Emergence of self-similarity in football dynamics

Abstract

The multiplayer dynamics of a football game is analyzed to unveil self-similarities in the time evolution of player and ball positioning. Temporal fluctuations in both the team-turf boundary and the ball location are uncovered to follow the rules of fractional Brownian motion with a Hurst exponent of H=0.7. The persistence time below which self-similarity holds is found to be several tens of seconds, implying a characteristic time scale that governs far-from-equilibrium motion on a playing field.

Figures 1 and 2 are blurred due to file-size restriction. Sharply-defined images can be viewed in the final version published by European Physical Journal B

References in corpus (6)

• Statistical physics of social dynamics
• Soccer: is scoring goals a predictable Poissonian process?
• Football fever: goal distributions and non-Gaussian statistics
• Statistics of football dynamics
• Self-affirmation model for football goal distributions
• Randomness in Competitions

Cited by in corpus (7)

• Data-driven Analysis for Understanding Team Sports Behaviors
• Evaluation of soccer team defense based on prediction models of ball recovery and being attacked: A pilot study
• Action valuation of on- and off-ball soccer players based on multi-agent deep reinforcement learning
• Stochastic model for football's collective dynamics
• Degree distribution of position-dependent ball-passing networks in football games
• Analytical representation of Gaussian processes in the $\mathcal{A}-\mathcal{T}$ plane
• Statistical properties for directional alignment and chasing of players in football games