Academic Journal of Science and Technology 
ISSN: 2771-3032 | Vol. 12, No. 1, 2024 

 

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Research	on	Professional	Tennis	Performance	Metrics	
Based	on	Random	Forest	and	Analytic	Hierarchy	
Process	Algorithms	
Jinyu Dai 1, #, Kunyan Hu 1, #, Ding Zhang 2, # 

1 Academy of Astronautics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China 
2 Faculty of Physics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China 

#These authors contributed equally 

 

Abstract: Understanding the dynamics of player performance in professional tennis, particularly how quantifiable metrics 
such as momentum influence match outcomes, is crucial for advancing sports analytics and enhancing coaching strategies. This 
study investigates performance metrics and momentum in professional tennis. The research introduced an innovative method of 
quantifying "momentum" in the sport, analyzing its impact alongside other performance indicators. We applied the Analytic 
Hierarchy Process (AHP) to determine the relative importance of various performance factors, revealing technical skills as the 
predominant influence. The study employed Random Forest algorithms to model match outcomes, contrasting predictions with 
and without momentum as a variable. Our results significantly demonstrated that momentum plays a critical role in the dynamics 
of match outcomes, challenging the notion that player success sequences are merely random. The robustness of the Random 
Forest model was further validated through sensitivity analysis, highlighting its effectiveness as a predictive tool in sports 
analytics. This research not only enhances the understanding of player performance in tennis but also supports the incorporation 
of momentum in sports performance evaluations. 

Keywords: Tennis; Momentum; Random Forest; Analytic Hierarchy Process. 
 

1. Introduction 
In professional tennis, understanding the factors that 

influence match outcomes is paramount for both coaching 
strategies and performance improvement[1, 2]. Traditional 
analyses have predominantly focused on physical attributes 
and simple match statistics, such as serve speed and error 
counts[3]. However, the dynamic nature of the sport suggests 
that other, less tangible factors, such as a player’s momentum 
during a match, also play a crucial role in determining the 
outcome[4]. 

In this study, this paper first preprocessed the data and then 
built a hierarchical analysis framework based on players' 
match data, which defined the concept of "momentum." 
Subsequently, to validate its impact on player performance, 
this research explored the predictive performance of 
algorithms both with and without the inclusion of momentum. 
Finally, we conducted a sensitivity analysis centered around 
the Random Forest algorithm. 

2. Analyzing Momentum and 
Performance Metrics in Tennis 

2.1. Data Preprocessing and Preparation 
The data for this study comes from https:// www. 

comap.com/contests/mcm-icm. The dataset from 23 years of 
Wimbledon men's singles matches is utilized to understand 
and analyze match dynamics. The initial focus is on 
comprehending the specifics of the provided datasets: 
Wimbledon_featured_matches.csv and data_dictionary.csv, 
which detail each match point, including scores, servers, 
scorers, and other pertinent data. In preprocessing, outliers are 
eliminated, and duplications are resolved by integrating data 
for similar elements like point_victor, p1_points_won, and 

p2_points_won, reflecting athletes' performance more clearly. 
Key factors are selected from the dataset for in-depth research 
and analysis. The study then plans to generalize and validate 
the developed model using data from both men’s and 
women’s singles matches at the 2021 U.S. Open and 
Wimbledon. 

Before the model is built, it is necessary to understand the 
concept of "momentum," which refers to the advantage or 
force gained by one side in a game as a result of a series of 
events. To quantify momentum, specific metrics defined in 
the next chapter are selected to evaluate a player's momentum. 

2.2. Tennis Player Performance Evaluation 
Criteria 

For the evaluation criteria of players, we assess the 
following aspects: the winning situation of the match plate 
points, the player's technique, the player's mentality, and the 
endurance. This chapter will focus on the following aspects 
[5]. 

Scoring a point on a serve revolves primarily around two 
situations: the situation of serves and defense serves. The 
former is considered the most direct evaluation metric in 
tennis, where the serving side typically holds an advantage. 
As a server, a player can control the pace of the game and 
maintain offensive initiative, while minimizing errors to keep 
the game close. Thus, the effectiveness of a serve can be 
evaluated based on its speed, position, and depth. On the other 
hand, an opponent's serve often sets the pace of the match. 
Failing to effectively handle your opponent’s serve can make 
it challenging to seize the initiative. The depth and power of 
a return are critical in assessing a good defensive serve. By 
successfully defending against the serve, one can diminish the 
opponent's advantage. 

The skills of tennis players can be notably assessed by 



 

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examining the number of high-end balls they serve during a 
match. For instance, a player's ability to serve unreturnable 
balls, execute untouchable counter serves, skillfully catch 
balls at the net, and score points on match points are all 
significant indicators of their skill level. These elements not 
only reflect their technical prowess but also their tactical 
acumen and mental strength under pressure. 

