Improved Rugby Ball Behavior Model for Kick-pass Simulation Using Beta and von Mises-Fisher Distributions

In recent years, rugby has been rapidly gaining popularity worldwide, accompanied by a growing fan base. However, due to the complexity of the rules and the flow of the game, it is essential to provide explanatory information to retain existing fans and further expand the fan base. Such information can help viewers better understand the game, the plays, and the rules, particularly during broadcasts and livestreams. Against this backdrop, several studies have focused on methods for determining normative attacking sequences in rugby sevens based on player position and velocity information, aiming to support counterfactual visualization that allows viewers to explore alternative tactical options and potential outcomes. In addition, a previous study aimed to improve a rugby ball behavior model for kick-pass simulation used in some of these studies, which aims to reproduce the irregular bouncing behavior of a rugby ball. Specifically, in that study, the empirically defined model was refined using actual ball behavior data collected during a real kick-pass practice session. Although this refined model produced more realistic simulated results compared to those with the original model, it still occasionally exhibited unrealistic features, such as overly high trajectories after the first bounce, indicating that further improvement is needed. In this context, this study proposes a novel model that adopts a different modeling approach from the previous two models, based on the beta and von Mises-Fisher distributions, aiming for better alignment with actual irregular bouncing behavior. This study also conducts quantitative comparisons to evaluate the effectiveness of the proposed model.