept-2276	194	10	data	datum	NOUN
concept-2276	194	11	and	and	CCONJ
concept-2276	194	12	the	the	DET
concept-2276	194	13	other	other	ADJ
concept-2276	194	14	two	two	NUM
concept-2276	194	15	are	be	AUX
concept-2276	194	16	created	create	VERB
concept-2276	194	17	by	by	ADP
concept-2276	194	18	simulation	simulation	NOUN
concept-2276	194	19	with	with	ADP
concept-2276	194	20	the	the	DET
concept-2276	194	21	second	second	ADJ
concept-2276	194	22	model	model	NOUN
concept-2276	194	23	.	.	PUNCT
concept-2276	195	1	11	11	NUM
concept-2276	195	2	iv	iv	NOUN
concept-2276	195	3	.	.	PUNCT
concept-2276	196	1	finding	find	VERB
concept-2276	196	2	the	the	DET
concept-2276	196	3	posterior	posterior	ADJ
concept-2276	196	4	distribution	distribution	NOUN
concept-2276	196	5	i.	i.	NOUN
concept-2276	196	6	using	use	VERB
concept-2276	196	7	the	the	DET
concept-2276	196	8	first	first	ADJ
concept-2276	196	9	model	model	NOUN
concept-2276	196	10	in	in	ADP
concept-2276	196	11	order	order	NOUN
concept-2276	196	12	to	to	PART
concept-2276	196	13	find	find	VERB
concept-2276	196	14	the	the	DET
concept-2276	196	15	posterior	posterior	ADJ
concept-2276	196	16	true	true	ADJ
concept-2276	196	17	ability	ability	NOUN
concept-2276	196	18	p	p	NOUN
concept-2276	196	19	based	base	VERB
concept-2276	196	20	on	on	ADP
concept-2276	196	21	obp	obp	PROPN
concept-2276	196	22	alone	alone	ADV
concept-2276	196	23	,	,	PUNCT
concept-2276	196	24	we	we	PRON
concept-2276	196	25	need	need	VERB
concept-2276	196	26	to	to	PART
concept-2276	196	27	find	find	VERB
concept-2276	196	28	the	the	DET
concept-2276	196	29	true	true	ADJ
concept-2276	196	30	ability	ability	NOUN
concept-2276	196	31	given	give	VERB
concept-2276	196	32	obp	obp	PROPN
concept-2276	196	33	.	.	PUNCT
concept-2276	197	1	we	we	PRON
concept-2276	197	2	can	can	AUX
concept-2276	197	3	use	use	VERB
concept-2276	197	4	the	the	DET
concept-2276	197	5	fact	fact	NOUN
concept-2276	197	6	that	that	SCONJ
concept-2276	197	7	p(prior	p(prior	ADJ
concept-2276	197	8	true	true	ADJ
concept-2276	197	9	ability	ability	NOUN
concept-2276	197	10	)	)	PUNCT
concept-2276	197	11	∼	∼	NOUN
concept-2276	197	12	beta(α	beta(α	NOUN
concept-2276	197	13	,	,	PUNCT
concept-2276	197	14	β	β	NOUN
concept-2276	197	15	)	)	PUNCT
concept-2276	197	16	and	and	CCONJ
concept-2276	197	17	x|p(prior	x|p(prior	ADJ
concept-2276	197	18	true	true	ADJ
concept-2276	197	19	ability	ability	NOUN
concept-2276	197	20	)	)	PUNCT
concept-2276	197	21	∼	∼	NOUN
concept-2276	197	22	binomial(n	binomial(n	NOUN
concept-2276	197	23	,	,	PUNCT
concept-2276	197	24	p	p	NOUN
concept-2276	197	25	)	)	PUNCT
concept-2276	197	26	=	=	NOUN
concept-2276	197	27	⇒	⇒	NOUN
concept-2276	197	28	p(posterior	p(posterior	ADJ
concept-2276	197	29	true	true	ADJ
concept-2276	197	30	ability)|x	ability)|x	NOUN
concept-2276	197	31	∼	∼	NOUN
concept-2276	197	32	beta(α	beta(α	ADV
concept-2276	197	33	+	+	CCONJ
concept-2276	197	34	x	x	NOUN
concept-2276	197	35	,	,	PUNCT
concept-2276	197	36	β	β	X
concept-2276	197	37	+	+	CCONJ
concept-2276	197	38	n−	n−	NOUN
concept-2276	197	39	x	x	NOUN
concept-2276	197	40	)	)	PUNCT
concept-2276	197	41	where	where	SCONJ
concept-2276	197	42	a	a	DET
concept-2276	197	43	∼	∼	NOUN
concept-2276	197	44	b	b	NOUN
concept-2276	197	45	means	mean	VERB
concept-2276	197	46	that	that	SCONJ
concept-2276	197	47	random	random	ADJ
concept-2276	197	48	variable	variable	NOUN
concept-2276	197	49	a	a	PRON
concept-2276	197	50	has	have	VERB
concept-2276	197	51	distribution	distribution	NOUN
concept-2276	197	52	b.	b.	PROPN
concept-2276	197	53	frey	frey	PROPN
concept-2276	197	54	(	(	PUNCT
concept-2276	197	55	2007	2007	NUM
concept-2276	197	56	)	)	PUNCT
concept-2276	197	57	found	find	VERB
concept-2276	197	58	that	that	SCONJ
concept-2276	197	59	for	for	ADP
concept-2276	197	60	batting	batting	NOUN
concept-2276	197	61	averages	average	NOUN
concept-2276	197	62	,	,	PUNCT
concept-2276	197	63	one	one	PRON
concept-2276	197	64	can	can	AUX
concept-2276	197	65	find	find	VERB
concept-2276	197	66	the	the	DET
concept-2276	197	67	posterior	posterior	ADJ
concept-2276	197	68	distribution	distribution	NOUN
concept-2276	197	69	conditional	conditional	ADJ
concept-2276	197	70	on	on	ADP
concept-2276	197	71	a	a	DET
concept-2276	197	72	given	give	VERB
concept-2276	197	73	batting	batting	NOUN
concept-2276	197	74	average	average	NOUN
concept-2276	197	75	by	by	ADP
concept-2276	197	76	listing	list	VERB
concept-2276	197	77	all	all	PRON
concept-2276	197	78	of	of	ADP
concept-2276	197	79	the	the	DET
concept-2276	197	80	ways	way	NOUN
concept-2276	197	81	(	(	PUNCT
concept-2276	197	82	a1,h1	a1,h1	PROPN
concept-2276	197	83	)	)	PUNCT
concept-2276	197	84	,	,	PUNCT
concept-2276	197	85	(	(	PUNCT
concept-2276	197	86	a2,h2),	a2,h2),	NOUN
concept-2276	197	87	...	...	PUNCT
concept-2276	198	1	(ak	(ak	PROPN
concept-2276	198	2	,	,	PUNCT
concept-2276	198	3	hk	hk	PROPN
concept-2276	198	4	)	)	PUNCT
concept-2276	198	5	a	a	DET
concept-2276	198	6	batting	batting	NOUN
concept-2276	198	7	average	average	NOUN
concept-2276	198	8	b	b	NOUN
concept-2276	198	9	can	can	AUX
concept-2276	198	10	occur	occur	VERB
concept-2276	198	11	and	and	CCONJ
concept-2276	198	12	summing	sum	VERB
concept-2276	198	13	a	a	DET
concept-2276	198	14	mixture	mixture	NOUN
concept-2276	198	15	of	of	ADP
concept-2276	198	16	their	their	PRON
concept-2276	198	17	corresponding	correspond	VERB
concept-2276	198	18	distributions	distribution	NOUN
concept-2276	198	19	,	,	PUNCT
concept-2276	198	20	which	which	PRON
concept-2276	198	21	,	,	PUNCT
concept-2276	198	22	in	in	ADP
concept-2276	198	23	this	this	DET
concept-2276	198	24	case	case	NOUN
concept-2276	198	25	,	,	PUNCT
concept-2276	198	26	each	each	DET
concept-2276	198	27	one	one	NOUN
concept-2276	198	28	is	be	AUX
concept-2276	198	29	a	a	DET
concept-2276	198	30	beta	beta	ADJ
concept-2276	198	31	distribution	distribution	NOUN
concept-2276	198	32	.	.	PUNCT
concept-2276	199	1	frey	frey	NOUN
concept-2276	199	2	(	(	PUNCT
concept-2276	199	3	2007	2007	NUM
concept-2276	199	4	)	)	PUNCT
concept-2276	199	5	also	also	ADV
concept-2276	199	6	showed	show	VERB
concept-2276	199	7	that	that	SCONJ
concept-2276	199	8	the	the	DET
concept-2276	199	9	posterior	posterior	NOUN
concept-2276	199	10	p	p	NOUN
concept-2276	199	11	given	give	VERB
concept-2276	199	12	a	a	DET
concept-2276	199	13	batting	batting	NOUN
concept-2276	199	14	average	average	NOUN
concept-2276	199	15	b	b	PROPN
concept-2276	199	16	is	be	AUX
concept-2276	199	17	the	the	DET
concept-2276	199	18	mixture	mixture	NOUN
concept-2276	200	1	k	k	PROPN
concept-2276	200	2	∑	∑	PROPN
concept-2276	200	3	i=1	i=1	PROPN
concept-2276	200	4	(	(	PUNCT
concept-2276	200	5	p(hi	p(hi	PROPN
concept-2276	200	6	hits	hit	VERB
concept-2276	200	7	and	and	CCONJ
concept-2276	200	8	ai	ai	VERB
concept-2276	200	9	at	at	ADP
concept-2276	200	10	bats	bat	NOUN
concept-2276	200	11	)	)	PUNCT
concept-2276	201	1	∑k	∑k	PROPN
concept-2276	201	2	j=1	j=1	PROPN
concept-2276	201	3	p(hj	p(hj	NOUN
concept-2276	201	4	hits	hit	VERB
concept-2276	201	5	and	and	CCONJ
concept-2276	201	6	aj	aj	PROPN
concept-2276	201	7	at	at	ADP
concept-2276	201	8	bats	bat	NOUN
concept-2276	201	9	)	)	PUNCT
concept-2276	201	10	)	)	PUNCT
concept-2276	201	11	×	×	NOUN
concept-2276	201	12	beta(cµ(ai	beta(cµ(ai	NOUN
concept-2276	201	13	)	)	PUNCT
concept-2276	202	1	+	+	CCONJ
concept-2276	202	2	hi	hi	ADJ
concept-2276	202	3	,	,	PUNCT
concept-2276	202	4	c(1−	c(1−	NOUN
concept-2276	202	5	µ(ai	µ(ai	NOUN
concept-2276	202	6	)	)	PUNCT
concept-2276	202	7	)	)	PUNCT
concept-2276	203	1	+	+	CCONJ
concept-2276	203	2	ai	ai	VERB
concept-2276	203	3	−	−	PROPN
concept-2276	203	4	hi	hi	INTJ
concept-2276	203	5	)	)	PUNCT
concept-2276	203	6	(	(	PUNCT
concept-2276	203	7	2	2	X
concept-2276	203	8	)	)	PUNCT
concept-2276	203	9	where	where	SCONJ
concept-2276	203	10	p(hi	p(hi	X
concept-2276	203	11	hits	hit	VERB
concept-2276	203	12	and	and	CCONJ
concept-2276	203	13	ai	ai	VERB
concept-2276	203	14	at	at	ADP
concept-2276	203	15	bats	bat	NOUN
concept-2276	203	16	)	)	PUNCT
concept-2276	203	17	=	=	SYM
concept-2276	204	1	d(a	d(a	PROPN
concept-2276	204	2	)	)	PUNCT
concept-2276	204	3	(	(	PUNCT
concept-2276	204	4	γ(a	γ(a	NOUN
concept-2276	204	5	+	+	CCONJ
