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Interactions between soccer teams reveal both design and emergence: Cooperation, competition and Zipf-Mandelbrot regularity

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  • Ramos, João Paulo
  • Lopes, Rui J.
  • Araújo, Duarte

Abstract

Considering soccer matches as complex systems facilitates the identification of properties that emerge from the interactions between players. Such properties include the regularities and statistical patterns that characterize couplings and sets between players established during matches. Empirical studies on the statistical distributions of number of items (e.g., words in texts) have shown that these distributions follow scaling properties according to empirical laws known as Zipf-Mandelbrot. Here we investigate whether the (re)occurrence of pitch location of sets of players in a soccer match also obeys these empirical laws. Data collected from 10 soccer matches shows that, for most sets of players, this seems to be the case. Exceptions were found in particular types of sets, such as goalkeeper and goal, and left defender and right attacker from opposite teams. Rather than challenging the hypothesis that a Zipf-Mandelbrot law defines this system, these exceptions may be explained by the players configuration design, which is a trait of human interaction within complex systems. This design expresses match strategy, before the team enters in such dynamical processes (the game).

Suggested Citation

  • Ramos, João Paulo & Lopes, Rui J. & Araújo, Duarte, 2020. "Interactions between soccer teams reveal both design and emergence: Cooperation, competition and Zipf-Mandelbrot regularity," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    • Handle: RePEc:eee:chsofr:v:137:y:2020:i:c:s0960077920302721
    DOI: 10.1016/j.chaos.2020.109872
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    References listed on IDEAS

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    1. Gang Li & Xiaoyan Wang, 2019. "Prediction Accuracy Measures for a Nonlinear Model and for Right-Censored Time-to-Event Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(528), pages 1815-1825, October.
    2. Babu, G. J. & Bose, A., 1988. "Bootstrap confidence intervals," Statistics & Probability Letters, Elsevier, vol. 7(2), pages 151-160, September.
    3. Malacarne, L.C & Mendes, R.S, 2000. "Regularities in football goal distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 286(1), pages 391-395.
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    Cited by:

    1. Pereira, Luis Ramada & Lopes, Rui J. & Louçã, Jorge & Araújo, Duarte & Ramos, João, 2021. "The soccer game, bit by bit: An information-theoretic analysis," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    2. Yu, Dakuan & Ta, Wurui & Zhou, Youhe, 2021. "Fractal diffusion patterns of periodic points in the Mandelbrot set," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).

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