Statistical properties for directional alignment and chasing of players in football games

Abstract

Focusing on motion of two interacting players in football games, two velocity vectors for the pair of one player and the nearest opponent player exhibit strong alignment. Especially, we find that there exists a characteristic interpersonal distance r 500 cm below which the circular variance for their alignment decreases rapidly. By introducing the order parameter φ(t) in order to measure degree of alignment of players' velocity vectors, we also find that the angle distribution between the nearest players' velocity vectors becomes wrapped Cauchy (φ 0.7) and the mixture of von Mises and wrapped Cauchy distributions (φ 0.7), respectively. To understand these findings, we construct a simple model for the motion of the two interacting players with the following rules: chasing between the players and the reset of the chasing. We numerically show that our model successfully reproduce the results obtained from the actual data. Moreover, from the numerical study, we find that there is another characteristic distance r 1000 cm below which player's chasing starts.

Collective states and their transitions in football

“…The work by Narizuka and Yamazaki [ 38 ] investigated the statistics that govern the alignment of players during chase behaviour in soccer. In this research, group order parameters, including the polarisation and circular variance [ 39 ], are calculated across the angles between the movement vectors from players on opposing teams.…”

“…Aside from the work of Narizuka and Yamazaki [ 38 ] focusing on chase events, there has been no comprehensive study in soccer (based on the analysis of order parameters) that investigates the existence of collective states within player movement or the transitions between these states during gameplay. The aim of this research is to build on the existing body of work by analysing the movement of players across the different phases of play to understand the patterns of ordered/disordered behaviour that exist and the nature of the transitions between them.…”

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

“…We can apply some techniques developed for characterizing the self-propelled particles, including flocks of birds or fish schools 14 . The examples include the detection of highly correlated segments using directional correlation functions 15 , the characterization of order-disorder transition 16 , and the modeling of soccer players’ motion by the self-propelled player model 17 . Furthermore, the dynamics of player interactions and ball passing in soccer games are described as stochastic processes, such as the Markov chain 18 and the first-passage process 19 .…”

Stochastic model for football's collective dynamics

“…Usually, features of these collective behaviors are described by using simple group-level metrics [17][18][19][20][21][22]. Furthermore, temporal sequences of ball and player movements in football, showing traits of complex behaviors, have been reported and studied using stochastic models and statistical analysis [23][24][25][26].…”

“…Usually, features of these collective behaviors are described by using simple group-level metrics [17][18][19][20][21][22]. Furthermore, temporal sequences of ball and player movements in football, showing traits of complex behaviors, have been reported and studied using stochastic models and statistical analysis [23][24][25][26].Recent works has focused on describing cooperative on-ball interaction in football within the framework of network science [27][28][29][30][31]. In [32], for instance, D. Garrido et al studied the so call Pitch Passing Networks in the games of the Spanish League at 2018/2019 season.…”