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arXiv · 1402.0912

Emergence of self-similarity in football dynamics

Akifumi Kijima·Keiko Yokoyama·Hiroyuki Shima·Yuji Yamamoto
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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.

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Akifumi Kijima, Keiko Yokoyama, Hiroyuki Shima, Yuji Yamamoto. 2014-02-04. Emergence of self-similarity in football dynamics. https://doi.org/10.1140/epjb/e2014-40987-5

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