## 3 Results
### Explainability  
To enhance the interpretability of our ML models, we employed the SHAP method on the best-performing classifier. SHAP values offer a comprehensive understanding of how each feature impacts the model's predictions, making it easier to interpret complex machine learning models. The SHAP summary plots presented in the images provide insights into the most influential features and their contributions to the model's output. The first SHAP summary plot displays the mean SHAP value for each feature, indicating the average impact of each feature on the model's predictions (Figure 3a). In this plot, \"SHORT PASSES\" emerged as the most significant feature, having the highest mean SHAP value. This indicates that the number of short passes has the greatest influence on the model's output. Other important features include \"THROUGH BALLS\", \"TACKLES ATTEMPTED\", and \"LONG BALLS\", all of which significantly impact the model's predictions. These features are essential in determining the ranking of teams, highlighting the importance of both offensive and defensive play metrics. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Features** & **Relative Importance** & **Description** & **Variable’s Type** \\ \hline SHORT PASSES & 0.71 & \begin{tabular}{c} Passes shorter than \\ 15 yards \\ \end{tabular} & Numeric \\ \hline THROUGH BALLS & 0.48 & \begin{tabular}{c} An \\ attempted/accurate \\ pass between \\ opposition players in \\ their defensive line to \\ find an ornushing \\ teammate \\ \end{tabular} & Numeric \\ \hline LONG BALLS & \(-\)0.58 & \begin{tabular}{c} Passes longer than \\ 25 yards \\ \end{tabular} & Numeric \\ \hline TACKLES & \(-\)0.46 & \begin{tabular}{c} Dispossessing an \\ opponent, whether \\ the tackling player \\ comes away with the \\ ball or not \\ \end{tabular} & Numeric \\ \hline SHOTS TOTAL & 0.12 & \
\begin{tabular}{c} All attempts to score \\ a goal made with any \\ (legal) part of the \\ body, either on or off \\ target \\ \end{tabular} & Numeric \\ \hline ATTEMPTTS SET & \(-\)0.06 &
\begin{tabular}{c} The percentage of \\ attempts that have \\ been made via a set \\ piece situation (in \\ relation to the total \\ attempts from set \\ pieces and open \\ play). \\ \end{tabular} & Numeric \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Selected features of best-performing classifier (LR). The second SHAP summary plot provides a more detailed view, showing the distribution of SHAP values for each feature along with their respective feature values (Figure 3b). In this plot, each point represents a SHAP value for a specific feature in a single instance. The color of the points corresponds to the feature value (with red indicating high values and blue indicating low values). For instance, higher values of \"SHORT PASSES\" generally have a positive impact on the model's output, pushing predictions toward higher rankings. Conversely, lower values of \"SHORT PASSES\" have a negative impact. A similar pattern can be observed for \"THROUGH BALLS\", where higher values tend to positively influence the model's predictions. Furthermore, we can also observe that higher values of \"TACK-ELS ATTEMPTED\" and \"LONG BALLS\" have a negative impact on the model's output, pushing predictions toward medium to lower rankings. This detailed SHAP analysis elucidates how specific features contribute to the likelihood of higher or lower rankings. For example, the positive impact of high \"SHORT PASSES\" and \"THROUGH BALLS\" values indicates that effective passing strategies are crucial for achieving higher rankings. Conversely, features like \"ATTEMPTTS SET PIECES\" and \" SHOTS TOTAL COUNT \" show a neutral relationship with the model's predictions. By employing SHAP, we can unravel the significance of each identified factor, providing clear insights into how different aspects of team performance influence the model's predictions.