Emergence of self-similarity in football dynamics

Akifumi Kijima; Keiko Yokoyama; Hiroyuki Shima; Yuji Yamamoto

doi:10.1140/epjb/e2014-40987-5

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The European Physical Journal B

February 2014, 87:41

Emergence of self-similarity in football dynamics

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Authors and affiliations

Akifumi Kijima
Keiko Yokoyama
Hiroyuki ShimaEmail author
Yuji Yamamoto

Open Access

Regular Article

First Online:: 19 February 2014

Received:: 25 April 2013
Revised:: 07 November 2013

DOI: 10.1140/epjb/e2014-40987-5

Cite this article as:: Kijima, A., Yokoyama, K., Shima, H. et al. Eur. Phys. J. B (2014) 87: 41. doi:10.1140/epjb/e2014-40987-5

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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.

Keywords

Statistical and Nonlinear Physics

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Authors and Affiliations

Akifumi Kijima
- 1
Keiko Yokoyama
- 2
- 3
Hiroyuki Shima
- 4
Email author
Yuji Yamamoto
- 5

1.Graduate School of Education, University of YamanashiYamanashiJapan
2.Division of Applied Physics, Faculty of Engineering, Hokkaido UniversityHokkaidoJapan
3.Japan Society for the Promotion of ScienceTokyoJapan
4.Department of Environmental Sciences & Interdisciplinary Graduate School of Medicine and EngineeringUniversity of YamanashiYamanashiJapan
5.Research Center of Health, Physical Fitness and Sports & Department of Psychology and Human Developmental Sciences, Nagoya UniversityNagoyaJapan

Emergence of self-similarity in football dynamics

Abstract

Keywords

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