# Analyzing Momentum Shifts in Tennis: A Machine-Learning Approach to Predicting Match Outcomes
## 4 Discussion
The Q-Q plot illustrates the distribution of \(\Delta\dot{m}\), showing alignment with a normal distribution near the mean (0) but significant deviations at extreme values (absolute values \(\geq\) 3). These findings align with the Shapiro-Wilk and Kolmogorov-Smirnov tests, confirming that \(\Delta\dot{m}\) does not really follow the normal distribution. We speculate that \(\Delta\dot{m}\) might follow a t-distribution. However, further analysis would be needed to better understand its underlying characteristics. The model's predictions closely align with actual outcomes, with its prediction success rate standing at 78.1%, demonstrating its reliability and consistency with real-world performance. Through comparison with traditional machine-learning models [31], the model employed in this study demonstrates superior accuracy, offering optimizations and innovations over conventional methods.By incorporating probability-driven assessments, the model effectively captures the nuances of point-by-point dynamics, accurately reflecting the tendencies of each player [32; 33]. The minimal discrepancies between predictions and actual results further highlight the model's robustness in forecasting match outcomes, providing a reliable tool for analyzing performance trends in competitive settings [34]. The evaluation of the model's predictions is consistent with findings in the existing literature on probability-based sports analytics, demonstrating its reliability in forecasting match outcomes [35; 36]. As highlighted in prior studies, models incorporating probability ranges effectively capture the nuances of competitive dynamics, distinguishing scenarios that favor different players [37; 38]. The observed probability concentrations align with established methods for assessing performance trends, further validating the model's capability to accurately predict real-world outcomes and its potential contribution to advanced match analysis in tennis [39; 40]. To validate the generalizability of the model, we used the match data from the 2017 Qatar Open as the training set. After constructing the neural network and adjusting the parameters defining momentum, we tested the momentum for the match between [PERSON] and [PERSON] on 9 January. By comparing the predicted momentum with the actual momentum, we found that our model is also applicable to hard-court tennis matches. In addition, this model also demonstrates promising applications in other sports. To take the 2023 WTT Singapore Open Women's Singles match between [PERSON] and [PERSON] as an example, the study focuses on score progression and momentum shifts. Initially, [PERSON] led in momentum after winning the first set, but consecutive losses caused a decline. By the seventh round, [PERSON] gained momentum, but an error in the eighth round marked a turning point. [PERSON] capitalized on this shift, regaining momentum and achieving a ten-match winning streak, ultimately securing victory, as [PERSON]'s coach failed to call a timeout to halt the reversal. Our model offered some practical advice to both players and their coaches. During training, athletes should focus on enhancing their serve to avoid unnecessary errors. In actual matches, coaches should closely monitor the athletes' performance and promptly call timeouts when mistakes or consecutive losses occur to help them regain composure. Athletes themselves should adopt a more aggressive approach when facing adversity. A notable example is the 2011 World Table Tennis Championships, where Chinese player [PERSON], trailing 0-3 against Japanese player [PERSON], began the fourth game with persistent long-ball attacks. After winning one game, [PERSON]'s momentum significantly increased, allowing him to win three consecutive games and secure the match 4-3.