# Rugby Sevens sRPE Workload Imputation Using Objective Models of Measurement
## 1 Introduction  
In the women's rugby sevens competition environment, teams play five or six games over two to three days, with multiple tournaments happening in the span of a few weeks. This high competition volume means that managing an athlete's physical load to ensure safe and successful participation is of critical importance. By monitoring the physical output of athletes in the competition space, practitioners gain an understanding of their performance demands, allowing for the appropriate design and deployment of training programs to meet these demands, ensuring protective effects against injuries for athletes in future competitions [1]. More immediately, in rugby sevens tournaments, monitoring the physical load provides information on tactical strategies for the substitution of players to manage in-game fatigue and inform optimal recovery strategies [2]. The use of sensor technology, including athlete tracking devices (ATDs) like GNSS monitors, is a popular option for load monitoring in team sports and is permitted by the governing body for rugbysevens for use in competition [3; 4]. However, proprietary algorithms may include metrics that are either not defined or not optimized to accurately quantify the loads experienced by female athletes [5; 6]. With concerns regarding the suitability of proprietary ATD metrics, many teams continue to rely on subjective workload measures, such as the session rating of perceived exertion training load or competition load (sRPE-TL or sRPE-CL) [7; 8; 9]. The sRPE-TL, or the sRPE-CL when the data comes from competitions, is the product of an athlete's playing time and their self-reported session rating of perceived exertion (sRPE), which is used to assign an average value to the level of effort at which the athlete felt they worked, or the intensity of their exertion, during the particular session or match [7]. While the use of the sRPE-CL is a fast way to glean insights into an athlete's workload, it relies on regular reporting by athletes and is known to be sensitive to factors like experience with the sRPE scale [10]. While the sRPE scale acts as a proxy measure of the sessional intensity, it remains a subjective element as it reflects the perception of effort [7]. However, the use of the sRPE to inform the sRPE-CL enables a holistic approach to understanding an athlete's response to the stress of training or a competition [10]. The imputation of sRPE data to ensure continuity in sRPE-CL athlete load data allows insights into the athlete's psychological and physiological experiences to continue to be generated [10]. Further, in competition settings the demands on athletes between matches to recover and prepare for the upcoming matches mean that sRPE values may not be reported, with lower compliance and missing data, making the calculation of the sRPE-CL not feasible [11]. Missing or incomplete load information may create unnecessary risks for athletes due to an inability to consistently quantify athletes' performance, either over- or underestimating the load experienced [12; 13; 14]. Therefore, there is a need to find ways to mitigate missing data, such as using imputation techniques, as well as potentially identifying other load monitoring approaches that may rely less on subjective inputs and compliance. The use of mathematical techniques for the imputation of missing values presents a unique solution to incomplete sRPE datasets, potentially enabling the retention of elements of the athlete's perception of the event [4; 9; 13]. Missing value imputation (MVI) commonly occurs in sport research using value substitution, classification, or regression models [14]. In sport data, the use of group mean substitution is a popular strategy for its ease of use [8; 9]. While group mean substitution is a common approach, this technique was outperformed by multiple different models in the imputation of the competition sRPE for a cohort of rugby sevens athletes, including linear regression, random forest, support vector machine, \(k\)-nearest neighbors, and neural network models [13].