IJAHP Essay: Mu/An MCDM Reflection on the FIFA 2014 World Cup Golden Ball Award International Journal of the Analytic Hierarchy Process ISSN 1936-6744 124 Vol. 6 Issue 2 2014 http://dx.doi.org/10.13033/ijahp.v6i1.241 ESSAY An MCDM Reflection on the FIFA 2014 World Cup Golden Ball Award Enrique Mu, PhD --------------------------------------------------------------------------------------------------- Another World Cup is over and with that another controversy about the rightful winner of the most prestigious award of the tournament, the Golden Ball. The former Argentinian player and current celebrity Diego Maradona was most likely right when he argued that his fellow countryman Lionel Messi should not have accepted the Golden Ball (“Balon de Oro”) award (La Nacion, 2014). There was even a viral video of a little girl who was crying because she thought that Messi should have given the Golden Ball award to James Rodriguez from Colombia (youtube, 2014). From a Multi-criteria Decision Making (MCDM) point of view, both Maradona and the little girl were right and in the following article we will attempt to explain why. Table 1 shows the statistics provided by FIFA for the Golden Ball player candidates. We have taken the FIFA numbers and averaged all the statistics with respect to a single game. For example, James Rodriguez scored 6 goals in 5 games; therefore, his average goals/game score is 6/5 = 1.2. On the other hand, a player that did not score any goals, such as Philipp Lahm from Germany, has 0/7 = 0 as his score for the criterion goals/game, as shown below. AN ANALYTIC HIERARCHY APPROACH The problem of selecting the Golden Ball award winner from among ten candidates constitutes a classic prioritization problem in the context of multi-criteria decision analysis. The Analytic Hierarchy Process is an ideal methodology to model this decision (Saaty, 1980). Figure 1 shows the selection problem graphically. The scores from Table 1 were converted into proportional ratings on a scale of 1 to 10. For example, the maximum score for goals/game is 1.2 (James); therefore, whoever has a score of 1.2 score has 10 points. The minimum score is 0 (Lahm and Mascherano); therefore, whoever has this score obtains 0 points. Scores that fall between 0 and 1.2 are allocated points from 1 to 10 proportionally. This same procedure was applied to each of the 8 criteria in Table 1. IJAHP Essay: Mu/An MCDM Reflection on the FIFA 2014 World Cup Golden Ball Award International Journal of the Analytic Hierarchy Process ISSN 1936-6744 125 Vol. 6 Issue 2 2014 http://dx.doi.org/10.13033/ijahp.v6i1.241 Table 1 FIFA 2014 Player Game Average Statistics Lionel Messi Toni Kroos Arjen Robben Mats Hummels Thomas Muller Philipp Lahm James Rodriguez Neymar Jr Javier Mascherano Angel Di Maria COUNTRY ARG GER HOL GER GER GER COL BRA ARG ARG GAMES PLAYED 1 1 1 1 1 1 1 1 1 1 C1 Goals Scored 0.6 0.3 0.4 0.3 0.7 0.0 1.2 0.8 0.0 0.2 C2 Assists 0.1 0.6 0.1 0.8 0.4 0.3 0.4 0.2 0.0 0.0 C3 Crosses Success Ratio * 45.5 31.0 38.0 0.0 9.0 46.2 41.7 21.0 0.0 22.4 C4 Passes Complete Ratio * 34.0 84.8 95.0 81.4 62.5 86.3 69.0 72.2 85.6 65.7 C5 Recovered Balls 3.7 2.9 2.7 7.8 1.7 5.6 2.0 3.2 7.0 1.8 C6 Fouls Committed 0.9 1.0 1.4 0.7 2.0 0.4 2.0 1.6 1.3 0.6 C7 Yellow Cards 0.0 0.0 0.1 0.0 0.0 0.1 0.2 0.2 0.1 0.2 C8 Red Cards 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 * % remains the same IJAHP Essay: Mu/An MCDM Reflection on the FIFA 2014 World Cup Golden Ball Award International Journal of the Analytic Hierarchy Process ISSN 1936-6744 126 Vol. 6 Issue 2 2014 http://dx.doi.org/10.13033/ijahp.v6i1.241 Figure 1. AHP Ratings Model for the Selection of the Golden Ball (“Balon de Oro”) Award Winner THE “BALON DE ORO” EVALUATION Finally, the eight criteria and the ten player candidates were entered into Decision Lens TM , a commercial software package that operationalizes an Analytic Hierarchy Process Ratings Model, and we proceeded to consider different scenarios in which the criteria have different weights as follows: Attack Performance Criteria 1 to 4 (goals, assists, crosses, and passes) can be considered player’s attack performance ratings. Four scenarios are possible depending on which criteria combination (C1, C1 & C2, C1 – C3, C1 – C4) is considered the most important. Figure 2 shows the results. Notice that in all the cases, James Rodriguez is the clear winner. The only exception is in the last scenario (4) where all the attack criteria were considered important. In this case Rodriguez is still the best, but is tied with Toni Kroos who has a higher rate of completed passes. 