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Modeling Tactical Changes of Formation in Association Football as a Non-Zero-Sum Game

Author

Listed:
  • Hirotsu Nobuyoshi

    (Juntendo University)

  • Ito Masamitsu

    (Nippon Sport Science University)

  • Miyaji Chikara

    (Japan Institute of Sports Sciences)

  • Hamano Koji

    (Juntendo University)

  • Taguchi Azuma

    (Chuo University)

Abstract

In football leagues, a won match produces three points (all for the winner) whereas a drawn match produces only two (one for each team). Here, the total resource from the viewpoint of league points is not constant and the gain of the match for both teams changes depending on the result of the match. To cater for this situation, we propose a formulation for modelling tactical changes of formation in an association football match as a non-zero-sum game using game theory. In this paper, we focus on two well-known teams in the J. League and analyse their offensive and defensive strengths based on their formation, i.e., a combination of the number of each type of outfield player on the pitch. Using these estimated offensive and defensive strengths, we develop the mathematical formulation for analyzing tactical changes of these teams' formations from the viewpoint to increase their expected number of league points gained in a match, and quantitatively demonstrate not only the effect of the introduction of the league point system on the tactical change, but also the effect of cooperation between managers which could make both teams benefit in terms of the expected number of league points gained in a match.

Suggested Citation

  • Hirotsu Nobuyoshi & Ito Masamitsu & Miyaji Chikara & Hamano Koji & Taguchi Azuma, 2009. "Modeling Tactical Changes of Formation in Association Football as a Non-Zero-Sum Game," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 5(3), pages 1-15, July.
    • Handle: RePEc:bpj:jqsprt:v:5:y:2009:i:3:n:2
    DOI: 10.2202/1559-0410.1138
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    References listed on IDEAS

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    1. M Wright & N Hirotsu, 2003. "The professional foul in football: Tactics and deterrents," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(3), pages 213-221, March.
    2. Hirotsu Nobuyoshi & Wright Mike B, 2006. "Modeling Tactical Changes of Formation in Association Football as a Zero-Sum Game," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 2(2), pages 1-22, April.
    3. M. J. Maher, 1982. "Modelling association football scores," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 36(3), pages 109-118, September.
    4. D Dyte & S R Clarke, 2000. "A ratings based Poisson model for World Cup soccer simulation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 51(8), pages 993-998, August.
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    Cited by:

    1. Myers Bret R., 2012. "A Proposed Decision Rule for the Timing of Soccer Substitutions," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 8(1), pages 1-24, March.

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