A Study on the Optimisation of Tennis Players’ Match Strategies from the Perspective of Momentum
Abstract
:1. Introduction
- The development of a quantification system for tennis players’ momentum. Initially, data cleansing is conducted to guarantee the precision and thoroughness of the data. The subsequent integration of the Markov chain [10] involves the utilisation of its state-transition characteristics for the purpose of capturing the dynamic changes in the match state. Concurrently, multi-dimensional indicators with a high degree of relevance to the match are selected for the purpose of comprehensively constructing a dynamic momentum quantification system, with the objective of accurately describing the changes in players’ momentum during the match;
- The subsequent objective is to reveal the influence mechanism of players’ momentum on match trends. Firstly, the types of research data are to be determined as continuous variables and categorical variables, and the Eta correlation coefficient method [11] is to be used to analyse their correlations. Subsequently, the robustness of the research results will be ensured by verifying the correlations from different angles using the Spearman correlation coefficient [12];
- The construction of a player match strategy optimisation model based on momentum is imperative. The entropy weight method [13] is used to assign weights to the quantified momentum and other indicators. The weights are determined based on the contribution of each indicator to the player’s performance. The TOPSIS method [13] is then used to calculate the player’s final performance score, thereby evaluating their performance in the match. Concurrently, a multiple linear regression model [14] is employed to analyse the key indicators affecting the match trends. The establishment of a BP neural network prediction model [15] is then informed by these indicators. Through the implementation of non-linear fitting, the match trends are predicted, and the accuracy and stability of the model are evaluated. Finally, based on the analysis results from the above steps, targeted match-related suggestions are provided to help players optimise their strategies and improve their performance.
2. Construction of the Tennis Players’ Momentum Quantification System
2.1. Data Feature Analysis
2.2. Construction of the Dynamic Momentum Quantification System
3. The Mechanism of How Player Momentum Affects Match Trends
3.1. The Association Strength Between Continuous and Categorical Variables
3.2. Consistency Test for the Correlation Between Player Momentum and Match Trends
4. Construction of a Momentum-Based Player Match Strategy Optimisation Model
4.1. Evaluation of Player Match Performance
4.1.1. Weight Allocation for Key Indicators
4.1.2. Calculation of Player Performance Scores
4.2. Prediction of Match Trends
4.2.1. Key Indicators Influencing Match Trends
4.2.2. BP Heteroskedasticity Test
4.2.3. Multicollinearity Test
4.2.4. Sensitivity Analysis
4.2.5. Nonlinear Fitting for Predicting Match Trends
4.2.6. Validation of the Match Trends Prediction Model
5. Conclusions
- A system was constructed for the quantification of momentum in tennis players, with the objective of calculating the momentum scores of players in order to reflect critical moments and turning points in matches. The verification results were found to be consistent with actual match scenarios;
- The present study sought to explore the influence mechanism of player momentum on match trends, by means of a comprehensive analysis of momentum scores derived from momentum quantification. The findings demonstrate that, within a 95% confidence interval, the cumulative momentum scores for each game exhibit a high correlation with the win–loss changes of players in that game, while the momentum scores for each point show a weaker correlation with the win–loss changes at that point. The correlation analysis results indicate that cumulative momentum can, to a certain extent, reflect match trends. The success of players in matches is not entirely random, suggesting that player match strategies can be optimised using momentum;
- A player match strategy optimisation model based on momentum scores was constructed, with the objective of optimising real-time match strategies from two major aspects: player performance scores and match trends prediction. The performance scores calculated using the entropy weight-TOPSIS model are capable of reflecting changes in the player’s state in real time, while the BP neural network model is capable of predicting changes in match trends. The integration of these two approaches enables coaches and players to dynamically adjust their strategies during the match. For instance, when the performance score indicates that the player is in an advantageous position, the player can adopt a more aggressive offensive strategy to consolidate the advantage by combining the trends prediction model to assess the likelihood of a counterattack from the opponent. Conversely, when the performance score indicates that the player is at a disadvantage, the player can adopt a more robust defensive strategy to identify opportunities to reverse the situation by combining the trends prediction model to assess the opponent’s weaknesses. Furthermore, by monitoring the changes in performance scores and trends predictions in real time, players can make more precise tactical adjustments at critical moments, such as break points and match points, thereby increasing their chances of winning. This integrated analysis method not only enhances the real-time and scientific nature of match analysis, but also provides players and coaches with more intuitive and actionable strategy optimisation recommendations.
