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Highlights in Science, Engineering and Technology
ICMEA 2024
Volume 100 (2024)
177
Quantitative Analysis and Prediction Methods for Sports
Competition Results
Junyi Liu*, Xiaozhe Zhu#, Shiying Wang#
School of Information and Communication Engineering, Communication University of China,
Beijing, China, 100024
* Corresponding Author Email: L1968851627@163.com
#These authors contributed equally.
Abstract. In the era of big data, sports performance prediction becomes critical by analyzing
accumulated competition data, especially the influence of momentum factors on competition results,
although its definition and quantification are controversial in academia. This study explores the
application of momentum in predicting the results of sports competitions and proposes a
comprehensive research framework combining sports science and sports psychology. By collecting
and analyzing the competition data, the feasibility of momentum as an important index in predicting
the results of the competition is confirmed. The results show that momentum not only reflects the
immediate performance of athletes in the game but also predicts their future results. This finding is
of great significance for coaches and athletes to formulate strategies and adjust tactics in the game.
Through continuous accumulation and analysis of data, we can more accurately predict the results
of the game, and improve the level and fairness of sports competition.
Keywords: Sports psychology, Entropy Weight-Topsis, Momentum, PSO-BP neural network.
1. Introduction
In the context of today's big data era, the collection and analysis of sports data have become
increasingly important [1]. With the continuous accumulation and in-depth excavation of sports
competition data, the performance prediction of athletes has become the focus of researchers.
Accurate prediction of sports performance not only helps coaches and athletes to better formulate
training and competition strategies but also has important value and significance for sports scientific
research. Among them, momentum is widely considered to be one of the key factors affecting the
results of the competition [2]. However, although the influence of momentum is widely accepted in
practice, the definition and quantification of the concept of momentum and its specific impact on
athletes' performance and competition results are still controversial in academia.
In the era of big data, there have been studies on big data analysis of tennis. Koronas V evaluated
tennis players' beliefs and positions through big data analysis in 2021 [3]. In the field of sports
psychology, Scamardella F applied psychology to the field of sports, which proved the applicability
of professional psychology in the field of sports [4]. Mahammed R F conducted a study on the
confident behavior of tennis and table tennis players [5]. In this study, we used the entropy weight-
TOPSIS method to evaluate the performance of the players and used the PSO-BP neural network to
predict the results of the game. For sports physique evaluation, Zhuo C proposed a new multi-
dimensional sports physique evaluation and ranking method based on TOPSIS theory [6]. Huang W
applied the BP neural network to study the prediction of the results of table tennis technical and
tactical diagnosis [7]. Zhao Z applied the PSO-BP neural network algorithm to airport passenger
prediction classification based on risk [8]. Yan L used computer vision to realize tennis recognition in
2021, which proved the feasibility of the application of intelligent algorithms in the field of sports [9].
In this work, this study used the Entropy Weight-TOPSIS model, derived the comprehensive
performance of each player at each scoring point, and visualized the game flow for comparison. To
determine whether "momentum" plays a role in the match, we constructed a momentum model based
on positive and negative indexes and conducted a Spearman correlation analysis on whether the point
was scored or not. We selected features such as scoring rate, return score rate, and wonder shot for
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quantification. Using the PSO-BP neural network model, we predicted the outcome of each set for
the players.
2. Exploring a Dynamic Scoring System for Athlete Performance
2.1. Data Processing
Through observing the provided data of www.contest.comap.com, we identified some issues and
took corresponding measures. Upon referencing the official match website, we discovered
inaccuracies in the attached data. These errors include discrepancies in the number of sets played and
missing information on running distances.
For instance, in the match labeled "2023-wimbledon-1403", only two sets were played, and further
investigation revealed that it was due to a player withdrawal. Additionally, in some match instances,
there was no record of the running distances for both players.
To address these issues, we conducted data cleaning to minimize errors and enhance the quality
and accuracy of the data.
Next, we select the indexes that are conducive to the results of the game, such as whether to serve,
continuous score, which are recorded as positive indexes; and unfavorable indexes of the results of
the game, such as double fault, break_pt_missed, are recorded as negative indexes. The specific
classification is shown in Table 1.
Table 1. Classification of positive and negative indexes
Positive
Negative
Break_pt_won
Break_pt_missed
Net_pt_won
Net_pt_missed
Server
Unf_err
Continuous score
Double_fault
Taking '' 2023-Wimbledon-1301 '' as an example, we use the indexes of player 1 as a benchmark.
Recalculate the original data, the formula is as follows:
12
IV IV IV=−
(1)
Except for continuous scores, other indices have original values in the table. The calculation
formula for continuous score is as follows:
1nn
CS PW PW −
=−
(2)
2.2. Solution
Figure 1. The fluctuation of the composite score index
Highlights in Science, Engineering and Technology
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Volume 100 (2024)
179
As shown in Figure 1, the comprehensive score exhibits regular fluctuations over time. When the
comprehensive score is greater than 0.5, it indicates that at that score point, P1 performs better, while
if it is less than 0.5, P2 performs better. The specific degree is reflected in the numerical values.
