# Rugby Sevens sRPE Workload Imputation Using Objective Models of Measurement
## 1 Introduction
This evaluation relied upon the available sRPE data for group mean substitution and compared the results to those values of a simple multicomponent model (sRPE = match number + player + opponent + total distance + playing time + contact count) augmented with machine learning techniques [14]. It is important to note that the best-performing model in this study was a random forest classifier. While this approach resulted in improved imputation performance compared to that of the standard DTMS, the random forest model's accuracy was still only 26.5% with an R\({}^{2}\) of 0.407, compared to the daily team mean, which had a model accuracy of 20.6% and an R\({}^{2}\) of 0.09 [14]. This suggests that the simple model employed may not have been a suitable approximation of athletes' physical load or sRPE. Similar results were echoed in a study on training sRPE data for Australian football athletes, where a random forest model outperformed even the more complex neural network, C5.0 decision rule, and naive Bayesian models [13]. This suggests an opportunity for other, statistically or theoretically driven objective models to improve the ability to impute missing sRPE data. Further, the performance of additional models developed will continue to need to be compared using a similar methodology for the imputation of the sRPE, as was originally presented by [PERSON] et al. (2022) [14]. An alternative workload metric which quantifies athletes' physical load through the use of data gathered by ATDs is the mechanical work [14; 15; 16; 17]. The use of the mechanical work is a popular strategy as it is minimally invasive to the athlete and represents a measure of both the intensity and duration [15; 16; 17; 18]. The mechanical work is the product of the force and distance and can be calculated using data from an ATD, including the speed and session duration, alongside athletes' mass data [14]. As an alternative to the mechanical work, other objective statistical models have been suggested to quantify athletes' load [12; 18]. One such example is the Speed-Deceleration-Contact (SDC) model proposed by [PERSON] et al. (2024), which uses the distances traveled by the athlete in distinct speed and deceleration zones, as well as the number and frequency of contacts experienced by the athlete [19; 20]. The SDC regression model is presented in Equation (1), where \(u_{ athlete}\) represents the random error of each athlete, and the distances in each zone are individualized to each athlete [18]. [PERSON] et al. (2024) provide more detail on the specifics of how these zones are individualized [20]. This model was found to have reasonable explanatory power, with a moderate to strong relationship to the sRPE-CL (R\({}_{\text{adjusted}}^{2}\) = 0.487), suggesting it may be used in place of the sRPE-CL as a load monitoring tool [20]. \[ \begin{array}{ll}sRPE_{CL}=&-0.852+53.87(Total\ High\ Deeleration\ Distance)+0.159(Contact\ Count)\\ &-53.46(High\ Speed\times High\ Deeleration\ Distance)\\ &-26.59(Low\ Speed\times High\ Deeleration\ Distance)+u_{ athlete}\pm 10.989\end{array}  \tag{1}\]  
Considering the relationships between objective load metrics, such as the mechanical work and SDC, and the sRPE-CL and the need for the imputation of the sRPE, it is possible that the use of current metrics augmented using different statistical approaches could improve the ability to impute the sRPE compared to current methods. The use of mathematical models like the mechanical work and the SDC are appealing alternatives to self-reported athlete data and may further be useful metrics to support MVI in the case of missing sRPE data when the sRPE-CL is used as an athlete load metric. Therefore, the purpose of this investigation was to assess the accuracy of the alternative load metrics of the mechanical work and SDC, augmented with linear regression and random forest classification, in computing the competition sRPE compared to that of DTMS. This novel approach assessed how two objective workload strategies behaved when used to impute sRPE-CL data.