concept-2276	204	6	1)γ(c)γ(h	1)γ(c)γ(h	NUM
concept-2276	204	7	+	+	PUNCT
concept-2276	204	8	cµ(a))γ(a−	cµ(a))γ(a−	PROPN
concept-2276	204	9	h	h	NOUN
concept-2276	204	10	+	+	NUM
concept-2276	204	11	c(1−	c(1−	NOUN
concept-2276	204	12	µ(a	µ(a	PROPN
concept-2276	204	13	)	)	PUNCT
concept-2276	204	14	)	)	PUNCT
concept-2276	204	15	)	)	PUNCT
concept-2276	205	1	γ(h	γ(h	PROPN
concept-2276	205	2	+	+	NOUN
concept-2276	205	3	1)γ(a	1)γ(a	NUM
concept-2276	205	4	+	+	CCONJ
concept-2276	205	5	1−	1−	NUM
concept-2276	205	6	h)γ(cµ(a))γ(c(1−	h)γ(cµ(a))γ(c(1−	PROPN
concept-2276	205	7	µ(a)))γ(a	µ(a)))γ(a	PROPN
concept-2276	205	8	+	+	PROPN
concept-2276	205	9	c	c	NOUN
concept-2276	205	10	)	)	PUNCT
concept-2276	205	11	)	)	PUNCT
concept-2276	205	12	.	.	PUNCT
concept-2276	206	1	(	(	PUNCT
concept-2276	206	2	3	3	X
concept-2276	206	3	)	)	PUNCT
concept-2276	206	4	in	in	ADP
concept-2276	206	5	equation	equation	NOUN
concept-2276	206	6	(	(	PUNCT
concept-2276	206	7	3	3	NUM
concept-2276	206	8	)	)	PUNCT
concept-2276	206	9	,	,	PUNCT
concept-2276	206	10	d(a	d(a	PROPN
concept-2276	206	11	)	)	PUNCT
concept-2276	206	12	is	be	AUX
concept-2276	206	13	defined	define	VERB
concept-2276	206	14	in	in	ADP
concept-2276	206	15	equation	equation	NOUN
concept-2276	206	16	(	(	PUNCT
concept-2276	206	17	1	1	NUM
concept-2276	206	18	)	)	PUNCT
concept-2276	206	19	.	.	PUNCT
concept-2276	207	1	we	we	PRON
concept-2276	207	2	can	can	AUX
concept-2276	207	3	do	do	VERB
concept-2276	207	4	the	the	DET
concept-2276	207	5	same	same	ADJ
concept-2276	207	6	thing	thing	NOUN
concept-2276	207	7	with	with	ADP
concept-2276	207	8	obp	obp	NOUN
concept-2276	207	9	by	by	ADP
concept-2276	207	10	substituting	substitute	VERB
concept-2276	207	11	h	h	NOUN
concept-2276	207	12	with	with	ADP
concept-2276	207	13	tob	tob	NOUN
concept-2276	207	14	and	and	CCONJ
concept-2276	207	15	a	a	PRON
concept-2276	207	16	with	with	ADP
concept-2276	207	17	pa	pa	PROPN
concept-2276	207	18	.	.	PROPN
concept-2276	208	1	due	due	ADP
concept-2276	208	2	to	to	ADP
concept-2276	208	3	the	the	DET
concept-2276	208	4	similarity	similarity	NOUN
concept-2276	208	5	the	the	DET
concept-2276	208	6	formula	formula	NOUN
concept-2276	208	7	is	be	AUX
concept-2276	208	8	retained	retain	VERB
concept-2276	208	9	.	.	PUNCT
concept-2276	209	1	using	use	VERB
concept-2276	209	2	the	the	DET
concept-2276	209	3	formula	formula	NOUN
concept-2276	209	4	,	,	PUNCT
concept-2276	209	5	we	we	PRON
concept-2276	209	6	can	can	AUX
concept-2276	209	7	find	find	VERB
concept-2276	209	8	the	the	DET
concept-2276	209	9	posterior	posterior	ADJ
concept-2276	209	10	p	p	NOUN
concept-2276	209	11	for	for	ADP
concept-2276	209	12	each	each	DET
concept-2276	209	13	obp	obp	NOUN
concept-2276	209	14	.	.	PUNCT
concept-2276	210	1	however	however	ADV
concept-2276	210	2	,	,	PUNCT
concept-2276	210	3	we	we	PRON
concept-2276	210	4	only	only	ADV
concept-2276	210	5	considered	consider	VERB
concept-2276	210	6	the	the	DET
concept-2276	210	7	obp	obp	NOUN
concept-2276	210	8	of	of	ADP
concept-2276	210	9	those	those	PRON
concept-2276	210	10	such	such	ADJ
concept-2276	210	11	that	that	DET
concept-2276	210	12	p(obp	p(obp	NOUN
concept-2276	210	13	=	=	SYM
concept-2276	210	14	obp	obp	PROPN
concept-2276	210	15	)	)	PUNCT
concept-2276	210	16	>	>	X
concept-2276	210	17	1	1	NUM
concept-2276	210	18	10,000,000	10,000,000	NUM
concept-2276	210	19	since	since	SCONJ
concept-2276	210	20	other	other	ADJ
concept-2276	210	21	obp	obp	PROPN
concept-2276	210	22	’s	’s	PART
concept-2276	210	23	are	be	AUX
concept-2276	210	24	pretty	pretty	ADV
concept-2276	210	25	much	much	ADV
concept-2276	210	26	impossible	impossible	ADJ
concept-2276	210	27	to	to	PART
concept-2276	210	28	see	see	VERB
concept-2276	210	29	in	in	ADP
concept-2276	210	30	practice	practice	NOUN
concept-2276	210	31	.	.	PUNCT
concept-2276	211	1	ii	ii	PROPN
concept-2276	211	2	.	.	PUNCT
concept-2276	212	1	using	use	VERB
concept-2276	212	2	the	the	DET
concept-2276	212	3	second	second	ADJ
concept-2276	212	4	model	model	NOUN
concept-2276	212	5	unfortunately	unfortunately	ADV
concept-2276	212	6	,	,	PUNCT
concept-2276	212	7	with	with	ADP
concept-2276	212	8	the	the	DET
concept-2276	212	9	second	second	ADJ
concept-2276	212	10	model	model	NOUN
concept-2276	212	11	,	,	PUNCT
concept-2276	212	12	one	one	PRON
concept-2276	212	13	can	can	AUX
concept-2276	212	14	not	not	PART
concept-2276	212	15	use	use	VERB
concept-2276	212	16	the	the	DET
concept-2276	212	17	same	same	ADJ
concept-2276	212	18	bayesian	bayesian	NOUN
concept-2276	212	19	techniques	technique	NOUN
concept-2276	212	20	for	for	ADP
concept-2276	212	21	the	the	DET
concept-2276	212	22	second	second	ADJ
concept-2276	212	23	model	model	NOUN
concept-2276	212	24	due	due	ADP
concept-2276	212	25	to	to	ADP
concept-2276	212	26	too	too	ADV
concept-2276	212	27	much	much	ADJ
concept-2276	212	28	storage	storage	NOUN
concept-2276	212	29	needed	need	VERB
concept-2276	212	30	to	to	PART
concept-2276	212	31	accomplish	accomplish	VERB
concept-2276	212	32	this	this	DET
concept-2276	212	33	task	task	NOUN
concept-2276	212	34	.	.	PUNCT
concept-2276	213	1	doing	do	VERB
concept-2276	213	2	this	this	DET
concept-2276	213	3	kind	kind	NOUN
concept-2276	213	4	of	of	ADP
concept-2276	213	5	calculation	calculation	NOUN
concept-2276	213	6	would	would	AUX
concept-2276	213	7	require	require	VERB
concept-2276	213	8	a	a	DET
concept-2276	213	9	14	14	NUM
concept-2276	213	10	billion	billion	NUM
concept-2276	213	11	entry	entry	NOUN
concept-2276	213	12	matrix	matrix	NOUN
concept-2276	213	13	and	and	CCONJ
concept-2276	213	14	unfortunately	unfortunately	ADV
concept-2276	213	15	r	r	NOUN
concept-2276	213	16	can	can	AUX
concept-2276	213	17	only	only	ADV
concept-2276	213	18	hold	hold	VERB
concept-2276	213	19	2	2	NUM
concept-2276	213	20	billion	billion	NUM
concept-2276	213	21	at	at	ADP
concept-2276	213	22	most	most	ADJ
concept-2276	213	23	.	.	PUNCT
concept-2276	214	1	instead	instead	ADV
concept-2276	214	2	,	,	PUNCT
concept-2276	214	3	we	we	PRON
concept-2276	214	4	simulated	simulate	VERB
concept-2276	214	5	some	some	DET
concept-2276	214	6	fake	fake	ADJ
concept-2276	214	7	baseball	baseball	NOUN
concept-2276	214	8	data	datum	NOUN
concept-2276	214	9	using	use	VERB
concept-2276	214	10	the	the	DET
concept-2276	214	11	second	second	ADJ
concept-2276	214	12	model	model	NOUN
concept-2276	214	13	similar	similar	ADJ
concept-2276	214	14	to	to	ADP
concept-2276	214	15	the	the	DET
concept-2276	214	16	simulation	simulation	NOUN
concept-2276	214	17	used	use	VERB
concept-2276	214	18	to	to	PART
concept-2276	214	19	test	test	VERB
concept-2276	214	20	the	the	DET
concept-2276	214	21	model	model	NOUN
concept-2276	214	22	.	.	PUNCT
concept-2276	215	1	we	we	PRON
concept-2276	215	2	made	make	VERB
concept-2276	215	3	10,000,000	10,000,000	NUM
concept-2276	215	4	fake	fake	ADJ
concept-2276	215	5	players	player	NOUN
concept-2276	215	6	each	each	PRON
concept-2276	215	7	with	with	ADP
concept-2276	215	8	their	their	PRON
concept-2276	215	9	own	own	ADJ
concept-2276	215	10	h	h	NOUN
concept-2276	215	11	,	,	PUNCT
concept-2276	215	12	bb	bb	PROPN
concept-2276	215	13	,	,	PUNCT
concept-2276	215	14	hbp	hbp	PROPN
concept-2276	215	15	,	,	PUNCT
concept-2276	215	16	pa	pa	PROPN
concept-2276	215	17	,	,	PUNCT
concept-2276	215	18	ph	ph	VERB
concept-2276	215	19	,	,	PUNCT
concept-2276	215	20	12	12	NUM
concept-2276	215	21	pbb	pbb	NOUN
concept-2276	215	22	,	,	PUNCT
concept-2276	215	23	and	and	CCONJ
concept-2276	215	24	phbp	phbp	NOUN
concept-2276	215	25	,	,	PUNCT
concept-2276	215	26	similar	similar	ADJ
concept-2276	215	27	to	to	ADP
concept-2276	215	28	how	how	SCONJ
concept-2276	215	29	we	we	PRON
concept-2276	215	30	checked	check	VERB
concept-2276	215	31	the	the	DET
concept-2276	215	32	second	second	ADJ
concept-2276	215	33	model	model	NOUN
concept-2276	215	34	by	by	ADP
concept-2276	215	35	simulating	simulate	VERB
concept-2276	215	36	fake	fake	ADJ
concept-2276	215	37	players	player	NOUN
concept-2276	215	38	in	in	ADP
concept-2276	215	39	section	section	NOUN
concept-2276	215	40	3.4	3.4	NUM
concept-2276	215	41	.	.	PUNCT
concept-2276	216	1	we	we	PRON
concept-2276	216	2	then	then	ADV
concept-2276	216	3	computed	compute	VERB
concept-2276	216	4	each	each	DET
