## 3 Results
### Testing Performance Metrics  
The application of various ML models, coupled with the SFFS method, yielded significant insights into the factors influencing the table rankings of French teams. The performance metrics for XGBoost, SVM, and LR models are summarized below.  
The XGBoost classifier achieved an accuracy of 88.42%, with a recall of 32.53%, an F1-score of 45.43%, and a precision of 77.51%, using 18 selected features (Table 2). Although the precision was high, indicating that the positive predictions were reliable, the recall was relatively low, suggesting that the model missed a substantial number of positive cases. The F1-score reflects a balance between precision and recall but shows room for improvement in model performance.  
The SVM classifier demonstrated an accuracy of 87.89%, with a recall of 27.19%, an F1-score of 39.54%, and a precision of 78.79%, using 10 features (Table 2). The high  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Position** & **Team** & **Points** & **Cluster** \\ \hline
1 & PSG & 85 & 1 \\
2 & Lens & 84 & 1 \\
3 & Marseille & 73 & 1 \\
4 & Rennes & 68 & 2 \\
5 & Lille & 67 & 2 \\
6 & Monaco & 65 & 2 \\
7 & Lyon & 62 & 2 \\
8 & Clermont & 59 & 2 \\
9 & Nice & 58 & 2 \\
10 & Lorient & 55 & 2 \\
11 & Reims & 51 & 3 \\
12 & Montpellier & 50 & 3 \\
13 & Toulouse & 48 & 3 \\
14 & Brest & 44 & 3 \\
15 & Strasbourg & 40 & 3 \\
16 & Nantes & 36 & 3 \\
17 & Auxerre & 35 & 3 \\
18 & Ajaccio & 26 & 3 \\
19 & Troyes & 24 & 3 \\
20 & Angers & 18 & 3 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Distribution of teams in each cluster.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**ML Models** & **Accuracy** & **Recall** & **F1-Score** & **Precision** & **Num of Features** \\ \hline XGBoost & 88.42\% & 32.53\% & 45.43\% & 77.51\% & 18 \\ \hline SVM & 87.89\% & 27.19\% & 39.54\% & 78.79\% & 10 \\ \hline \(LR\) & 75.13\% & 76.32\% & _48.03\%_ & 35.15\% & 6 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Testing performance metrics of the employed ML classifiers.  
precision indicates that when the SVM model predicted a positive case, it was usually correct. However, similar to XGBoost, the recall was low, indicating that many positive cases were not identified. The F1-score suggests that while precision is strong, the model's overall effectiveness in balancing precision and recall needs enhancement.  
The LR classifier, identified as the best-performing model, achieved an accuracy of 75.13%, with a recall of 76.32%, an F1-score of 48.03%, and a precision of 35.17%, using only six features (Table 2). Despite having a slightly lower accuracy than XGBoost and SVM, the LR model excelled in recall, capturing a higher proportion of true positives based only on six features. The superiority of the LR classifier is also shown below by observing the specificity and sensitivity in the confusion matrices.  
The normalized confusion matrices for the three classifiers (XGBoost, SVM, and LR) are illustrated in Figure 2, providing a visual representation of the classification performance and highlighting areas where each model struggles with class confusion. Specifically, the sensitivity and specificity for the best-performing ML classifier (LR) are 0.76 and 0.75, respectively.  
Figure 2: Normalized confusion matrixes for (**a**) XGBoost, (**b**) SVM, and (**c**) LR classifiers.