# Analyzing Momentum Shifts in Tennis: A Machine-Learning Approach to Predicting Match Outcomes
## 3 Results
### Accuracy of the Model Forecast  
The results of the model's forecast are presented in Figure 4, which illustrates the predicted outcomes for each point during the Wimbledon 2023 final using the proposed model. The \"Real Winner\" indicates the actual winner of each point, while the \"Predicted Winner\" reflects the outcome anticipated by the model. With a threshold of 55% applied to classify Player A as the predicted winner, which means when the prediction probability of A winning is higher than 55%, the model would regard A as the predicted winner, same for B. The reason we set the truncation threshold at 55% is that this value effectively retains a larger portion of the valid dataset while maintaining high accuracy. Table 9 shows the discard rate and accuracy when the truncation thresholds are set at 50%, 55%, and 60%, respectively. From the data presented in Table 9, it is evident that a truncation threshold of 50% retains the entire dataset; however, the resulting accuracy is relatively low, at only 74%. When the truncation threshold is set to 55%, the amount of discarded data is minimal, at merely 5%, while the prediction accuracy increases to 78.1%. Increasing the truncation threshold to 60% results in a marginal improvement in accuracy of only three percentage points, but the sample discard rate rises sharply to 34%. Such a high sample discard rate is deemed excessive. Consequently, we ultimately determined that a truncation threshold of 55% is optimal. Figure 3: Standard Normal Quantile. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Truncation Threshold** & **Discard Rate (\%)** & **Accuracy Rate (\%)** \\ \hline
50\% & 0 & 74 \\
55\% & 5 & 78.1 \\
60\% & 34 & 81.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Comparison of Discard Rate and Accuracy Under Different Truncation Thresholds. To further validate the rationality and accuracy of our method, we compared it with traditional machine-learning approaches. The discard rates and accuracy of traditional machine-learning methods under truncation thresholds of 50%, 55%, and 60%. The Discard Rate and Accuracy Rate can be seen in Table 10.  
By comparing Tables 9 and 10, it can be observed that the accuracy of traditional machine-learning methods is significantly lower than that of our proposed approach. Among the 334 test inspections, our model had successfully predicted 261 of them. The prediction success rate was standing at 78.1%, as demonstrated by the dense clustering of data points along the diagonal where the real and predicted winners coincide. This high concentration underscores the model's effectiveness in accurately predicting point outcomes. Conversely, off-diagonal points, representing mismatches between predictions and actual outcomes, account for only 21.9% of the data, highlighting areas for potential refinement. These results confirm the model's overall reliability and provide a foundation for further optimization. After conducting statistical validation, to prevent overfitting in machine learning, we employed the k-fold validation method, dividing the dataset into 10 parts for cross-validation. The results showed that the prediction accuracy consistently ranged between 75% and 80%, see in Table 11, indicating that the model has a high level of robustness. Figure 5 illustrates the probability predictions for the 2023 Wimbledon final, with the x-axis representing the actual winner and the y-axis displaying the predicted probability of Player B winning. When Player A wins, the predicted probability for Player B is predominantly between 7% and 36%, indicating the model's ability to correctly identify [PERSON] A's high likelihood of victory without overestimating [PERSON] B's chances. Conversely, when Player B wins, the predicted probability for Player B falls between 58% and 96%, reflecting a strong correlation between predicted and actual outcomes.