concept-2276	216	5	player	player	NOUN
concept-2276	216	6	’s	’s	PART
concept-2276	216	7	obp	obp	NOUN
concept-2276	216	8	,	,	PUNCT
concept-2276	216	9	and	and	CCONJ
concept-2276	216	10	summed	sum	VERB
concept-2276	216	11	each	each	DET
concept-2276	216	12	player	player	NOUN
concept-2276	216	13	’s	’s	PART
concept-2276	216	14	ph	ph	NOUN
concept-2276	216	15	,	,	PUNCT
concept-2276	216	16	pbb	pbb	ADJ
concept-2276	216	17	,	,	PUNCT
concept-2276	216	18	and	and	CCONJ
concept-2276	216	19	phbp	phbp	NOUN
concept-2276	216	20	to	to	PART
concept-2276	216	21	find	find	VERB
concept-2276	216	22	each	each	DET
concept-2276	216	23	player	player	NOUN
concept-2276	216	24	’s	’s	PART
concept-2276	216	25	overall	overall	ADJ
concept-2276	216	26	true	true	ADJ
concept-2276	216	27	ability	ability	NOUN
concept-2276	216	28	.	.	PUNCT
concept-2276	217	1	we	we	PRON
concept-2276	217	2	then	then	ADV
concept-2276	217	3	did	do	VERB
concept-2276	217	4	an	an	DET
concept-2276	217	5	aggregate	aggregate	ADJ
concept-2276	217	6	mean	mean	NOUN
concept-2276	217	7	on	on	ADP
concept-2276	217	8	the	the	DET
concept-2276	217	9	true	true	ADJ
concept-2276	217	10	ability	ability	NOUN
concept-2276	217	11	by	by	ADP
concept-2276	217	12	obp	obp	PROPN
concept-2276	217	13	.	.	PUNCT
concept-2276	218	1	this	this	PRON
concept-2276	218	2	will	will	AUX
concept-2276	218	3	give	give	VERB
concept-2276	218	4	us	we	PRON
concept-2276	218	5	the	the	DET
concept-2276	218	6	posterior	posterior	ADJ
concept-2276	218	7	mean	mean	NOUN
concept-2276	218	8	p	p	NOUN
concept-2276	218	9	for	for	ADP
concept-2276	218	10	the	the	DET
concept-2276	218	11	players	player	NOUN
concept-2276	218	12	.	.	PUNCT
concept-2276	219	1	one	one	NUM
concept-2276	219	2	thing	thing	NOUN
concept-2276	219	3	to	to	PART
concept-2276	219	4	take	take	VERB
concept-2276	219	5	into	into	ADP
concept-2276	219	6	account	account	NOUN
concept-2276	219	7	with	with	ADP
concept-2276	219	8	using	use	VERB
concept-2276	219	9	this	this	DET
concept-2276	219	10	model	model	NOUN
concept-2276	219	11	is	be	AUX
concept-2276	219	12	that	that	SCONJ
concept-2276	219	13	we	we	PRON
concept-2276	219	14	will	will	AUX
concept-2276	219	15	need	need	VERB
concept-2276	219	16	to	to	PART
concept-2276	219	17	watch	watch	VERB
concept-2276	219	18	for	for	ADP
concept-2276	219	19	simulation	simulation	NOUN
concept-2276	219	20	errors	error	NOUN
concept-2276	219	21	.	.	PUNCT
concept-2276	220	1	however	however	ADV
concept-2276	220	2	with	with	ADP
concept-2276	220	3	10,000,000	10,000,000	NUM
concept-2276	220	4	players	player	NOUN
concept-2276	220	5	being	be	AUX
concept-2276	220	6	simulated	simulate	VERB
concept-2276	220	7	,	,	PUNCT
concept-2276	220	8	the	the	DET
concept-2276	220	9	issue	issue	NOUN
concept-2276	220	10	of	of	ADP
concept-2276	220	11	simulation	simulation	NOUN
concept-2276	220	12	error	error	NOUN
concept-2276	220	13	is	be	AUX
concept-2276	220	14	probably	probably	ADV
concept-2276	220	15	negligible	negligible	ADJ
concept-2276	220	16	since	since	SCONJ
concept-2276	220	17	the	the	DET
concept-2276	220	18	sample	sample	NOUN
concept-2276	220	19	size	size	NOUN
concept-2276	220	20	is	be	AUX
concept-2276	220	21	really	really	ADV
concept-2276	220	22	high	high	ADJ
concept-2276	220	23	.	.	PUNCT
concept-2276	221	1	v.	v.	ADP
concept-2276	221	2	results	result	NOUN
concept-2276	221	3	i.	i.	PROPN
concept-2276	221	4	using	use	VERB
concept-2276	221	5	the	the	DET
concept-2276	221	6	first	first	ADJ
concept-2276	221	7	model	model	NOUN
concept-2276	221	8	table	table	NOUN
concept-2276	221	9	1	1	NUM
concept-2276	221	10	gives	give	VERB
concept-2276	221	11	the	the	DET
concept-2276	221	12	posterior	posterior	ADJ
concept-2276	221	13	true	true	ADJ
concept-2276	221	14	abilities	ability	NOUN
concept-2276	221	15	and	and	CCONJ
concept-2276	221	16	posterior	posterior	ADJ
concept-2276	221	17	standard	standard	ADJ
concept-2276	221	18	deviations	deviation	NOUN
concept-2276	221	19	for	for	ADP
concept-2276	221	20	the	the	DET
concept-2276	221	21	corresponding	correspond	VERB
concept-2276	221	22	top	top	ADJ
concept-2276	221	23	ten	ten	NUM
concept-2276	221	24	obp	obp	PROPN
concept-2276	221	25	’s	’s	PART
concept-2276	221	26	and	and	CCONJ
concept-2276	221	27	the	the	DET
concept-2276	221	28	corresponding	corresponding	ADJ
concept-2276	221	29	bottom	bottom	ADJ
concept-2276	221	30	ten	ten	NUM
concept-2276	221	31	obp	obp	PROPN
concept-2276	221	32	’s	’s	PART
concept-2276	221	33	using	use	VERB
concept-2276	221	34	the	the	DET
concept-2276	221	35	first	first	ADJ
concept-2276	221	36	model	model	NOUN
concept-2276	221	37	.	.	PUNCT
concept-2276	222	1	the	the	DET
concept-2276	222	2	posterior	posterior	ADJ
concept-2276	222	3	true	true	ADJ
concept-2276	222	4	ability	ability	NOUN
concept-2276	222	5	tells	tell	VERB
concept-2276	222	6	us	we	PRON
concept-2276	222	7	what	what	PRON
concept-2276	222	8	the	the	DET
concept-2276	222	9	real	real	ADJ
concept-2276	222	10	value	value	NOUN
concept-2276	222	11	of	of	ADP
concept-2276	222	12	a	a	DET
concept-2276	222	13	player	player	NOUN
concept-2276	222	14	’s	’s	PART
concept-2276	222	15	probability	probability	NOUN
concept-2276	222	16	of	of	ADP
concept-2276	222	17	getting	get	VERB
concept-2276	222	18	on	on	ADP
concept-2276	222	19	-	-	PUNCT
concept-2276	222	20	base	base	NOUN
concept-2276	222	21	given	give	VERB
concept-2276	222	22	the	the	DET
concept-2276	222	23	player	player	NOUN
concept-2276	222	24	’s	’s	PART
concept-2276	222	25	documented	document	VERB
concept-2276	222	26	obp	obp	PROPN
concept-2276	222	27	.	.	PUNCT
concept-2276	223	1	one	one	NUM
concept-2276	223	2	interesting	interesting	ADJ
concept-2276	223	3	observation	observation	NOUN
concept-2276	223	4	is	be	AUX
concept-2276	223	5	that	that	SCONJ
concept-2276	223	6	the	the	DET
concept-2276	223	7	top	top	ADJ
concept-2276	223	8	10	10	NUM
concept-2276	223	9	posterior	posterior	ADJ
concept-2276	223	10	true	true	ADJ
concept-2276	223	11	abilities	ability	NOUN
concept-2276	223	12	had	have	VERB
concept-2276	223	13	obp	obp	PROPN
concept-2276	223	14	’s	’s	PART
concept-2276	223	15	that	that	PRON
concept-2276	223	16	were	be	AUX
concept-2276	223	17	all	all	PRON
concept-2276	223	18	above	above	ADP
concept-2276	223	19	.35	.35	NUM
concept-2276	223	20	with	with	ADP
concept-2276	223	21	posterior	posterior	ADJ
concept-2276	223	22	true	true	ADJ
concept-2276	223	23	abilities	ability	NOUN
concept-2276	223	24	around	around	ADP
concept-2276	223	25	.34-.36	.34-.36	PUNCT
concept-2276	223	26	and	and	CCONJ
concept-2276	223	27	the	the	DET
concept-2276	223	28	bottom	bottom	ADJ
concept-2276	223	29	10	10	NUM
concept-2276	223	30	posterior	posterior	ADJ
concept-2276	223	31	true	true	ADJ
concept-2276	223	32	abilities	ability	NOUN
concept-2276	223	33	had	have	VERB
concept-2276	223	34	obp	obp	PROPN
concept-2276	223	35	’s	’s	PART
concept-2276	223	36	that	that	PRON
concept-2276	223	37	were	be	AUX
concept-2276	223	38	less	less	ADJ
concept-2276	223	39	than	than	ADP
concept-2276	223	40	.1	.1	NUM
concept-2276	223	41	with	with	ADP
concept-2276	223	42	posterior	posterior	ADJ
concept-2276	223	43	true	true	ADJ
concept-2276	223	44	abilities	ability	NOUN
concept-2276	223	45	around	around	ADP
concept-2276	223	46	.25	.25	NUM
concept-2276	223	47	.	.	PUNCT
concept-2276	224	1	this	this	DET
concept-2276	224	2	observation	observation	NOUN
concept-2276	224	3	makes	make	VERB
concept-2276	224	4	intuitive	intuitive	ADJ
concept-2276	224	5	sense	sense	NOUN
concept-2276	224	6	since	since	SCONJ
concept-2276	224	7	even	even	ADV
concept-2276	224	8	without	without	ADP
concept-2276	224	9	applying	apply	VERB
concept-2276	224	10	the	the	DET
concept-2276	224	11	analysis	analysis	NOUN
concept-2276	224	12	of	of	ADP
concept-2276	224	13	this	this	DET
concept-2276	224	14	paper	paper	NOUN
concept-2276	224	15	,	,	PUNCT
concept-2276	224	16	among	among	ADP
concept-2276	224	17	the	the	DET
concept-2276	224	18	laypersons	layperson	NOUN
concept-2276	224	19	,	,	PUNCT
concept-2276	224	20	a	a	DET
concept-2276	224	21	player	player	NOUN
concept-2276	224	22	with	with	ADP
concept-2276	224	23	an	an	DET
concept-2276	224	24	obp	obp	NOUN
concept-2276	224	25	of	of	ADP
concept-2276	224	26	more	more	ADJ