The mindset of tennis players is a crucial factor in their 
performance and the overall outcome of the match. A stable 
and positive mindset aids players in staying focused and 
confident, enabling them to handle challenges and pressures 
effectively during the game. Non-mandatory errors and 
match-point emotions are key aspects to consider. Non-
mandatory errors, such as double faults or balls hitting the net, 
occur without direct pressure from the opponent. These errors 
serve as important indicators of a player's technical 
consistency and mental concentration. On the other hand, the 
mental quality of players during critical moments, such as 
match points, often determines the game's outcome. Players 
with strong mental skills can maintain their composure under 
pressure and perform better. 

In tennis, a player's endurance is a crucial factor that 
influences their form. Endurance primarily pertains to a 
player's ability to sustain high-intensity exercise throughout a 
game, significantly impacting their performance and results. 
This aspect is often assessed by measuring the distance a 
player runs during a point, expressed in meters. The distance 
traveled during a match serves as a key indicator of their 
endurance and overall form. This movement distance not only 
relates to a player's stamina but also affects their 
explosiveness and decision-making ability during the game. 

2.3. Hierarchical Analysis to Determine 
Indicator Weights 

When we determined the weights of the main four 
dimensions, we chose AHP as the method to comply with the 
weighting coefficients of all indicators in the evaluation 
system. 

AHP method is called hierarchical analysis, is a 
combination of qualitative and quantitative decision-making 
analysis methods, mainly through the complex research 
object is divided into several levels and several indicators, 
two and two indicators for comparison, clear evaluation of the 
indicator system of the importance of each indicator of the 
percentage of the evaluation system, to clarify the evaluation 
system of the weight coefficient of each item. In this paper, 
the athletic performance of a tennis player needs to be 
evaluated concerning several objectives and attributes. 
Therefore, from a methodological point of view, the 
hierarchical analysis method is more suitable for this study. 
The hierarchical analysis method is used to analyze the 
significance of each index at different levels in the evaluation 
system of tennis players' sports performance, construct a 
suitable judgment matrix, test the consistency, and 
scientifically evaluate the weights of each type of index at all 
levels in the system of tennis players' sports index. 

First, we construct a good judgment matrix, which is a 
subjective method of determining the weights of the 
indicators, the judgment matrix is constructed as follows: 

After constructing the judgment matrix An×n, calculate its 
eigenvalues and eigenvectors, find the largest eigenvalue λmax 
and the eigenvector corresponding to the largest eigenvalue T. 
Further conducting consistency tests for judgment matrices. 

 

Table 1. The construction meaning of the matrix 
Scale Connotation

1 Two factors are of importance.

3 
The former is slightly more 

important than the latter.

5 
The former is significantly more 

important than the latter.

7 
The former is more strongly 

important than the latter.

9 
The former is extremely more 

important than the latter.

2,4,6,8 
Intermediate values of the above 

adjacent judgments.

RECIPROCAL 
(MATH.) 

If the ratio of the importance of 
factor i to that of factor j is aij , then 
the ratio of the importance of factor j 

to that of factor i is 
aji=1/ aij 

             (1) 

The following table shows that according to the dimension 
n of the judgment matrix, RI can be judged. 

 
Table 2. Criteria for judging matrix dimensions 

n 1 2 3 4 5 6 7 8 9
RI 0 0 0.58 0.9 1.12 1.24 1.32 1.41 1.45
Consistency calculation ratios are as follows: 

                 (2) 

If CR < 0.1 passes the consistency test, otherwise the 
consistency test fails. The eigenvector corresponding to the 
largest eigenvalue can be obtained, T. 

            (3) 
The weight vector is the W. 

               (4) 

           (5) 
Based on the data we collected, we solved the model and 

obtained the following results, the identity matrix as shown in 
Eq 6. 

              (6) 

This study visualizes the weights of the selected metrics as 
shown below: 

As shown in Figure 1, it can be seen that the technical 
factors of the athletes are dominant in assessing their 
performance ability, with an influence percentage of 51%, 
while the factors of endurance, mentality, and serve receive 
also have some influence on the athletes' performance in the 
game. 

 



 

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Figure 1. (a) Weight vector 3D pie chart; (b) Demonstration of the weighting of different indicators. 

 

2.4. Score Visualization and Result Analysis 

 
Figure 2. Changes in player momentum as the game progresses 

 
Figure 2 above is a graph of the changing patterns of the 

two athletes' momentum with the course of the game, which 
we have visualized from the date of the game. Where the 
horizontal coordinate represents the course of the game 
(number of hits in the game) and the vertical coordinate 
represents the momentum score. Through the curve to analyze 
the state of the two contestants, the degree of the vertical 

coordinate of the curve can be converted into a reflection of 
the contestant's "momentum", the larger the value of the 
vertical coordinate, the higher the contestant's "momentum". 
The smaller value of the vertical coordinate can, to some 
extent, reflect that the player's own mistakes are more 
frequent and the state of the game is relatively poor. 

