## 3 Results
### Calculation of the Most Relevant Variables  
Once the reliability of the model in distinguishing between points that end with an ace and points that last for four or more strokes was established, the next step was to calculate the serve variables that had the greatest relevance for each type of effectiveness. Figures 3-5 depict the mean SHAP values, which indicate the average impact on the model outputs for each variable on the deuce and advantage sides, respectively. As it can be observed, the results of the most important variables were very similar for both sides. Regardless of the serving side, the variables that had the most relevance in the model were \(\delta\) and dL. Additionally, \"Speed\" was the other variable that had significant importance in the developed model. The mean SHAP values show the average impact on the model outputs for each variable. The results of the most important variables were very similar for the deuce and advantage sides. After separating highly correlated variables (\(\delta\) and dL) the SHAP values \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Effectiveness** & **Precision** & **Recall** & **F1-Score** & **Macro Average** & **Weighted Average** \\ \hline Type 1 & 0.91 & 0.99 & 0.95 & 0.95 & 0.94 \\ \hline Type 4 & 0.99 & 0.89 & 0.94 & 0.95 & 0.94 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Sklearn classification report type 1 vs. type 4—deuce and advantage. Figure 4: Effectiveness of type 1 vs. type 4 in the ADVANTAGE side. Figure 3: Effectiveness of type 1 vs. type 4 in the DEUCE side. summary, it was shown that in both cases, \(\delta\) and dL were the most important variables. The algorithm showed that the Speed is the next most important variable for the model. Values That Maximize the Effectiveness of Type 1 (and Minimize the Effectiveness of Type 4): That Is, Recommended Values  
Table 2 shows the distributions of the variables dL, \(\delta\), and Speed of the serves for points ending with an ace or with more than three shots for both sides of the court. Regarding dL, aces showed a similar distribution on both sides of the court. However, the serves for points with four or more shots showed significant differences in the distribution of their population. It can be observed that on the advantage side, a greater number of serves with higher values of dL were found. Regarding \(\delta\), the distribution of serves where the point lasted more than three strokes was similar on both sides of the court. However, it can be observed that aces have a wider range on the deuce side compared to the advantage side which indicates that, on the deuce side, larger angles would maximize the probability of achieving an ace to a greater extent than on the advantage side. Regarding Speed, again, the distribution of serves where the point lasted more than three strokes was similar on both sides of the court. However, the recommended values to maximize the probability of serving an ace were slightly lower on the deuce side than on the advantage side. The recommended values to maximize the probability of serving an ace would be somewhat lower for the deuce than for the advance side. For the other efficiencies, no significant differences were found.