Theory and data analysis of player and team ball possession time in football

TL;DR

This paper analyzes the stochastic properties of ball possession times in professional football, revealing gamma and geometric distribution patterns, and proposes a formula linking player and team possession times validated by data.

Contribution

It introduces a new probabilistic model for team possession time based on player data, with theoretical derivations and empirical validation.

Findings

Player possession time follows a gamma distribution.

Player count per possession follows a mixture of two geometric distributions.

Proposed formula accurately models team possession time.

Abstract

In this study, the stochastic properties of player and team ball possession times in professional football matches are examined. Data analysis shows that player possession time follows a gamma distribution and the player count of a team possession event follows a mixture of two geometric distributions. We propose a formula for expressing team possession time in terms of player possession time and player count in a team's possession, verifying its validity through data analysis. Furthermore, we calculate an approximate form of the distribution of team possession time, and study its asymptotic property.