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A Potential Function Approach to the Flow of Play in Soccer



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Journal of Quantitative Analysis in Sports A Potential Function Approach to the Flow of Play in Soccer David R Brillinger Statistics Department University of California Berkeley Abstract There is a growing literature on the statistical analysis of data from associationfootball soccer games seasons or groups of seasons In contrast this paper is concerned with a single play that is a sequence of successful passes The play studied contained 25 passes and ended in a goal for Argentina in World Cup 2006 One question addressed is how to describe analytically the spatial temporal movement of such a particular sequence of passes The basic data are points in the plane successively joined by straight lines The resulting figure represents the trajectory of the moving soccer ball The approach of this study is to develop a useful potential function a concept arising from physics and engineering In particular the potential function leads to a regression model that may be fit directly by linear least squares The resulting potential function may be used for simple description summary comparison simulation prediction model appraisal bootstrapping and employed for estimating quantities of interest The purpose illustrated here is to simulate play in a game where the ball goes back and forth between two teams each having their own potential function 1 Introduction The 2006 World Cup included some grand moments One of the most spectacular was the 25 pass scoring play of Argentina in the Serbia Montenegro S M game on 16 June The shot that ended the play was a goal scored by Cambiasso but some 8 players worked hard to get the ball into position for his shot The play has been described as one of the all time great World Cup goals the play of the tournament a joy forever a glorious goal mesmerizing and a string of pearls Not long after the game sketches of the path of the ball started to appear in newspapers e g Expressen Sweden and magazines e g Cambio Columbia Purposes of this paper are



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