# Analyzing Momentum Shifts in Tennis: A Machine-Learning Approach to Predicting Match Outcomes
## 3 Results
### Model Generalization  
#### 3.5.1 Examples of Tennis Match on Different Court Surfaces  
To demonstrate the applicability of our predictive model across different tennis court surfaces, we utilized data from the 2017 Qatar Tennis Open for training purposes.  
Due to the variations in court surfaces, we have made certain adjustments to the weighting of parameters that determine momentum using machine learning. The adjusted parameters are presented in Table 12.  
Figure 4: Confusion Matrix of the Prediction of the Real Winner of Each Score of the Wimbledon 2023 Final.  
Figure 5: Box-plot of the Model’s Possibility Prediction of the Real Winner of Each Score of the Wimbledon 2023 final.  
The explanations of the changes in the parameters are as follows:  
Increased Weights:  
* \(k_{1}\) (points): Continuous scoring is more likely on hard courts, increasing the weight.
* \(k_{2}\) (games won): Game wins remain significant on hard courts.
* \(k_{9}\) (running distance): Physical endurance plays a greater role on hard courts.
* \(k_{10}\) (set consumption): Matches on hard courts last longer, requiring more endurance.  
Decreased Weights:  
* \(k_{3}\) (serve wins): The advantage of holding serve is reduced as receiving becomes easier.
* \(k_{4}\) (aces): Aces are less frequent, decreasing their importance.
* \(k_{6}\) and \(k_{7}\) (break opportunities and success): Breaks are more common, reducing their impact slightly.  
Unchanged Weights:  
Factors like \(k_{5}\) (net play), \(k_{8}\) (service rights), and \(k_{12}\)\(k_{13}\) (failed break attempts) exhibit little variation between surfaces, so their weights remain unchanged.  
Figures 6 and 7 illustrates the changes in the predicted momentum for both sides, the actual momentum, and the momentum difference between [PERSON] and [PERSON] during their match on 9 January 2017, using the dataset for training. In the figure, the blue and yellow lines represent the momentum of the two athletes, respectively, corresponding to the left vertical axis. The green line represents the momentum difference between the two athletes, corresponding to the right vertical axis.  
From the perspective of the match progression, [PERSON] took a significant lead in the first set, and the actual result showed that [PERSON] won the first set 6-3. At this point, the momentum difference between [PERSON] and [PERSON] reached its maximum (corresponding to the 60-point mark in the figure). In the second set, [PERSON] adjusted their form, and the match became highly competitive. Initially, the momentum of both sides was evenly matched, but as the second set approached its conclusion, [PERSON] gained a slight edge in momentum and won the set 6-4. At the start of the third set, the match remained tightly contested. However, around the 160-point mark, [PERSON] made a critical error and had already used up all their timeouts. [PERSON]'s momentum surged again, and they ultimately won the third set 6-3.  
\begin{table}
\begin{tabular}{c c c} \hline
**Coefficient** & **Grass Court Value** & **Hard-Court Value (Adjusted)** \\ \hline \(k_{1}\) & 0.2 & 0.22 \\ \(k_{2}\) & 0.4 & 0.44 \\ \(k_{3}\) & 0.6 & 0.5 \\ \(k_{4}\) & 0.1 & 0.08 \\ \(k_{5}\) & 0.1 & 0.1 \\ \(k_{6}\) & 0.1 & 0.09 \\ \(k_{7}\) & 0.1 & 0.09 \\ \(k_{8}\) & 0.1 & 0.1 \\ \(k_{9}\This analysis shows that the changes in momentum accurately reflect the shifts in the match dynamics, further proving that our model plays a meaningful role in hard-court tennis matches.