Figure 2. The fluctuation of points_won
In addition, we also conducted data visualization of the game scoring process. It can be seen from
Figure 2 that the scores of the two sides in the first half of the game were very close. However, in the
second half of the game, the score gap between the two sides gradually expanded, and one side began
to occupy a clear advantage.
3. Exploring Momentum's Impact on Match Outcomes
3.1. Establishment of the Model
To address the momentum of players during the match, we propose the Momentum Model.
1
1ij
j
i
m P N
=
=
=−
(3)
This model is primarily composed of positive indexes, negative indexes, and the momentum at the
previous scoring point. The positive and negative indexes are manually selected, and their respective
weights have been determined using the entropy weight- TOPSIS model used in the previous section.
The formula is as follows:
10
1 (1 ) 1
i
i
ii
P
PWP
=
= + =
(4)
01
1 (1 ) 0
j
j
jj
N
NWN
=
= + =
(5)
At the same time, we get the weight of each index, as shown in Figure 3. It can be seen that the
weight value of double_fault is the smallest, 0.184, and the weight value of break_pt_won is the largest,
31.515.
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Volume 100 (2024)
180
Figure 3. The weight of each index
3.2. Solution
Jaworski J et al. used Spearman correlation analysis to identify the causal relationship between the
position in the sports ranking and the analytical variables of postural stability and proved the
correlation [10].
After data processing, we used Spearman correlation analysis between the momentum model score
and the ''winner of the point''. The result was a correlation coefficient of 0.884, indicating a strong
correlation. This proves that ''momentum'' has a significant impact during the game.
4. Competition Trend Prediction and Momentum Analysis
4.1. Data Processing
To determine the change of flow direction in a game, it is necessary to predict the flow direction of
the game according to the results of each set in the game and the performance of the players. We use
the original data to calculate more performance of the players, such as the first-serve scoring rate, the
second-serve scoring rate, and so on. The calculation process of some indicators is shown in Figure 4.
Figure 4. The calculation process of some indexes
31.515
24.953
21.437
15.496
5.355
0.822
0.238
0.184
0 5 10 15 20 25 30 35
break_pt_won
continuous score
net_pt_won
server
net_pt missed
unf_err
break_pt_missed
double_fault
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For indicators that do not have a given value, such as serve depth, we simply score different
situations, as shown in the Table 2, Table 3, and Table 4.
Table 2. The rating of serve_width
Serve_width
Score
1
2
3
4
5
Table 3. The rating of serve_depth
Serve_depth
Score
1
3
Table 4. The rating of return_depth
Return_depth
Score
1
3
Table 5 is part of the processed data of Carlos Alcaraz in ''2023-wimbledon-1301''. After the above
data processing of the 31 games of this Wimbledon, the feature data are normalized by min-max. The
normalized feature variables are used as the input layer of the BP neural network, and the results of
each disc are used as the output layer. The victory is 1, and the failure is 0. The PSO-BP neural network
is used for binary classification prediction. The data set is divided into training sets, verification sets,
and test sets, and the ratio is 70: 20: 10.
Table 5. Processed data of Carlos Alcaraz's 2023-wimbledon-1301
Set
1stSPW
RPW
ACE
Winner
Serve depth
Serve width
1
0.786
0.348
3
9
60
115
2
0.778
0.277
4
10
63
136
3
0.857
0.452
4
11
50
94
4
0.708
0.438
1
11
65
119
4.2. Solution
In the construction of the model, the Trainlm function in the MATLAB toolbox is used to realize
the binary classification prediction of each game result based on the PSO-BP neural network. We only
need to set the parameters of the model to test the prediction effect of the model.
To predict the fluctuation of the game and judge which player can win the game, the input data of
the two are the selected characteristics, and the output is the result of their respective wins and losses.
For example, the input data of player 1 is the service scoring rate, receiving scoring rate, total scoring
rate, wonder shot, physical fitness, and skills. If the output data is 1, the failure is 0.
To avoid overfitting, the sample data is randomly divided for training, and the ratio of training,
testing, and verification data is 70: 20: 10. The learning rate is set to 0.01, the minimum initialization
error is 0.00001, and the mean square error is used to measure the network performance. When the
number of training times reaches 1000, the iteration stops.