1.2 (10 pts) 0.8 (10 pts) 46.2% (10 pts) 7.8 (10 pts) 0.4 (10 pts) 0.0 (10 pts) 0.0 (10 pts) 95% (10 pts) 34% (1 pt) 0.0 (1 pt) 0.0 (1 pt) 0.0 (1 pt) 1.7 (1 pt) 2.0 (1 pt) 0.2 (1 pt) C1 Goals C2 Assists C3 Crosses C4 Passes C5 Balls Recovered C6 Fouls C7 Yellow Cards C8 Red Cards Award Winner Selectio n IJAHP Essay: Mu/An MCDM Reflection on the FIFA 2014 World Cup Golden Ball Award International Journal of the Analytic Hierarchy Process ISSN 1936-6744 127 Vol. 6 Issue 2 2014 http://dx.doi.org/10.13033/ijahp.v6i1.241 Figure 2a. Scenario 1: C1 – Goals Scored is most important criterion Figure 2b. Scenario 2: C1 Goals and C2 Assists are most important criteria Figure 2c. Scenario 3: C1 Goals, C2 Assists and C3 - Crosses are most important criteria IJAHP Essay: Mu/An MCDM Reflection on the FIFA 2014 World Cup Golden Ball Award International Journal of the Analytic Hierarchy Process ISSN 1936-6744 128 Vol. 6 Issue 2 2014 http://dx.doi.org/10.13033/ijahp.v6i1.241 Figure 2d. Scenario 4: C1 Goals, C2 Assists, C3 – Crosses, and C4 – Recovered Balls are most important criteria Defense Performance Criteria 4 and 5 (passes completed and balls recovered) can be considered defense performance criteria (yes, C4 is double dipping since passes completed can be considered important performance for both attack and defense). Figure 3 shows that in this case Matts Hummels (Germany) is the clear winner, followed by Mascherano (Argentina). Figure 3a. Scenario 5: C5 – Recovered Balls is the most important criterion IJAHP Essay: Mu/An MCDM Reflection on the FIFA 2014 World Cup Golden Ball Award International Journal of the Analytic Hierarchy Process ISSN 1936-6744 129 Vol. 6 Issue 2 2014 http://dx.doi.org/10.13033/ijahp.v6i1.241 Figure 3b. Scenario 6: C4 – Passes Completed and C5 – Recovered Balls are the most important criteria Fair Play Performance Finally, C6 to C8 (fouls, yellow cards, and red cards) can be considered a measure of fair play performance 1 . When the results were modeled based on C6 – C8 being the most important criteria, the winner is again Matts Hummels. Figure 4. Scenario 7: C6 – Fouls, C7 – Yellow and C8 – Red Cards are the most important criteria CONCLUSION This analysis suggests that in any circumstance; that is, any combination of criteria, in which attack performance criteria have greater importance than defense and fair-play performance criteria, James Rodriguez should have been the winner of the “Balon de Oro” award! Although it is not possible to know how FIFA weighs the different criteria, we could not find any scenario, i.e. changing criteria weights, where Lionel Messi could have been a potential winner for this award. Furthermore, given the AHP’s capability to 1 In this case, the less number of fouls, yellow cards, and red cards average per game, the highest the player rating. IJAHP Essay: Mu/An MCDM Reflection on the FIFA 2014 World Cup Golden Ball Award International Journal of the Analytic Hierarchy Process ISSN 1936-6744 130 Vol. 6 Issue 2 2014 http://dx.doi.org/10.13033/ijahp.v6i1.241 include intangible criteria such as team leadership, public charisma and so forth; we strongly suggest the use of an AHP evaluation approach that can make the award decision as transparent as possible. When half the world is watching this tournament, it is the least that FIFA can do for soccer fans worldwide. IJAHP Essay: Mu/An MCDM Reflection on the FIFA 2014 World Cup Golden Ball Award International Journal of the Analytic Hierarchy Process ISSN 1936-6744 131 Vol. 6 Issue 2 2014 http://dx.doi.org/10.13033/ijahp.v6i1.241 REFERENCES El Comercio (2014). En Cifras: Lionel Messi Merecio Ganar el Balon de Oro? [In Numbers: Did Lionel Messi deserve the Golden Ball Award?] July 16. Retrieved from http://elcomercio.pe/deporte-total/brasil-2014/lionel-messi-balon-oro-cifras-estadisticas- noticia-1743512 La Nacion (2014). Diego Maradona Critico el Balon de Oro para Messi. [Diego Maradona Criticized the Golden Ball Award given to Messi]. July 14. Retrieved from http://canchallena.lanacion.com.ar/1709807-diego-maradona-critico-el-balon-de-oro- para-lionel-messi-quieren-hacerle-ganar-algo-que-no-gano Saaty, T. L. (1980). Decision-Making for Leaders. New York: Mc-Graw Hill. Youtube 2014). Nina llora al ver que Messi le “robo” el balon de oro a James. Little girl cries because she argues that Messi stole the Golden Ball from James. Retrieved from https://www.youtube.com/watch?v=OBiapIIwz2c http://elcomercio.pe/deporte-total/brasil-2014/lionel-messi-balon-oro-cifras-estadisticas-noticia-1743512 http://elcomercio.pe/deporte-total/brasil-2014/lionel-messi-balon-oro-cifras-estadisticas-noticia-1743512 http://canchallena.lanacion.com.ar/1709807-diego-maradona-critico-el-balon-de-oro-para-lionel-messi-quieren-hacerle-ganar-algo-que-no-gano http://canchallena.lanacion.com.ar/1709807-diego-maradona-critico-el-balon-de-oro-para-lionel-messi-quieren-hacerle-ganar-algo-que-no-gano https://www.youtube.com/watch?v=OBiapIIwz2c