Modeling Tactical Changes of Formation in Association Football as a Non-Zero-Sum Game
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Nobuyoshi Hirotsu
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.
©2011 Walter de Gruyter GmbH & Co. KG, Berlin/Boston
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Articles in the same Issue
- Article
- Research on the Prediction of the likely Winners of the Euro 2008 Football Tournament
- Modeling Tactical Changes of Formation in Association Football as a Non-Zero-Sum Game
- Estimating Quality in Home Advantage and Competitive Balance in the Portuguese Football League
- Testing for Bias and Manipulation in the National Basketball Association Playoffs
- A Parametric Control Chart for Monitoring Individual Batting Performances in Cricket
- Dominance, Intimidation, and 'Choking' on the PGA Tour
- Monte Carlo Tennis: A Stochastic Markov Chain Model
- NCAA Tournament Games: The Real Nitty-Gritty
- The Effect of the Scoring System Changes in Volleyball: A Model and an Empirical Test
- Differentiating the Top English Premier League Football Clubs from the Rest of the Pack: Identifying the Keys to Success