concept-2276	224	27	than	than	ADP
concept-2276	224	28	.35	.35	NUM
concept-2276	224	29	is	be	AUX
concept-2276	224	30	considered	consider	VERB
concept-2276	224	31	to	to	PART
concept-2276	224	32	be	be	AUX
concept-2276	224	33	talented	talente	VERB
concept-2276	224	34	and	and	CCONJ
concept-2276	224	35	a	a	DET
concept-2276	224	36	player	player	NOUN
concept-2276	224	37	with	with	ADP
concept-2276	224	38	an	an	DET
concept-2276	224	39	obp	obp	NOUN
concept-2276	224	40	of	of	ADP
concept-2276	224	41	less	less	ADJ
concept-2276	224	42	than	than	ADP
concept-2276	224	43	.1	.1	NUM
concept-2276	224	44	would	would	AUX
concept-2276	224	45	be	be	AUX
concept-2276	224	46	considered	consider	VERB
concept-2276	224	47	to	to	PART
concept-2276	224	48	be	be	AUX
concept-2276	224	49	terrible	terrible	ADJ
concept-2276	224	50	.	.	PUNCT
concept-2276	225	1	another	another	DET
concept-2276	225	2	observation	observation	NOUN
concept-2276	225	3	to	to	PART
concept-2276	225	4	make	make	VERB
concept-2276	225	5	is	be	AUX
concept-2276	225	6	that	that	SCONJ
concept-2276	225	7	the	the	DET
concept-2276	225	8	top	top	ADJ
concept-2276	225	9	10	10	NUM
concept-2276	225	10	posterior	posterior	ADJ
concept-2276	225	11	true	true	ADJ
concept-2276	225	12	abilities	ability	NOUN
concept-2276	225	13	needed	need	VERB
concept-2276	225	14	at	at	ADP
concept-2276	225	15	least	least	ADV
concept-2276	225	16	100	100	NUM
concept-2276	225	17	plate	plate	NOUN
concept-2276	225	18	appearances	appearance	NOUN
concept-2276	225	19	in	in	ADP
concept-2276	225	20	order	order	NOUN
concept-2276	225	21	for	for	SCONJ
concept-2276	225	22	such	such	ADJ
concept-2276	225	23	values	value	NOUN
concept-2276	225	24	to	to	PART
concept-2276	225	25	exist	exist	VERB
concept-2276	225	26	.	.	PUNCT
concept-2276	226	1	this	this	PRON
concept-2276	226	2	also	also	ADV
concept-2276	226	3	lines	line	VERB
concept-2276	226	4	up	up	ADP
concept-2276	226	5	with	with	ADP
concept-2276	226	6	intuition	intuition	NOUN
concept-2276	226	7	as	as	SCONJ
concept-2276	226	8	better	well	ADJ
concept-2276	226	9	players	player	NOUN
concept-2276	226	10	will	will	AUX
concept-2276	226	11	have	have	VERB
concept-2276	226	12	more	more	ADJ
concept-2276	226	13	opportunities	opportunity	NOUN
concept-2276	226	14	to	to	PART
concept-2276	226	15	contribute	contribute	VERB
concept-2276	226	16	offensively	offensively	ADV
concept-2276	226	17	.	.	PUNCT
concept-2276	227	1	one	one	NUM
concept-2276	227	2	more	more	ADV
concept-2276	227	3	interesting	interesting	ADJ
concept-2276	227	4	thing	thing	NOUN
concept-2276	227	5	to	to	PART
concept-2276	227	6	notice	notice	VERB
concept-2276	227	7	is	be	AUX
concept-2276	227	8	that	that	SCONJ
concept-2276	227	9	the	the	DET
concept-2276	227	10	bottom	bottom	ADJ
concept-2276	227	11	10	10	NUM
concept-2276	227	12	posterior	posterior	ADJ
concept-2276	227	13	true	true	ADJ
concept-2276	227	14	abilities	ability	NOUN
concept-2276	227	15	require	require	VERB
concept-2276	227	16	more	more	ADJ
concept-2276	227	17	than	than	ADP
concept-2276	227	18	100	100	NUM
concept-2276	227	19	plate	plate	NOUN
concept-2276	227	20	appearances	appearance	NOUN
concept-2276	227	21	which	which	PRON
concept-2276	227	22	suggests	suggest	VERB
concept-2276	227	23	that	that	SCONJ
concept-2276	227	24	only	only	ADV
concept-2276	227	25	having	have	VERB
concept-2276	227	26	a	a	DET
concept-2276	227	27	high	high	ADJ
concept-2276	227	28	number	number	NOUN
concept-2276	227	29	of	of	ADP
concept-2276	227	30	plate	plate	NOUN
concept-2276	227	31	appearances	appearance	NOUN
concept-2276	227	32	is	be	AUX
concept-2276	227	33	n’t	not	PART
concept-2276	227	34	sufficient	sufficient	ADJ
concept-2276	227	35	for	for	ADP
concept-2276	227	36	being	be	AUX
concept-2276	227	37	a	a	DET
concept-2276	227	38	good	good	ADJ
concept-2276	227	39	player	player	NOUN
concept-2276	227	40	.	.	PUNCT
concept-2276	228	1	an	an	DET
concept-2276	228	2	interesting	interesting	ADJ
concept-2276	228	3	comparison	comparison	NOUN
concept-2276	228	4	to	to	PART
concept-2276	228	5	make	make	VERB
concept-2276	228	6	is	be	AUX
concept-2276	228	7	with	with	ADP
concept-2276	228	8	frey	frey	PROPN
concept-2276	228	9	(	(	PUNCT
concept-2276	228	10	2007	2007	NUM
concept-2276	228	11	)	)	PUNCT
concept-2276	228	12	’s	’s	PART
concept-2276	228	13	data	datum	NOUN
concept-2276	228	14	for	for	ADP
concept-2276	228	15	batting	batting	NOUN
concept-2276	228	16	average	average	NOUN
concept-2276	228	17	.	.	PUNCT
concept-2276	229	1	while	while	SCONJ
concept-2276	229	2	his	his	PRON
concept-2276	229	3	top	top	ADJ
concept-2276	229	4	10	10	NUM
concept-2276	229	5	posterior	posterior	ADJ
concept-2276	229	6	true	true	ADJ
concept-2276	229	7	abilities	ability	NOUN
concept-2276	229	8	contained	contain	VERB
concept-2276	229	9	a	a	DET
concept-2276	229	10	similar	similar	ADJ
concept-2276	229	11	pattern	pattern	NOUN
concept-2276	229	12	of	of	ADP
concept-2276	229	13	having	have	VERB
concept-2276	229	14	batting	batting	NOUN
concept-2276	229	15	averages	average	NOUN
concept-2276	229	16	above	above	ADP
concept-2276	229	17	.3	.3	NUM
concept-2276	229	18	,	,	PUNCT
concept-2276	229	19	his	his	PRON
concept-2276	229	20	bottom	bottom	ADJ
concept-2276	229	21	10	10	NUM
concept-2276	229	22	posterior	posterior	ADJ
concept-2276	229	23	true	true	ADJ
concept-2276	229	24	abilities	ability	NOUN
concept-2276	229	25	only	only	ADV
concept-2276	229	26	contained	contain	VERB
concept-2276	229	27	batting	batting	NOUN
concept-2276	229	28	averages	average	NOUN
concept-2276	229	29	that	that	PRON
concept-2276	229	30	can	can	AUX
concept-2276	229	31	be	be	AUX
concept-2276	229	32	achieved	achieve	VERB
concept-2276	229	33	with	with	ADP
concept-2276	229	34	a	a	DET
concept-2276	229	35	low	low	ADJ
concept-2276	229	36	number	number	NOUN
concept-2276	229	37	of	of	ADP
concept-2276	229	38	at	at	ADP
concept-2276	229	39	bats	bat	NOUN
concept-2276	229	40	(	(	PUNCT
concept-2276	229	41	frey	frey	PROPN
concept-2276	229	42	(	(	PUNCT
concept-2276	229	43	2007	2007	NUM
concept-2276	229	44	)	)	PUNCT
concept-2276	229	45	lacks	lack	VERB
concept-2276	229	46	low	low	ADJ
concept-2276	229	47	batting	batting	NOUN
concept-2276	229	48	averages	average	NOUN
concept-2276	229	49	for	for	ADP
concept-2276	229	50	his	his	PRON
concept-2276	229	51	bottom	bottom	ADJ
concept-2276	229	52	10	10	NUM
concept-2276	229	53	posterior	posterior	ADJ
concept-2276	229	54	true	true	ADJ
concept-2276	229	55	abilities	ability	NOUN
concept-2276	229	56	other	other	ADJ
concept-2276	229	57	than	than	ADP
concept-2276	229	58	.000	.000	NUM
concept-2276	229	59	.	.	PUNCT
concept-2276	229	60	)	)	PUNCT
concept-2276	229	61	.	.	PUNCT
concept-2276	230	1	the	the	DET
concept-2276	230	2	posterior	posterior	ADJ
concept-2276	230	3	standard	standard	ADJ
concept-2276	230	4	deviations	deviation	NOUN
concept-2276	230	5	show	show	VERB
concept-2276	230	6	how	how	SCONJ
concept-2276	230	7	much	much	ADJ
concept-2276	230	8	a	a	DET
concept-2276	230	9	player	player	NOUN
concept-2276	230	10	’s	’s	PART
concept-2276	230	11	posterior	posterior	ADJ
concept-2276	230	12	true	true	ADJ
concept-2276	230	13	ability	ability	NOUN
concept-2276	230	14	can	can	AUX
concept-2276	230	15	vary	vary	VERB
concept-2276	230	16	.	.	PUNCT
concept-2276	231	1	the	the	DET
concept-2276	231	2	fact	fact	NOUN
concept-2276	231	3	that	that	SCONJ
concept-2276	231	4	the	the	DET
concept-2276	231	5	posterior	posterior	ADJ
concept-2276	231	6	deviations	deviation	NOUN
concept-2276	231	7	are	be	AUX
concept-2276	231	8	between	between	ADP
concept-2276	231	9	.015	.015	NUM
concept-2276	231	10	and	and	CCONJ
concept-2276	231	11	.04	.04	NUM
concept-2276	231	12	for	for	ADP
concept-2276	231	13	the	the	DET
concept-2276	231	14	top	top	ADJ
concept-2276	231	15	10	10	NUM
concept-2276	231	16	obp	obp	PROPN
concept-2276	231	17	’s	’s	PART
concept-2276	231	18	suggest	suggest	VERB
concept-2276	231	19	that	that	SCONJ
concept-2276	231	20	there	there	PRON
concept-2276	231	21	is	be	VERB
concept-2276	231	22	a	a	DET
concept-2276	231	23	reasonable	reasonable	ADJ
concept-2276	231	24	amount	amount	NOUN
concept-2276	231	25	of	of	ADP
concept-2276	231	26	variation	variation	NOUN
concept-2276	231	27	with	with	ADP
concept-2276	231	28	posterior	posterior	ADJ
