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

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Author Info

  • 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)

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    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.

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    File URL: http://www.degruyter.com/view/j/jqas.2009.5.3/jqas.2009.5.3.1138/jqas.2009.5.3.1138.xml?format=INT
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    Bibliographic Info

    Article provided by De Gruyter in its journal Journal of Quantitative Analysis in Sports.

    Volume (Year): 5 (2009)
    Issue (Month): 3 (July)
    Pages: 1-15

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    Handle: RePEc:bpj:jqsprt:v:5:y:2009:i:3:n:2

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    Web page: http://www.degruyter.com

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