 
Figure 3. Player momentum in every game 

 
Figure 3 shows the overall data, the data is relatively large, and it is difficult to analyze the specific state of the player's 



 

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game, so we further decomposition the data, respectively, to 
study the changes in the player's "momentum" and the state 
of the game in each game. It can be concluded that there is a 
certain periodicity in the "momentum" of the two players in 
each game and the "momentum" of the two players alternates. 
We analyze that it may be due to the greater influence of the 
players' techniques, such as the influence of the high-end balls 
served by the players such as the untriggered balls, 
untouchable counterattacks, and the points scored at the nets, 
etc. The "momentum" of the two players in each set can be 
analyzed as the influence of the players' techniques. 

3. The Role of Momentum and 
Prediction Accuracy 

The tennis coach is skeptical that "momentum" plays any 
role in the game, believing that a player's fluctuations and 
successful runs are random. Therefore, we need to analyze 

and verify whether "momentum" has a significant impact on 
the outcome of the game. After determining the influencing 
factors, we performed multivariate categorization, and for the 
first time, we selected the other four factors except 
"momentum", and analyzed the correctness of the results of 
the game through the Random Forest algorithm of 
multivariate categorization; The second time, the influence of 
"momentum" was added to the four influences, resulting in 
the correct-ness of the results of the second analysis. The 
coach's opinion is determined by comparing the correct rates 
of the two classifications and determining the significance of 
the impact of "momentum" on the outcome of the game based 
on the difference in the correct rates. 

The outcome of a tennis match is influenced by a variety of 
elements, and in this part, this study has selected the following 
factors that have a significant impact on the outcome of the 
match: 

 
Figure 4. Metrics that influence the game 

 
To achieve the effects described above, this study will 

utilize Random Forest as a tool. Random Forest is a model 
based on the Bootstrap resampling technique, composed of 
multiple decision trees. The indicators in Figure 4 will be used 

as independent variables, with match outcomes serving as the 
dependent variable output. The specific results are shown in 
Figure 5. 

 
Figure 5. a and b predict without considering momentum, while c and d incorporate momentum into their predictions 



 

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Analyzing the results of the first classification, we can 

conclude that the correct rate of judging the result of the 
match through the classification of the first four indicators is 
66.209%, the correct rate of judging the result of the match as 
a win is 67.8%, and the correct rate of judging the result of 
the match as a loss is 69.6%, which is not a very high value, 
and there is a large discrepancy between the actual value and 
the predicted value. 

In the second classification, the factor of "momentum" was 
added to the four influencing factors, and we can see from the 

results that the correct rate of judging the outcome of the 
match increased greatly, reaching 98.352%. The error rate of 
judging the outcome of the match as a loss is 2.5%, and the 
error rate of judging the outcome of the match as a win is only 
0.8%, which is a significant decrease compared to the first 
classification. The true values also largely match the predicted 
values, with only a few lines of discrepancy. Therefore, we 
can conclude that "momentum" plays an important role in 
predicting the outcome of a game, and that player fluctuations 
and successful runs are not random. 

 

 
Figure 6. Model parameter validation chart 

 
Furthermore, to verify the impact of model parameters on 

model performance, this study conducts further sensitivity 
analysis. As shown in Figure 6, we analyze the sensitivity of 
the random forest model established in this chapter, firstly, we 
control the number of features is 4 to keep the same, and 
analyze the change of the correct rate by changing the value 
of the feature tree, then we exchange the fixed parameter with 
the input variable, control the number of features is 50 to keep 
the same, and analyze the change of the correct rate by 
changing the value of the number of features, which can be 
seen that, when the input variable changes, the fluctuation 
value of the correct rate is less than 0.01 both before and after 
the factor "momentum" is added. It can be seen that when the 
input variables are changed, before and after adding the factor 
of "momentum", the fluctuation value of the correct rate is 
less than 0.01, which can be judged that the stability of the 
model we have established is high. 

4. Conclusion 
This study meticulously analyzed performance metrics and 

momentum in professional tennis, using data from major 
tournaments like Wimbledon. The data preprocessing 
effectively cleaned the dataset, setting a robust foundation for 
nuanced analysis. Employing the Analytic Hierarchy Process 
(AHP), technical skills emerged as the most influential factor 
in player performance, validated by hierarchical analysis. The 
investigation into the impact of momentum on match 
outcomes revealed that including it as a variable significantly 
enhances predictive accuracy. This finding disputes the belief 
that success sequences in tennis are random, highlighting 

momentum's pivotal role in match dynamics. Furthermore, 
the robustness of the Random Forest model was confirmed 
through sensitivity analysis, showcasing its potential as a 
reliable predictive tool in sports analytics. Overall, this 
research advances the understanding of player dynamics and 
supports the integration of momentum in sports performance 
analysis. 

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