concept-2276	231	29	true	true	ADJ
concept-2276	231	30	abilities	ability	NOUN
concept-2276	231	31	.	.	PUNCT
concept-2276	232	1	13	13	NUM
concept-2276	232	2	obp	obp	NOUN
concept-2276	232	3	posterior	posterior	ADJ
concept-2276	232	4	true	true	ADJ
concept-2276	232	5	ability	ability	NOUN
concept-2276	232	6	p	p	NOUN
concept-2276	232	7	posterior	posterior	ADJ
concept-2276	232	8	sd	sd	NOUN
concept-2276	232	9	for	for	ADP
concept-2276	232	10	p	p	PROPN
concept-2276	232	11	obp	obp	NOUN
concept-2276	232	12	posterior	posterior	ADJ
concept-2276	232	13	true	true	ADJ
concept-2276	232	14	ability	ability	NOUN
concept-2276	232	15	p	p	NOUN
concept-2276	232	16	posterior	posterior	ADJ
concept-2276	232	17	sd	sd	NOUN
concept-2276	232	18	for	for	ADP
concept-2276	232	19	p	p	NOUN
concept-2276	232	20	0.428	0.428	NUM
concept-2276	232	21	0.362	0.362	NUM
concept-2276	232	22	0.031	0.031	NUM
concept-2276	232	23	0.022	0.022	NUM
concept-2276	232	24	0.249	0.249	NUM
concept-2276	232	25	0.019	0.019	NUM
concept-2276	232	26	0.401	0.401	NUM
concept-2276	232	27	0.356	0.356	NUM
concept-2276	232	28	0.026	0.026	NUM
concept-2276	232	29	0.023	0.023	NUM
concept-2276	232	30	0.249	0.249	NUM
concept-2276	232	31	0.019	0.019	NUM
concept-2276	232	32	0.399	0.399	NUM
concept-2276	232	33	0.355	0.355	NUM
concept-2276	232	34	0.026	0.026	NUM
concept-2276	232	35	0.024	0.024	NUM
concept-2276	232	36	0.249	0.249	NUM
concept-2276	232	37	0.019	0.019	NUM
concept-2276	232	38	0.445	0.445	NUM
concept-2276	232	39	0.349	0.349	NUM
concept-2276	232	40	0.038	0.038	NUM
concept-2276	232	41	0.025	0.025	NUM
concept-2276	232	42	0.250	0.250	NUM
concept-2276	232	43	0.019	0.019	NUM
concept-2276	232	44	0.416	0.416	NUM
concept-2276	232	45	0.347	0.347	NUM
concept-2276	232	46	0.038	0.038	NUM
concept-2276	232	47	0.039	0.039	NUM
concept-2276	232	48	0.250	0.250	NUM
concept-2276	232	49	0.019	0.019	NUM
concept-2276	232	50	0.384	0.384	NUM
concept-2276	232	51	0.346	0.346	NUM
concept-2276	232	52	0.029	0.029	NUM
concept-2276	232	53	0.026	0.026	NUM
concept-2276	232	54	0.250	0.250	NUM
concept-2276	232	55	0.019	0.019	NUM
concept-2276	232	56	0.398	0.398	NUM
concept-2276	232	57	0.345	0.345	NUM
concept-2276	232	58	0.033	0.033	NUM
concept-2276	232	59	0.041	0.041	NUM
concept-2276	232	60	0.250	0.250	NUM
concept-2276	232	61	0.019	0.019	NUM
concept-2276	232	62	0.402	0.402	NUM
concept-2276	232	63	0.345	0.345	NUM
concept-2276	232	64	0.035	0.035	NUM
concept-2276	232	65	0.027	0.027	NUM
concept-2276	232	66	0.250	0.250	NUM
concept-2276	232	67	0.019	0.019	NUM
concept-2276	232	68	0.374	0.374	NUM
concept-2276	232	69	0.343	0.343	NUM
concept-2276	232	70	0.026	0.026	NUM
concept-2276	232	71	0.028	0.028	NUM
concept-2276	232	72	0.250	0.250	NUM
concept-2276	232	73	0.019	0.019	NUM
concept-2276	232	74	0.376	0.376	NUM
concept-2276	232	75	0.343	0.343	NUM
concept-2276	232	76	0.027	0.027	NUM
concept-2276	232	77	0.052	0.052	NUM
concept-2276	232	78	0.250	0.250	NUM
concept-2276	232	79	0.019	0.019	NUM
concept-2276	232	80	table	table	NOUN
concept-2276	232	81	1	1	NUM
concept-2276	232	82	:	:	PUNCT
concept-2276	232	83	obp	obp	PROPN
concept-2276	232	84	corresponding	correspond	VERB
concept-2276	232	85	to	to	ADP
concept-2276	232	86	the	the	DET
concept-2276	232	87	highest	high	ADJ
concept-2276	232	88	and	and	CCONJ
concept-2276	232	89	lowest	low	ADJ
concept-2276	232	90	posterior	posterior	ADJ
concept-2276	232	91	true	true	ADJ
concept-2276	232	92	abilities	ability	NOUN
concept-2276	232	93	p.	p.	NOUN
concept-2276	232	94	we	we	PRON
concept-2276	232	95	only	only	ADV
concept-2276	232	96	consider	consider	VERB
concept-2276	232	97	obp	obp	NOUN
concept-2276	232	98	with	with	ADP
concept-2276	232	99	at	at	ADV
concept-2276	232	100	least	least	ADJ
concept-2276	232	101	a	a	DET
concept-2276	232	102	one	one	NUM
concept-2276	232	103	in	in	ADP
concept-2276	232	104	10,000,000	10,000,000	NUM
concept-2276	232	105	chance	chance	NOUN
concept-2276	232	106	of	of	ADP
concept-2276	232	107	occurring	occur	VERB
concept-2276	232	108	.	.	PUNCT
concept-2276	233	1	ii	ii	PROPN
concept-2276	233	2	.	.	PUNCT
concept-2276	234	1	using	use	VERB
concept-2276	234	2	the	the	DET
concept-2276	234	3	second	second	ADJ
concept-2276	234	4	model	model	NOUN
concept-2276	234	5	table	table	NOUN
concept-2276	234	6	2	2	NUM
concept-2276	234	7	gives	give	VERB
concept-2276	234	8	posterior	posterior	ADJ
concept-2276	234	9	true	true	ADJ
concept-2276	234	10	abilities	ability	NOUN
concept-2276	234	11	,	,	PUNCT
concept-2276	234	12	posterior	posterior	ADJ
concept-2276	234	13	standard	standard	ADJ
concept-2276	234	14	deviations	deviation	NOUN
concept-2276	234	15	,	,	PUNCT
concept-2276	234	16	and	and	CCONJ
concept-2276	234	17	average	average	ADJ
concept-2276	234	18	plate	plate	NOUN
concept-2276	234	19	appearances	appearance	VERB
concept-2276	234	20	for	for	ADP
concept-2276	234	21	the	the	DET
concept-2276	234	22	corresponding	correspond	VERB
concept-2276	234	23	top	top	ADJ
concept-2276	234	24	ten	ten	NUM
concept-2276	234	25	obp	obp	PROPN
concept-2276	234	26	’s	’s	PART
concept-2276	234	27	and	and	CCONJ
concept-2276	234	28	the	the	DET
concept-2276	234	29	corresponding	corresponding	ADJ
concept-2276	234	30	bottom	bottom	ADJ
concept-2276	234	31	ten	ten	NUM
concept-2276	234	32	obp	obp	PROPN
concept-2276	234	33	’s	’s	PART
concept-2276	234	34	using	use	VERB
concept-2276	234	35	the	the	DET
concept-2276	234	36	second	second	ADJ
concept-2276	234	37	model	model	NOUN
concept-2276	234	38	(	(	PUNCT
concept-2276	234	39	we	we	PRON
concept-2276	234	40	were	be	AUX
concept-2276	234	41	able	able	ADJ
concept-2276	234	42	to	to	PART
concept-2276	234	43	find	find	VERB
concept-2276	234	44	the	the	DET
concept-2276	234	45	posterior	posterior	ADJ
concept-2276	234	46	mean	mean	NOUN
concept-2276	234	47	for	for	ADP
concept-2276	234	48	plate	plate	NOUN
concept-2276	234	49	appearances	appearance	NOUN
concept-2276	234	50	with	with	ADP
concept-2276	234	51	this	this	DET
concept-2276	234	52	model	model	NOUN
concept-2276	234	53	)	)	PUNCT
concept-2276	234	54	.	.	PUNCT
concept-2276	235	1	a	a	DET
concept-2276	235	2	similar	similar	ADJ
concept-2276	235	3	analysis	analysis	NOUN
concept-2276	235	4	regarding	regard	VERB
concept-2276	235	5	the	the	DET
concept-2276	235	6	usage	usage	NOUN
concept-2276	235	7	of	of	ADP
concept-2276	235	8	the	the	DET
concept-2276	235	9	first	first	ADJ
concept-2276	235	10	model	model	NOUN
concept-2276	235	11	can	can	AUX
concept-2276	235	12	be	be	AUX
concept-2276	235	13	said	say	VERB
concept-2276	235	14	with	with	ADP
concept-2276	235	15	the	the	DET
concept-2276	235	16	second	second	ADJ
concept-2276	235	17	model	model	NOUN
concept-2276	235	18	since	since	SCONJ
concept-2276	235	19	the	the	DET
concept-2276	235	20	general	general	ADJ
concept-2276	235	21	patterns	pattern	NOUN
concept-2276	235	22	of	of	ADP
concept-2276	235	23	both	both	DET
concept-2276	235	24	tables	table	NOUN
concept-2276	235	25	are	be	AUX
concept-2276	235	26	relatively	relatively	ADV
concept-2276	235	27	similar	similar	ADJ
concept-2276	235	28	(	(	PUNCT
concept-2276	235	29	i.e.	i.e.	X
concept-2276	235	30	,	,	PUNCT
concept-2276	235	31	the	the	DET
concept-2276	235	32	top	top	ADJ
concept-2276	235	33	10	10	NUM
concept-2276	235	34	obp	obp	PROPN
concept-2276	235	35	’s	’s	PART
concept-2276	235	36	are	be	AUX
concept-2276	235	37	above	above	ADP
concept-2276	235	38	.35	.35	NUM
concept-2276	235	39	and	and	CCONJ
concept-2276	235	40	the	the	DET
concept-2276	235	41	bottom	bottom	ADJ
concept-2276	235	42	10	10	NUM
concept-2276	235	43	obp	obp	PROPN
concept-2276	235	44	’s	’s	PART
concept-2276	235	45	are	be	AUX
concept-2276	235	46	mostly	mostly	ADV
concept-2276	235	47	below	below	ADP
concept-2276	235	48	.1	.1	NUM
concept-2276	235	49	as	as	ADV
concept-2276	235	50	well	well	ADV
concept-2276	235	51	as	as	ADP
concept-2276	235	52	the	the	DET
concept-2276	235	53	relatively	relatively	ADV
concept-2276	235	54	similar	similar	ADJ
concept-2276	235	55	posterior	posterior	ADJ
concept-2276	235	56	standard	standard	ADJ
concept-2276	235	57	deviations	deviation	NOUN
concept-2276	235	58	)	)	PUNCT
concept-2276	235	59	.	.	PUNCT
concept-2276	236	1	unlike	unlike	ADP
concept-2276	236	2	the	the	DET
