## 3 Results
### Predictive Explanation  
In order to obtain as much information as possible from the predictive models used, 2 types of representation are proposed here:  
* graphs corresponding to decision trees for legitimate configuration (i.e., when decision tree performs well according to Section 3.1)
* the weights of predictive variables obtained from tree-based models  
In both cases, the models were learned over the entire dataset so as to use the maximum available information. Figure 5: One-week predictive performance of best models according to three types (in color) of data sets. Predictive results are presented as box plots, in which the box indicates quartile values; the whiskers indicate the upper and lower values; circle indicates outlier. Table 4 represents the best (feature set & classifier) couples for all configurations (horizons & metrics) according to Figures 4 and 5. Thus, classification tree learnt on the questionnaires data is the best 1-week injury prediction model for precision. Figure 6 represents the top of the classification trees obtained for 1-week prediction of injuries with a hyper-parameters tuning toward precision evaluation metric on questionnaires data (according to Table 4). The complete tree is given in Appendix A (see Figure A1). All nodes contain different information:  
* a discriminative condition relatively to 1 feature (with a numerical threshold) that determines which is the next node to be considered given features values (e.g., \(RPE_{3}w\leq 4.43\) for the initial node). * the proportion of the learning dataset that _falls_ into the node (e.g., 100% for the initial node). * the labels proportions of the examples contained in the node (e.g., the initial node contains 13.1% of injured players and 86.9% of not injured ones). * the label attached to the node which is the most frequent one in the subset of the learning examples it contains. If a node's condition is verified (for any new example), the next node to read is the left child one (\"True\" branch below the initial node) and the right one if not. In Figure 6, only the 6 first depth levels of the tree are represented in order to be readable as possible to the naked eye. The most significant players set (17.7% of the dataset) at high injury risk (P(injury risk) = 0.201) felt depressed precisely during the last week (\(RPE\_{3}w\leq 4.43\) and \(RPE\_{2}w>2.992\)), were relatively worried about injury during the last month (\(0.18\leq inj_{w}orry_{4}w\leq 0.969\)) and tall (height \(>\) 171 cm). This draws a player profile (tall player recently depressed and consistently worried) for which short-term injury risk seems reliable. Figures 7 and 8 respectively represent the 10 highest features importance for 1-week and 1-month injury predictions computed with the best (classifier, feature set) configuratio \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Horizon** & **Metric** & **Set Name** & **Classifier** \\ \hline
1 week & precision & questionnaires & tree \\
1 week & recall & questionnaires & forest \\
1 month & precision & all & XGB \\
1 month & recall & all & XGB \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Features importance configurations. Figure 6: Decision tree learnt on _questionnaires_ dataset for one-month injury prediction optimised for precision metric. The features importance weights are calculated with two different approaches: \(CART\) impurity decrease which is available only for tree-based classifiers and features permutation scrambling sensitivity which can be computed on any predictive model. In \(CART\) approach the features importance weights correspond to the average impurity decrease along the tree achieved by the different feature during split selection. With the permutation approach, features are randomly scrambled several times and their importance weights are computed as the mean classifiers sensitivity in terms of predictive performance to the features scrambling.