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In soccer game analysis, the widespread availability of play-by-play andtracking data has made it possible to test mathematical models that have beendiscussed mainly theoretically. One of the essential models in soccer gameanalysis is a motion model that predicts the arrival point of a player in $ t $s. Although many space evaluation and pass prediction methods rely on motionmodels, the validity of each has not been fully clarified. This study focuseson the motion model proposed by Fujimura and Sugihara (Fujimura-Sugihara model)under sprint conditions based on the equation of motion. A previous studyindicated that the Fujimura-Sugihara model is ineffective for soccer gamesbecause it generates a circular arrival region. This study aims to examine thevalidity of the Fujimura-Sugihara model using soccer tracking data.Specifically, we quantitatively compare the arrival regions of players betweenthe model and real data. We show that the boundary of the player's arrivalregion is circular rather than elliptical, which is consistent with the model.We also show that the initial speed dependence of the arrival region satisfiesthe solution of the model. Furthermore, we propose a method for estimatingvalid kinetic parameters in the model directly from tracking data and discussthe limitations of the model for soccer games based on the estimatedparameters.

Validation of a motion model for soccer players' sprint by means of tracking data