concept-2276	236	3	posterior	posterior	ADJ
concept-2276	236	4	true	true	ADJ
concept-2276	236	5	abilities	ability	NOUN
concept-2276	236	6	in	in	ADP
concept-2276	236	7	the	the	DET
concept-2276	236	8	first	first	ADJ
concept-2276	236	9	model	model	NOUN
concept-2276	236	10	,	,	PUNCT
concept-2276	236	11	the	the	DET
concept-2276	236	12	second	second	ADJ
concept-2276	236	13	model	model	NOUN
concept-2276	236	14	have	have	VERB
concept-2276	236	15	lower	low	ADJ
concept-2276	236	16	posterior	posterior	ADJ
concept-2276	236	17	true	true	ADJ
concept-2276	236	18	abilities	ability	NOUN
concept-2276	236	19	for	for	ADP
concept-2276	236	20	the	the	DET
concept-2276	236	21	bottom	bottom	ADJ
concept-2276	236	22	10	10	NUM
concept-2276	236	23	obp	obp	NOUN
concept-2276	236	24	.	.	PUNCT
concept-2276	237	1	another	another	DET
concept-2276	237	2	thing	thing	NOUN
concept-2276	237	3	to	to	PART
concept-2276	237	4	notice	notice	VERB
concept-2276	237	5	is	be	AUX
concept-2276	237	6	that	that	SCONJ
concept-2276	237	7	the	the	DET
concept-2276	237	8	average	average	ADJ
concept-2276	237	9	plate	plate	NOUN
concept-2276	237	10	appearances	appearance	VERB
concept-2276	237	11	for	for	ADP
concept-2276	237	12	the	the	DET
concept-2276	237	13	top	top	ADJ
concept-2276	237	14	10	10	NUM
concept-2276	237	15	obp	obp	PROPN
concept-2276	237	16	’s	’s	PART
concept-2276	237	17	are	be	AUX
concept-2276	237	18	around	around	ADV
concept-2276	237	19	400	400	NUM
concept-2276	237	20	to	to	PART
concept-2276	237	21	500	500	NUM
concept-2276	237	22	while	while	SCONJ
concept-2276	237	23	the	the	DET
concept-2276	237	24	bottom	bottom	ADJ
concept-2276	237	25	ten	ten	NUM
concept-2276	237	26	obp	obp	PROPN
concept-2276	237	27	’s	’s	PART
concept-2276	237	28	are	be	AUX
concept-2276	237	29	less	less	ADJ
concept-2276	237	30	than	than	ADP
concept-2276	237	31	65	65	NUM
concept-2276	237	32	.	.	PUNCT
concept-2276	238	1	one	one	NUM
concept-2276	238	2	standout	standout	NOUN
concept-2276	238	3	contrast	contrast	NOUN
concept-2276	238	4	though	though	ADV
concept-2276	238	5	is	be	AUX
concept-2276	238	6	that	that	SCONJ
concept-2276	238	7	the	the	DET
concept-2276	238	8	top	top	ADJ
concept-2276	238	9	obp	obp	PROPN
concept-2276	238	10	’s	’s	PART
concept-2276	238	11	for	for	ADP
concept-2276	238	12	both	both	DET
concept-2276	238	13	models	model	NOUN
concept-2276	238	14	are	be	AUX
concept-2276	238	15	similar	similar	ADJ
concept-2276	238	16	while	while	SCONJ
concept-2276	238	17	the	the	DET
concept-2276	238	18	bottom	bottom	ADJ
concept-2276	238	19	ten	ten	NUM
concept-2276	238	20	obp	obp	PROPN
concept-2276	238	21	’s	’s	PART
concept-2276	238	22	are	be	AUX
concept-2276	238	23	different	different	ADJ
concept-2276	238	24	.	.	PUNCT
concept-2276	239	1	a	a	DET
concept-2276	239	2	standout	standout	NOUN
concept-2276	239	3	figure	figure	NOUN
concept-2276	239	4	that	that	PRON
concept-2276	239	5	appears	appear	VERB
concept-2276	239	6	with	with	ADP
concept-2276	239	7	this	this	DET
concept-2276	239	8	model	model	NOUN
concept-2276	239	9	is	be	AUX
concept-2276	239	10	the	the	DET
concept-2276	239	11	obp	obp	NOUN
concept-2276	239	12	value	value	NOUN
concept-2276	239	13	of	of	ADP
concept-2276	239	14	.889	.889	NUM
concept-2276	239	15	.	.	PUNCT
concept-2276	240	1	though	though	SCONJ
concept-2276	240	2	this	this	DET
concept-2276	240	3	value	value	NOUN
concept-2276	240	4	is	be	AUX
concept-2276	240	5	significantly	significantly	ADV
concept-2276	240	6	greater	great	ADJ
concept-2276	240	7	than	than	ADP
concept-2276	240	8	.35	.35	NUM
concept-2276	240	9	,	,	PUNCT
concept-2276	240	10	it	it	PRON
concept-2276	240	11	can	can	AUX
concept-2276	240	12	easily	easily	ADV
concept-2276	240	13	be	be	AUX
concept-2276	240	14	achieved	achieve	VERB
concept-2276	240	15	with	with	ADP
concept-2276	240	16	8	8	NUM
concept-2276	240	17	times	time	NOUN
concept-2276	240	18	-	-	PUNCT
concept-2276	240	19	on	on	ADP
concept-2276	240	20	-	-	PUNCT
concept-2276	240	21	base	base	NOUN
concept-2276	240	22	out	out	ADP
concept-2276	240	23	of	of	ADP
concept-2276	240	24	9	9	NUM
concept-2276	240	25	plate	plate	NOUN
concept-2276	240	26	appearances	appearance	NOUN
concept-2276	240	27	which	which	PRON
concept-2276	240	28	does	do	AUX
concept-2276	240	29	not	not	PART
concept-2276	240	30	really	really	ADV
concept-2276	240	31	indicate	indicate	VERB
concept-2276	240	32	the	the	DET
concept-2276	240	33	batter	batter	NOUN
concept-2276	240	34	is	be	AUX
concept-2276	240	35	a	a	DET
concept-2276	240	36	good	good	ADJ
concept-2276	240	37	player	player	NOUN
concept-2276	240	38	.	.	PUNCT
concept-2276	241	1	this	this	DET
concept-2276	241	2	example	example	NOUN
concept-2276	241	3	shows	show	VERB
concept-2276	241	4	that	that	SCONJ
concept-2276	241	5	only	only	ADV
concept-2276	241	6	having	have	VERB
concept-2276	241	7	a	a	DET
concept-2276	241	8	high	high	ADJ
concept-2276	241	9	valued	value	VERB
concept-2276	241	10	obp	obp	NOUN
concept-2276	241	11	is	be	AUX
concept-2276	241	12	n’t	not	PART
concept-2276	241	13	sufficient	sufficient	ADJ
concept-2276	241	14	enough	enough	ADV
concept-2276	241	15	for	for	ADP
concept-2276	241	16	determining	determine	VERB
concept-2276	241	17	a	a	DET
concept-2276	241	18	player	player	NOUN
concept-2276	241	19	’s	’s	PART
concept-2276	241	20	offensive	offensive	ADJ
concept-2276	241	21	capacities	capacity	NOUN
concept-2276	241	22	.	.	PUNCT
concept-2276	242	1	vi	vi	X
concept-2276	242	2	.	.	NOUN
concept-2276	242	3	conclusion	conclusion	NOUN
concept-2276	242	4	when	when	SCONJ
concept-2276	242	5	it	it	PRON
concept-2276	242	6	comes	come	VERB
concept-2276	242	7	to	to	ADP
concept-2276	242	8	finding	find	VERB
concept-2276	242	9	the	the	DET
concept-2276	242	10	best	good	ADJ
concept-2276	242	11	batters	batter	NOUN
concept-2276	242	12	,	,	PUNCT
concept-2276	242	13	it	it	PRON
concept-2276	242	14	is	be	AUX
concept-2276	242	15	n’t	not	PART
concept-2276	242	16	always	always	ADV
concept-2276	242	17	the	the	DET
concept-2276	242	18	case	case	NOUN
concept-2276	242	19	that	that	SCONJ
concept-2276	242	20	a	a	DET
concept-2276	242	21	batter	batter	NOUN
concept-2276	242	22	with	with	ADP
concept-2276	242	23	a	a	DET
concept-2276	242	24	higher	high	ADJ
concept-2276	242	25	obp	obp	NOUN
concept-2276	242	26	alone	alone	ADV
concept-2276	242	27	implies	imply	VERB
concept-2276	242	28	a	a	DET
concept-2276	242	29	better	well	ADJ
concept-2276	242	30	hitting	hitting	NOUN
concept-2276	242	31	.	.	PUNCT
concept-2276	243	1	we	we	PRON
concept-2276	243	2	need	need	VERB
concept-2276	243	3	a	a	DET
concept-2276	243	4	player	player	NOUN
concept-2276	243	5	to	to	PART
concept-2276	243	6	have	have	VERB
concept-2276	243	7	both	both	CCONJ
concept-2276	243	8	a	a	DET
concept-2276	243	9	high	high	ADJ
concept-2276	243	10	number	number	NOUN
concept-2276	243	11	of	of	ADP
concept-2276	243	12	plate	plate	NOUN
concept-2276	243	13	appearances	appearance	VERB
concept-2276	243	14	14	14	NUM
concept-2276	243	15	obp	obp	NOUN
concept-2276	243	16	p	p	X
concept-2276	243	17	sd	sd	NOUN
concept-2276	243	18	for	for	ADP
concept-2276	243	19	p	p	PRON
concept-2276	243	20	posterior	posterior	ADJ
concept-2276	243	21	mean	mean	NOUN
concept-2276	243	22	for	for	ADP
concept-2276	243	23	pa	pa	PROPN
concept-2276	243	24	obp	obp	PROPN
concept-2276	243	25	p	p	PROPN
concept-2276	243	26	sd	sd	NOUN
concept-2276	243	27	for	for	ADP
concept-2276	243	28	p	p	PRON
concept-2276	243	29	posterior	posterior	ADJ
concept-2276	243	30	mean	mean	NOUN
concept-2276	243	31	for	for	ADP
concept-2276	243	32	pa	pa	PROPN
concept-2276	243	33	0.445	0.445	NUM
concept-2276	243	34	0.366	0.366	NUM
concept-2276	243	35	0.035	0.035	NUM
concept-2276	243	36	449.5	449.5	NUM
concept-2276	243	37	0.052	0.052	NUM
concept-2276	243	38	0.217	0.217	NUM
concept-2276	243	39	0.000	0.000	NUM
concept-2276	243	40	58.0	58.0	NUM
concept-2276	243	41	0.428	0.428	NUM
concept-2276	243	42	0.365	0.365	NUM
concept-2276	243	43	0.029	0.029	NUM
concept-2276	243	44	493.9	493.9	NUM
concept-2276	243	45	0.022	0.022	NUM
concept-2276	243	46	0.219	0.219	NUM
concept-2276	243	47	0.017	0.017	NUM
concept-2276	243	48	45.5	45.5	NUM
concept-2276	243	49	0.401	0.401	NUM
concept-2276	243	50	0.357	0.357	NUM
concept-2276	243	51	0.024	0.024	NUM
