Football as Foraging? Movements by Individual Players and Whole Teams Exhibit Lévy Walk Dynamics

Abstract

Many organisms, ranging from modern humans to extinct species, exhibit movement patterns that can be described by Lévy walk dynamics. It has been demonstrated that such behavior enables optimal foraging when resource distribution is sparse. Here, we analyze a dataset of football player trajectories, recorded during the matches of the Japanese football league, to elucidate the presence of statistical signatures of Lévy walks, such as the heavy-tailed distribution of distances traveled between significant turns and the characteristic superdiffusive behavior. We conjecture that the competitive environment of a football game leads to bursty movement dynamics reminiscent of that observed in hunter-gathering populations and more broadly in any biological organisms foraging for resources, whose exact distribution is unknown to them. Apart from analyzing individual players’ movements, we investigate the dynamics of the whole team by studying the movements of its center of mass (team’s centroid). Remarkably, the trajectory of the centroid also exhibits Lévy walk properties, marking the first instance of such type of motion observed at the group level. Our work concludes with a comparative analysis of different teams and some discussion on the relevance of our findings to sports science and science more generally.