6. Future Work
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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No. | Classification | Number of Indicators | Indicator Description |
---|---|---|---|
1 | Basic Match Information | 12 | match_id, player1/2, set_no, game_no, point_no, etc. |
2 | Player Performance Statistics | 16 | p1/p2_ace, p1/p2_winner, p1/p2_double_fault, p1/p2_unf_err, p1/p2_break_pt, etc. |
3 | Match Event Information | 18 | p1/p2_sets, p1/p2_games, p1/p2_score, server, p1/p2_distance, etc. |
No. | Symbol | Description |
---|---|---|
1 | Momentum score of pl at point t. | |
2 | Probability of the server winning a point | |
3 | Probability of the returner winning a break point. | |
4 | Difference in the current point score between player 1 and player 2 in the current game. | |
5 | Probability of a player winning a point after losing the previous one. | |
6 | Probability of a player winning a point after winning the previous one. | |
7 | i = 1 means “player 1 is the server and won the point”; i = 0 represents “else.” | |
8 | j = 1 means “player is returner and won a break point”; j = 0 represents “else.” | |
9 | q = 1 means “player lost the previous point”; q = 0 represents “else”. |
No. | Match | Each Game | Each Point | ||
---|---|---|---|---|---|
P1 Eta | P2 Eta | P1 Eta | P2 Eta | ||
1 | 1304 | 0.470 | 0.505 | 0.209 | 0.206 |
2 | 1406 | 0.752 | 0.800 | 0.310 | 0.338 |
3 | 1502 | 0.544 | 0.731 | 0.144 | 0.311 |
4 | 1601 | 0.780 | 0.752 | 0.274 | 0.265 |
5 | 1701 | 0.717 | 0.491 | 0.208 | 0.202 |
No. | Match | Each Game | Each Point | ||||||
---|---|---|---|---|---|---|---|---|---|
P1 Spearman | P1 Sig. | P2 Spearman | P2 Sig. | P1 Spearman | P1 Sig. | P2 Spearman | P2 Sig. | ||
1 | 1304 | 0.600 | 0.000 | 0.619 | 0.000 | 0.208 | 0.000 | 0.206 | 0.000 |
2 | 1406 | 0.782 | 0.000 | 0.807 | 0.000 | 0.308 | 0.000 | 0.347 | 0.000 |
3 | 1502 | 0.521 | 0.000 | 0.764 | 0.000 | 0.135 | 0.023 | 0.315 | 0.000 |
4 | 1601 | 0.768 | 0.000 | 0.699 | 0.000 | 0.293 | 0.000 | 0.229 | 0.004 |
5 | 1701 | 0.725 | 0.000 | 0.611 | 0.000 | 0.202 | 0.000 | 0.214 | 0.000 |
No. | Index Type | Index Name | Normalisation Formula | Description |
---|---|---|---|---|
1 | Positive | Momentum | Momentum score | |
2 | Positive | Ace | Winning serve | |
3 | Positive | Winner | Winning shot | |
4 | Negative | Double-fault | Double miss | |
5 | Negative | Unf-err | Unforced error | |
6 | Negative | Rally-count | The number of strokes back and forth | |
7 | Negative | Dtop | The difference in the distance run between the two players during a point |
No. | Index Item | P1 | P2 | ||||
---|---|---|---|---|---|---|---|
Entropy Value e | Utility Value d | Weight (%) | Entropy Value e | Utility Value d | Weight (%) | ||
1 | Momentum | 0.986 | 0.014 | 1.475 | 0.987 | 0.013 | 0.990 |
2 | Ace | 0.384 | 0.616 | 65.461 | 0.148 | 0.852 | 65.697 |
3 | Winner | 0.722 | 0.278 | 29.597 | 0.598 | 0.402 | 30.993 |
4 | Double_fault | 0.996 | 0.004 | 0.387 | 0.998 | 0.002 | 0.120 |
5 | Unf_err | 0.975 | 0.025 | 2.645 | 0.978 | 0.022 | 1.691 |
6 | Rally_count | 0.997 | 0.003 | 0.306 | 0.997 | 0.003 | 0.222 |
7 | Dtop | 0.999 | 0.001 | 0.129 | 0.996 | 0.004 | 0.287 |
Test NO. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|
Absolute ME (×10−4) | 9.27 | 8.32 | 8.87 | 9.12 | 9.02 | 8.46 | 9.41 | 8.77 |
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Wu, S.; Diao, M.; Wang, J.; Song, Z.; Zhang, C. A Study on the Optimisation of Tennis Players’ Match Strategies from the Perspective of Momentum. Appl. Sci. 2025, 15, 5624. https://doi.org/10.3390/app15105624
Wu S, Diao M, Wang J, Song Z, Zhang C. A Study on the Optimisation of Tennis Players’ Match Strategies from the Perspective of Momentum. Applied Sciences. 2025; 15(10):5624. https://doi.org/10.3390/app15105624
Chicago/Turabian StyleWu, Shiqi, Mingguang Diao, Jingwen Wang, Zihan Song, and Chuyan Zhang. 2025. "A Study on the Optimisation of Tennis Players’ Match Strategies from the Perspective of Momentum" Applied Sciences 15, no. 10: 5624. https://doi.org/10.3390/app15105624
APA StyleWu, S., Diao, M., Wang, J., Song, Z., & Zhang, C. (2025). A Study on the Optimisation of Tennis Players’ Match Strategies from the Perspective of Momentum. Applied Sciences, 15(10), 5624. https://doi.org/10.3390/app15105624