concept-2276	243	52	519.6	519.6	NUM
concept-2276	243	53	0.016	0.016	NUM
concept-2276	243	54	0.221	0.221	NUM
concept-2276	243	55	0.000	0.000	NUM
concept-2276	243	56	61.0	61.0	NUM
concept-2276	243	57	0.399	0.399	NUM
concept-2276	243	58	0.357	0.357	NUM
concept-2276	243	59	0.024	0.024	NUM
concept-2276	243	60	521.4	521.4	NUM
concept-2276	243	61	0.889	0.889	NUM
concept-2276	243	62	0.225	0.225	NUM
concept-2276	243	63	0.006	0.006	NUM
concept-2276	243	64	9.0	9.0	NUM
concept-2276	243	65	0.416	0.416	NUM
concept-2276	243	66	0.353	0.353	NUM
concept-2276	243	67	0.036	0.036	NUM
concept-2276	243	68	458.9	458.9	NUM
concept-2276	243	69	0.026	0.026	NUM
concept-2276	243	70	0.226	0.226	NUM
concept-2276	243	71	0.014	0.014	NUM
concept-2276	243	72	38.4	38.4	NUM
concept-2276	243	73	0.402	0.402	NUM
concept-2276	243	74	0.350	0.350	NUM
concept-2276	243	75	0.033	0.033	NUM
concept-2276	243	76	474.3	474.3	NUM
concept-2276	243	77	0.028	0.028	NUM
concept-2276	243	78	0.226	0.226	NUM
concept-2276	243	79	0.021	0.021	NUM
concept-2276	243	80	36.0	36.0	NUM
concept-2276	243	81	0.398	0.398	NUM
concept-2276	243	82	0.350	0.350	NUM
concept-2276	243	83	0.031	0.031	NUM
concept-2276	243	84	481.4	481.4	NUM
concept-2276	243	85	0.058	0.058	NUM
concept-2276	243	86	0.228	0.228	NUM
concept-2276	243	87	0.016	0.016	NUM
concept-2276	243	88	54.1	54.1	NUM
concept-2276	243	89	0.384	0.384	NUM
concept-2276	243	90	0.348	0.348	NUM
concept-2276	243	91	0.027	0.027	NUM
concept-2276	243	92	503.7	503.7	NUM
concept-2276	243	93	0.024	0.024	NUM
concept-2276	243	94	0.228	0.228	NUM
concept-2276	243	95	0.017	0.017	NUM
concept-2276	243	96	41.6	41.6	NUM
concept-2276	243	97	0.403	0.403	NUM
concept-2276	243	98	0.344	0.344	NUM
concept-2276	243	99	0.040	0.040	NUM
concept-2276	243	100	446.5	446.5	NUM
concept-2276	243	101	0.000	0.000	NUM
concept-2276	243	102	0.229	0.229	NUM
concept-2276	243	103	0.017	0.017	NUM
concept-2276	243	104	4.1	4.1	NUM
concept-2276	243	105	0.376	0.376	NUM
concept-2276	243	106	0.344	0.344	NUM
concept-2276	243	107	0.025	0.025	NUM
concept-2276	243	108	500.0	500.0	NUM
concept-2276	243	109	0.047	0.047	NUM
concept-2276	243	110	0.229	0.229	NUM
concept-2276	243	111	0.015	0.015	NUM
concept-2276	243	112	43.0	43.0	NUM
concept-2276	243	113	table	table	NOUN
concept-2276	243	114	2	2	NUM
concept-2276	243	115	:	:	PUNCT
concept-2276	243	116	obp	obp	PROPN
concept-2276	243	117	corresponding	correspond	VERB
concept-2276	243	118	to	to	ADP
concept-2276	243	119	the	the	DET
concept-2276	243	120	highest	high	ADJ
concept-2276	243	121	and	and	CCONJ
concept-2276	243	122	lowest	low	ADJ
concept-2276	243	123	posterior	posterior	ADJ
concept-2276	243	124	true	true	ADJ
concept-2276	243	125	abilities	ability	NOUN
concept-2276	243	126	p.	p.	NOUN
concept-2276	243	127	and	and	CCONJ
concept-2276	243	128	a	a	DET
concept-2276	243	129	high	high	ADJ
concept-2276	243	130	obp	obp	NOUN
concept-2276	243	131	.	.	PUNCT
concept-2276	244	1	both	both	PRON
concept-2276	244	2	of	of	ADP
concept-2276	244	3	the	the	DET
concept-2276	244	4	models	model	NOUN
concept-2276	244	5	used	use	VERB
concept-2276	244	6	show	show	VERB
concept-2276	244	7	that	that	SCONJ
concept-2276	244	8	the	the	DET
concept-2276	244	9	top	top	ADJ
concept-2276	244	10	obp	obp	PROPN
concept-2276	244	11	’s	’s	X
concept-2276	244	12	in	in	ADP
concept-2276	244	13	terms	term	NOUN
concept-2276	244	14	of	of	ADP
concept-2276	244	15	posterior	posterior	ADJ
concept-2276	244	16	true	true	ADJ
concept-2276	244	17	abilities	ability	NOUN
concept-2276	244	18	are	be	AUX
concept-2276	244	19	around	around	ADP
concept-2276	244	20	the	the	DET
concept-2276	244	21	.4	.4	NUM
concept-2276	244	22	values	value	NOUN
concept-2276	244	23	,	,	PUNCT
concept-2276	244	24	which	which	PRON
concept-2276	244	25	is	be	AUX
concept-2276	244	26	a	a	DET
concept-2276	244	27	reasonable	reasonable	ADJ
concept-2276	244	28	conclusion	conclusion	NOUN
concept-2276	244	29	to	to	PART
concept-2276	244	30	make	make	VERB
concept-2276	244	31	.	.	PUNCT
concept-2276	245	1	however	however	ADV
concept-2276	245	2	,	,	PUNCT
concept-2276	245	3	one	one	NUM
concept-2276	245	4	of	of	ADP
concept-2276	245	5	strange	strange	ADJ
concept-2276	245	6	results	result	NOUN
concept-2276	245	7	is	be	AUX
concept-2276	245	8	that	that	SCONJ
concept-2276	245	9	the	the	DET
concept-2276	245	10	bottom	bottom	ADJ
concept-2276	245	11	10	10	NUM
concept-2276	245	12	obp	obp	PROPN
concept-2276	245	13	’s	’s	PART
concept-2276	245	14	for	for	ADP
concept-2276	245	15	both	both	DET
concept-2276	245	16	models	model	NOUN
concept-2276	245	17	yields	yield	VERB
concept-2276	245	18	values	value	NOUN
concept-2276	245	19	that	that	PRON
concept-2276	245	20	require	require	VERB
concept-2276	245	21	a	a	DET
concept-2276	245	22	reasonably	reasonably	ADV
concept-2276	245	23	high	high	ADJ
concept-2276	245	24	number	number	NOUN
concept-2276	245	25	of	of	ADP
concept-2276	245	26	plate	plate	NOUN
concept-2276	245	27	appearances	appearance	NOUN
concept-2276	245	28	as	as	ADV
concept-2276	245	29	well	well	ADV
concept-2276	245	30	.	.	PUNCT
concept-2276	246	1	this	this	DET
concept-2276	246	2	result	result	NOUN
concept-2276	246	3	is	be	AUX
concept-2276	246	4	counter	counter	ADJ
concept-2276	246	5	-	-	ADJ
concept-2276	246	6	intuitive	intuitive	ADJ
concept-2276	246	7	to	to	ADP
concept-2276	246	8	the	the	DET
concept-2276	246	9	notion	notion	NOUN
concept-2276	246	10	that	that	SCONJ
concept-2276	246	11	worse	bad	ADJ
concept-2276	246	12	players	player	NOUN
concept-2276	246	13	tend	tend	VERB
concept-2276	246	14	to	to	PART
concept-2276	246	15	receive	receive	VERB
concept-2276	246	16	less	less	ADJ
concept-2276	246	17	opportunities	opportunity	NOUN
concept-2276	246	18	to	to	PART
concept-2276	246	19	go	go	VERB
concept-2276	246	20	to	to	ADP
concept-2276	246	21	the	the	DET
concept-2276	246	22	plate	plate	NOUN
concept-2276	246	23	as	as	SCONJ
concept-2276	246	24	they	they	PRON
concept-2276	246	25	are	be	AUX
concept-2276	246	26	less	less	ADV
concept-2276	246	27	reliable	reliable	ADJ
concept-2276	246	28	for	for	ADP
concept-2276	246	29	contributing	contribute	VERB
concept-2276	246	30	to	to	ADP
concept-2276	246	31	the	the	DET
concept-2276	246	32	team	team	NOUN
concept-2276	246	33	’s	’s	PART
concept-2276	246	34	offense	offense	NOUN
concept-2276	246	35	.	.	PUNCT
concept-2276	247	1	it	it	PRON
concept-2276	247	2	also	also	ADV
concept-2276	247	3	runs	run	VERB
concept-2276	247	4	a	a	DET
concept-2276	247	5	bit	bit	NOUN
concept-2276	247	6	contradictory	contradictory	ADJ
concept-2276	247	7	to	to	ADP
concept-2276	247	8	frey	frey	PROPN
concept-2276	247	9	(	(	PUNCT
concept-2276	247	10	2007	2007	NUM
concept-2276	247	11	)	)	PUNCT
concept-2276	247	12	’s	’s	PART
concept-2276	247	13	results	result	NOUN
concept-2276	247	14	on	on	ADP
concept-2276	247	15	the	the	DET
concept-2276	247	16	optimal	optimal	ADJ
concept-2276	247	17	batting	batting	NOUN
concept-2276	247	18	average	average	NOUN
concept-2276	247	19	.	.	PUNCT
concept-2276	248	1	nevertheless	nevertheless	ADV
concept-2276	248	2	,	,	PUNCT
concept-2276	248	3	this	this	DET
concept-2276	248	4	analysis	analysis	NOUN
concept-2276	248	5	shows	show	VERB
concept-2276	248	6	us	we	PRON
concept-2276	248	7	that	that	SCONJ
concept-2276	248	8	we	we	PRON
concept-2276	248	9	can	can	AUX
concept-2276	248	10	make	make	VERB
concept-2276	248	11	a	a	DET
concept-2276	248	12	model	model	NOUN
concept-2276	248	13	out	out	ADP
concept-2276	248	14	of	of	ADP
concept-2276	248	15	limited	limited	ADJ
concept-2276	248	16	real	real	ADJ
concept-2276	248	17	data	datum	NOUN
concept-2276	248	18	and	and	CCONJ
concept-2276	248	19	apply	apply	VERB
concept-2276	248	20	simulations	simulation	NOUN
concept-2276	248	21	along	along	ADP
concept-2276	248	22	with	with	ADP
concept-2276	248	23	bayesian	bayesian	NOUN
concept-2276	248	24	analysis	analysis	NOUN
concept-2276	248	25	to	to	PART
concept-2276	248	26	make	make	VERB
concept-2276	248	27	a	a	DET
concept-2276	248	28	practical	practical	ADJ
concept-2276	248	29	conclusion	conclusion	NOUN
concept-2276	248	30	.	.	PUNCT
concept-2276	249	1	with	with	ADP
concept-2276	249	2	knowing	know	VERB
concept-2276	249	3	only	only	ADV
concept-2276	249	4	a	a	DET
concept-2276	249	5	subset	subset	NOUN
