## 1 Introduction
Although the long-term goal underlying relay simulator development is to demonstrate the transferability of virtual training, it seems necessary to first measure the simulator's validity and fidelity. This is precisely the objective pursued in this study. [PERSON] et al. proposed a complete framework to assess the validity and fidelity of training VEs [18]. These principles are subdivided into subtypes that are defined and discussed according to their importance for the transfer of training. According to this framework, the assessment of the validity and fidelity of a VE must be task-specific and exhaustive, considering various aspects of the behavior. Applying this to our simulator means answering the following two questions: does the relay simulator enable athletes to maintain their perceptual-motor behavior in comparison with a real relay initiation (physical fidelity, biomechanical fidelity, and psychological fidelity)? And can the relay simulator precisely track the virtual performance with consistency with the real-life performance or, in other words, are the performance measurements obtained in VR reliable and comparable to those made in reality (construct validity)? Consequently, we aimed to assess the validity of the simulator with several complementary variables. Each of them was chosen in light of [PERSON] et al. 's framework recommendations [18] and the results of [PERSON] et al. relating to the characterization of perceptual-motor behavior produced by athletes in the relay task [13]. The relay initiation task is an overall movement that can be broken down into three key events that occur in a specific order [13]. First, as the partner approaches, the athlete begins their motor routine by lowering their center of mass in a back-and-forth movement. This first event, called the wave, is followed by gaze release, i.e., the moment when the athlete stops taking visual information from their partner's approach and turns their head in the direction of the run. Finally, gaze release is immediately followed by the rear foot lift, which is considered by the coach to be the initiation of the run. By extension, the anticipation performance corresponds to the difference in time between the passage of the approaching athlete over the mark (more precisely, the passage of the pelvis vertically above the mark) and the foot lift action performed by the receiving athlete. These key events are specific markers of the motor behavior during a relay initiation and are inherent to each individual. They constitute a perceptual-motor signature of the behavior performed and are totally linked from the very beginning of the movement to the foot lift action. In addition, the relative timing of the occurrence of each event is also an indicator of the underlying control process. It has been shown that high-level relay athletes are able to adjust the timing of the occurrence of these three events in order to initiate their run at the right time. Over trials, for a specific athlete, the wave initiation is very variable over time, while the foot lift action is relatively stable and more precise. From a behavioral perspective, this variability reduction reflects athletes' ability to use the information related to the temporal proximity of the partner in order to adapt their movement online to optimize the final result. This control process has already been described in relay [13] and in other sports [19; 20]. Assuming that these specificities are representative of relay initiation, the assessment of validity and fidelity is mainly based on a comparison of athletes' behaviors at the group and athlete levels in two conditions: VE and RWE (construct validity). From a biomechanical point of view, we compared the timing of occurrence for each key event between VE and RWE conditions (biomechanical fidelity). This measure also enables us to assess whether the variability pattern is maintained in the VE, i.e., whether the control process involved is similar (psychological fidelity).