## 2 Materials and Methods
### Prediction of RPE and S-RPE through ML
#### 2.3.2 Experiments  
First of all, for both \(\text{T}_{\text{S}}\text{RPE}\) and \(\text{T}_{\text{S}}\text{S}^{\text{-RPE}}\), a feature selection process was performed on 20% of the dataset randomly selected to determine the most relevant features for classification. This process was performed to reduce the dimensionality of the feature space and the risk of overfitting, allowing a more straightforward interpretation of the machine learning models, due to the lower number of features [24]. To this aim, a recursive feature elimination with cross-validation (RFECV) [25] was used to select the best subset of features. RFECV is a wrapper method for feature selection [26], which initially starts by training a predictive model (a decision tree in our experiments) with all the features in the feature set. Then at every step, RFECV eliminates one feature, trains the decision tree on the reduced feature set, and calculates the score on the validation data. For each feature, its weight was extracted from the constructed ordinal regressor. The weights range in the interval [\(-\infty\), \(+\infty\)], where values lower than 0 negatively affect the RPE or S-RPE, while vice-versa for the positive values. The subset of features producing the maximum score on the validation data is considered to be the best feature subset [25]. In addition to the ordinal regressor (ordinal), the following state-of-the-art classifiers were also constructed: decision tree regression (DT), random forest regression (RF), epsilon-support vector regression (SVR), logistic regression (logit), K-nearest neighbors (KNN), and linear regression (LR). Even if several other ML approaches were tested during analysis, we provide the results of the best ones.  
Our classifiers were validated on the remaining 80% of the dataset with a 3-fold stratified cross-validation strategy [27], stratified by player identification (ID); the dataset was divided into 3 folds. For each fold, 90% of the dataset was used as a training set and 10% of it as a test set. Each fold was made by preserving the percentage of samples for each class. Thus, each sample in the dataset was tested once, using a model that was not fitted with that sample. The goodness of the classifiers was measured by a root mean squared error (RMSE) and mean of absolute difference (MAD). Low values of RMSE and MAD indicate a high accuracy of the model. The goodness of our models was also assessed by the relationship (i.e., Pearson correlation coefficient) between RPE or S-RPE observed and predicted. The Pearson correlation coefficient (r) can take a range of values from \(-1\) (negative correlation) to \(+1\) (positive correlation). In addition, the agreement between the real effort perceived and the predicted one was assessed using Bland-Altman analysis [28]. This analysis was used in order to assess the bias (i.e., mean difference between RPE or S-RPE observed and predicted) and the systematic error (i.e., the relationship among the mean and the difference between RPE or S-RPE predicted and observed) of our classifiers compared to the perceived exertion filled by the players.  
Finally, our predictive models were compared with two baselines: baseline \(B_{1}\) randomly assigns a class to an example by respecting the distribution of classes; baseline \(B_{2}\) always assigns to an example the majority class.