concept-2276	249	6	of	of	ADP
concept-2276	249	7	the	the	DET
concept-2276	249	8	full	full	ADJ
concept-2276	249	9	baseball	baseball	NOUN
concept-2276	249	10	data	datum	NOUN
concept-2276	249	11	,	,	PUNCT
concept-2276	249	12	we	we	PRON
concept-2276	249	13	can	can	AUX
concept-2276	249	14	conclude	conclude	VERB
concept-2276	249	15	that	that	SCONJ
concept-2276	249	16	a	a	DET
concept-2276	249	17	good	good	ADJ
concept-2276	249	18	baseball	baseball	NOUN
concept-2276	249	19	player	player	NOUN
concept-2276	249	20	will	will	AUX
concept-2276	249	21	have	have	VERB
concept-2276	249	22	an	an	DET
concept-2276	249	23	obp	obp	NOUN
concept-2276	249	24	of	of	ADP
concept-2276	249	25	.445	.445	NUM
concept-2276	249	26	,	,	PUNCT
concept-2276	249	27	.421	.421	NUM
concept-2276	249	28	,	,	PUNCT
concept-2276	249	29	.401	.401	NUM
concept-2276	249	30	and	and	CCONJ
concept-2276	249	31	other	other	ADJ
concept-2276	249	32	values	value	NOUN
concept-2276	249	33	that	that	PRON
concept-2276	249	34	are	be	AUX
concept-2276	249	35	high	high	ADJ
concept-2276	249	36	in	in	ADP
concept-2276	249	37	magnitude	magnitude	NOUN
concept-2276	249	38	and	and	CCONJ
concept-2276	249	39	are	be	AUX
concept-2276	249	40	only	only	ADV
concept-2276	249	41	achievable	achievable	ADJ
concept-2276	249	42	through	through	ADP
concept-2276	249	43	a	a	DET
concept-2276	249	44	high	high	ADJ
concept-2276	249	45	number	number	NOUN
concept-2276	249	46	of	of	ADP
concept-2276	249	47	plate	plate	NOUN
concept-2276	249	48	appearances	appearance	NOUN
concept-2276	249	49	.	.	PUNCT
concept-2276	250	1	vii	vii	PROPN
concept-2276	250	2	.	.	PUNCT
concept-2276	250	3	acknowledgements	acknowledgement	NOUN
concept-2276	250	4	i	i	PRON
concept-2276	250	5	would	would	AUX
concept-2276	250	6	like	like	VERB
concept-2276	250	7	to	to	PART
concept-2276	250	8	acknowledge	acknowledge	VERB
concept-2276	250	9	dr	dr	PROPN
concept-2276	250	10	.	.	PROPN
concept-2276	250	11	jesse	jesse	PROPN
concept-2276	250	12	frey	frey	PROPN
concept-2276	250	13	for	for	ADP
concept-2276	250	14	guiding	guide	VERB
concept-2276	250	15	me	i	PRON
concept-2276	250	16	with	with	ADP
concept-2276	250	17	thoughts	thought	NOUN
concept-2276	250	18	and	and	CCONJ
concept-2276	250	19	insights	insight	NOUN
concept-2276	250	20	as	as	SCONJ
concept-2276	250	21	i	i	PRON
concept-2276	250	22	worked	work	VERB
concept-2276	250	23	out	out	ADP
concept-2276	250	24	the	the	DET
concept-2276	250	25	details	detail	NOUN
concept-2276	250	26	of	of	ADP
concept-2276	250	27	this	this	DET
concept-2276	250	28	paper	paper	NOUN
concept-2276	250	29	as	as	ADV
concept-2276	250	30	well	well	ADV
concept-2276	250	31	as	as	ADP
concept-2276	250	32	answering	answer	VERB
concept-2276	250	33	questions	question	NOUN
concept-2276	250	34	that	that	PRON
concept-2276	250	35	i	i	PRON
concept-2276	250	36	had	have	VERB
concept-2276	250	37	regarding	regard	VERB
concept-2276	250	38	the	the	DET
concept-2276	250	39	work	work	NOUN
concept-2276	250	40	that	that	PRON
concept-2276	250	41	he	he	PRON
concept-2276	250	42	has	have	AUX
concept-2276	250	43	done	do	VERB
concept-2276	250	44	with	with	ADP
concept-2276	250	45	this	this	DET
concept-2276	250	46	field	field	NOUN
concept-2276	250	47	of	of	ADP
concept-2276	250	48	study	study	NOUN
concept-2276	250	49	.	.	PUNCT
concept-2276	251	1	references	reference	NOUN
concept-2276	251	2	[	[	X
concept-2276	251	3	1	1	X
concept-2276	251	4	]	]	PUNCT
concept-2276	251	5	jesse	jesse	PROPN
concept-2276	251	6	frey	frey	PROPN
concept-2276	251	7	“	"	PUNCT
concept-2276	251	8	is	be	AUX
concept-2276	251	9	an	an	DET
concept-2276	251	10	.833	.833	NUM
concept-2276	251	11	hitter	hitter	NOUN
concept-2276	251	12	better	well	ADJ
concept-2276	251	13	than	than	ADP
concept-2276	251	14	a	a	DET
concept-2276	251	15	.338	.338	NUM
concept-2276	251	16	hitter	hitter	NOUN
concept-2276	251	17	?	?	PUNCT
concept-2276	251	18	”	"	PUNCT
concept-2276	252	1	the	the	DET
concept-2276	252	2	american	american	PROPN
concept-2276	252	3	statistician	statistician	PROPN
concept-2276	252	4	,	,	PUNCT
concept-2276	252	5	vol	vol	NOUN
concept-2276	252	6	.	.	PROPN
concept-2276	252	7	61	61	NUM
concept-2276	252	8	,	,	PUNCT
concept-2276	252	9	no	no	INTJ
concept-2276	252	10	.	.	NOUN
concept-2276	252	11	2	2	NUM
concept-2276	252	12	,	,	PUNCT
concept-2276	252	13	may	may	AUX
concept-2276	252	14	2007	2007	NUM
concept-2276	252	15	,	,	PUNCT
concept-2276	252	16	pp	pp	ADJ
concept-2276	252	17	.	.	PUNCT
concept-2276	253	1	105–111	105–111	NUM
concept-2276	253	2	.	.	NOUN
concept-2276	253	3	15	15	NUM
concept-2276	254	1	[	[	SYM
concept-2276	254	2	2	2	NUM
concept-2276	254	3	]	]	PUNCT
concept-2276	254	4	lewis	lewis	PROPN
concept-2276	254	5	m.	m.	PROPN
concept-2276	254	6	2003	2003	NUM
concept-2276	254	7	.	.	PUNCT
concept-2276	255	1	moneyball	moneyball	NOUN
concept-2276	255	2	:	:	PUNCT
concept-2276	255	3	the	the	DET
concept-2276	255	4	art	art	NOUN
concept-2276	255	5	of	of	ADP
concept-2276	255	6	winning	win	VERB
concept-2276	255	7	an	an	DET
concept-2276	255	8	unfair	unfair	ADJ
concept-2276	255	9	game	game	NOUN
concept-2276	255	10	.	.	PUNCT
concept-2276	256	1	new	new	PROPN
concept-2276	256	2	york	york	PROPN
concept-2276	256	3	:	:	PUNCT
concept-2276	256	4	w.	w.	PROPN
concept-2276	256	5	w.	w.	PROPN
concept-2276	256	6	norton	norton	PROPN
concept-2276	256	7	.	.	PUNCT
concept-2276	257	1	[	[	X
concept-2276	257	2	3	3	X
concept-2276	257	3	]	]	PUNCT
concept-2276	257	4	"	"	PUNCT
concept-2276	257	5	mlb	mlb	NOUN
concept-2276	257	6	stats	stat	NOUN
concept-2276	257	7	,	,	PUNCT
concept-2276	257	8	scores	score	NOUN
concept-2276	257	9	,	,	PUNCT
concept-2276	257	10	history	history	NOUN
concept-2276	257	11	,	,	PUNCT
concept-2276	257	12	&	&	CCONJ
concept-2276	257	13	records	record	NOUN
concept-2276	257	14	.	.	PUNCT
concept-2276	257	15	"	"	PUNCT
concept-2276	258	1	baseball-reference.com	baseball-reference.com	NOUN
concept-2276	258	2	,	,	PUNCT
concept-2276	258	3	www.baseball-reference.com/.	www.baseball-reference.com/.	PROPN
concept-2276	258	4	16	16	NUM
concept-2276	258	5	introduction	introduction	NOUN
concept-2276	258	6	the	the	DET
concept-2276	258	7	first	first	ADJ
concept-2276	258	8	proposed	propose	VERB
concept-2276	258	9	model	model	NOUN
concept-2276	258	10	plate	plate	NOUN
concept-2276	258	11	appearances	appearance	VERB
concept-2276	258	12	true	true	ADJ
concept-2276	258	13	ability	ability	NOUN
concept-2276	258	14	times	time	NOUN
concept-2276	258	15	on	on	ADP
concept-2276	258	16	base	base	NOUN
concept-2276	258	17	checking	check	VERB
concept-2276	258	18	the	the	DET
concept-2276	258	19	model	model	NOUN
concept-2276	258	20	the	the	DET
concept-2276	258	21	second	second	ADJ
concept-2276	258	22	proposed	propose	VERB
concept-2276	258	23	model	model	NOUN
concept-2276	258	24	plate	plate	NOUN
concept-2276	258	25	appearances	appearance	VERB
concept-2276	258	26	true	true	ADJ
concept-2276	258	27	ability	ability	NOUN
concept-2276	258	28	hits	hit	NOUN
concept-2276	258	29	,	,	PUNCT
concept-2276	258	30	walks	walk	NOUN
concept-2276	258	31	,	,	PUNCT
concept-2276	258	32	hit	hit	NOUN
concept-2276	258	33	-	-	PUNCT
concept-2276	258	34	by	by	ADP
concept-2276	258	35	-	-	PUNCT
concept-2276	258	36	pitches	pitch	NOUN
concept-2276	258	37	checking	check	VERB
concept-2276	258	38	the	the	DET
concept-2276	258	39	model	model	NOUN
concept-2276	258	40	finding	find	VERB
concept-2276	258	41	the	the	DET
concept-2276	258	42	posterior	posterior	ADJ
concept-2276	258	43	distribution	distribution	NOUN
concept-2276	258	44	using	use	VERB
concept-2276	258	45	the	the	DET
concept-2276	258	46	first	first	ADJ
concept-2276	258	47	model	model	NOUN
concept-2276	258	48	using	use	VERB
concept-2276	258	49	the	the	DET
concept-2276	258	50	second	second	ADJ
concept-2276	258	51	model	model	NOUN
concept-2276	258	52	results	result	NOUN
concept-2276	258	53	using	use	VERB
concept-2276	258	54	the	the	DET
concept-2276	258	55	first	first	ADJ
concept-2276	258	56	model	model	NOUN
concept-2276	258	57	using	use	VERB
concept-2276	258	58	the	the	DET
concept-2276	258	59	second	second	ADJ
concept-2276	258	60	model	model	NOUN
concept-2276	258	61	conclusion	conclusion	NOUN
concept-2276	258	62	acknowledgements	acknowledgement	NOUN