# Rugby Sevens sRPE Workload Imputation Using Objective Models of Measurement
## 2 Materials and Methods
### Imputation of sRPE  
In order to model the relationship between the sRPE (dependent variable) and the imputation strategy (independent variable), statistical models were used to classify and predict the sRPE based on the daily team mean, the mechanical work, or the SDC model. Following this, comparisons between the true, calculated sRPE data and the imputed model data were made (R version 3.4.4, Vienna, Austria). A total of 1002 complete datasets were available for analysis. DTMS was one imputation strategy used, which relied on the sRPE values of other teammates from the same match and day. Mechanical work data were used to impute the sRPE based on the player and match number. SDC model data were used to impute sRPE data based on the player, opponent, match number, playing time, contact count, and total distance covered in zones of high deceleration and high speed, and high deceleration and low speed [20]. This investigation used DTMS, linear regression models (linear, R _stats_ package), and random forest models (R _randomForest_) to classify and predict the sRPE [8; 9; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32]. Linear regression was selected as it is a common and easy-to-administer approach currently used in sport research. Random forest regression was chosen as it has been shown to be a superior method for sRPE imputation that can be executed using open-source software [8; 9; 13; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32]. Previous work by [PERSON] et al. (2022) demonstrated that in a rugby sevens population, a random forest model outperformed other strategies including neural networks and lasso, ridge, and elastic net regression in the imputation of competition sRPE scores [14]. [PERSON] et al. (2016) imputed missing training load data for an Australian football program and again identified that random forest models outperformed even naive Bayesian models [13]. The data were split into training and test datasets, with 80% allocated for training the models and 20% for testing them. This process was repeated 100 times, and the mean values from these iterations were used for further analysis to generate predicted mechanical work scores. Following the process for the imputation of the sRPE from the mechanical work, the same models were used to impute the sRPE from the Speed-Deceleration-Contact (SDC) model using the same datasets, with a fixed random seed value set to 100. In this random forest model, the primary tuning decision involved adjusting the number of predictor variables considered at each decision point in the trees. This value was set to the square root of the total number of predictors, introducing greater randomness between the trees, which can improve generalizability and reduce overfitting and is especially useful when predicting bounded outcomes like sRPE scores. All the other model settings were kept at their default values within the randomForest package [28]. Specifically, the model generated 500 trees, ensuring stability in the predictions without excessive computation time. Each tree was built using a bootstrap sample of the training data, supporting ensemble diversity [28]. The trees were allowed to grow fully, with a minimum of five observations required to create a terminal node, which enabled the model to capture subtle patterns in the data [28]. Collectively, these default parameters provided a strong balance between predictive power, model interpretability, and computational efficiency, making them suitable for exploratory analysis or imputation tasks in moderately sized datasets [28]. The predicted sRPE values were then compared to the true, calculated values from the test dataset. The accuracy, R2, and root mean square error (RMSE) were used to evaluate the models' ability to impute the sRPE through a comparison with the true athlete-reported sRPE scores. The accuracy was defined as the proportion of the imputed sRPE scores that exactly matched the true sRPE scores. For each observation, an imputed score was considered accurate if it was numerically identical to the corresponding true score.