4.2.1 Model Solving
The test of PSO-BP neural network prediction model. Figure 5 is the mean square error analysis of
B
BC
BW
C
W
NCTL
CTL
ND
D
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the training set, the validation set, the test set, and the full set. The mean square error of the training
set is 0.85762, and the mean square error of the test set is about 0.86251, which is maintained at a high
value. It can be shown that our prediction results have a certain accuracy. However, because our model
is a binary classification model, only the MSE of the original data is not comprehensive, so we chose
the calculation accuracy to comprehensively evaluate the model.
Figure 5. Root mean square error results
To quantify the prediction effect of the BP neural network, the original data is compared for
visualization, and the results are shown in Figure 6. The accuracy rate, recall rate, and precision rate
of the prediction results are calculated, and the accuracy rate is as high as 81.8%.
Figure 6. Comparison of the predicted results with the real results
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In the classification problem, to avoid the interaction between the precision rate and the recall rate,
we calculated the F1 value of about 0.8, indicating that the PSO-BP neural network model we
established can identify the predicted correct samples as accurately as possible. The statistical results
of the test set are shown in Table 6, the confusion matrix heat map of the predicted results is in Figure
7.
Table 6. Model evaluation results
Accuracy
Recall
Precision
F1
Testing set
0.818
0.727
0.889
0.800
Note : F1 = 2 * ( precision * recall ) / ( precision + recall )
Figure 7. Confusion matrix heat map of prediction results
4.2.2 Correlation Analysis
According to the competition results predicted by the neural network, the accuracy rate reaches
81.8%, which shows that the change of the selected features has a certain influence on the fluctuation
of the competition, which leads to the change of the competition results.
To find out which factors are most relevant to the fluctuation of the competition, some
characteristics, and competition result data are selected to carry out correlation analysis and calculate
the correlation coefficient. Some results are shown in Table 7.
Table 7. Correlation analysis of various factors and results
Return
depth
Serve
depth
Winner
ACE
Distance
run
Unf_err
Return of serve
success rate
Total score
rate
Result
Result
0.382
(0.000***)
-0.023
(0.733)
0.274
(0.000***)
0.199
(0.003***)
0.009
(0.891)
-0.224
(0.001***)
0.543
(0.000***)
0.721
(0.000***)
1
(0.000***)
Note : * * * represents the significance level of 1 % respectively
By observing the significant level of the correlation coefficient, it can be found that the total score
rate and return of serve success rate are the most relevant to the results, and the correlation size also
lays the foundation for the selection of player performance indexes in the future.
4.3. Advise
Each player will have their own relatively strong or weak aspects. According to the different
fluctuations of the ''momentum'' in the historical competition, we can better give the athlete the
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suggestion of the competition, so that he can play his advantage in the field. To compare the ability
between athletes more clearly and intuitively, we cluster the same type of indexes, and finally
summarize them into five characteristics: Ingenuity, Resilience, Efficiency, Skill and Stamina, and
then score the players. The characteristics are shown in Figure 8.
Figure 8. Composition of characteristics
Taking the top four players of Wimbledon in 2023 as an example, this study draws a
characteristic radar map as shown in Figure 9, which can intuitively see the advantages and
disadvantages of each player.
Figure 9. The top four players' comprehensive scoring radar
Before the game, the coach needs to guide the players to understand their technical advantages and
disadvantages and clarify their shortcomings, to carry out targeted training and strengthening. Players'
deficiencies may be reflected in strength, speed, accuracy, or endurance. Coaches need to develop a
training plan suitable for players to improve their weak links. At the same time, given the advantages
and disadvantages of the opponent, the coach needs to study and analyze with the players to develop
a skilled preparation strategy. These strategies should include how to deal with the adversary's
advantage attack, how to crack the opponent's tactical layout, etc. Through the formulation and
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implementation of these strategies, players can better cope with the challenges of their opponents in
the game and improve their chances of winning.
5. Conclusions
To determine the player's performance and level in the competition, this study used the entropy
Weight-TOPSIS, the weight of each index, and the relative comprehensive score of the players
obtained. The highest and lowest weight indexes are break_pt_won and double_fault, which are 31.515%
and 0.184% respectively. The results show that the comprehensive score fluctuates regularly with time.
To further explore the influence of ''momentum'' in competition, we construct a momentum model
based on positive and negative indicators. Spearman correlation analysis results show that there is a
significant correlation between momentum and scorer, and the correlation coefficient is as high as
0.884. At last, we used the Particle Swarm Optimization- -back propagation (PSO-BP) neural network
to predict the results of the competition, and the accuracy of the model is 0.893, and the prediction
accuracy is 81.8%. In addition, we performed correlation analysis on the factors and obtained that the
total score rate and the return of serve success rate were most correlated with the results, and the
correlation coefficients were 0.721 and 0.543, respectively.
This study reveals a research idea and framework applied to the field of sports science and sports
psychology, which proves the feasibility that in the era of big data, we can quantitatively analyze the
momentum to predict the results of the competition according to the performance of athletes in the
competition.
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