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The optimal layout of football players: A case study for AC Milan

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  • Papahristodoulou, Christos

Abstract

This paper attempts to find the optimal formation of three midfielders and three forward football players on ground, using the classic Quadratic Assignment Problem or Facility Layout problem. Players are treated as “machines”, their positions as locations, and the flow of materials between machines as “flow of passes” and “flow of markings”. Based on detailed statistics from four matches of AC Milan, and formulated the problem as minimum (quick strategy), maximum (slow strategy), and mixed or balanced strategies, a number of various layouts emerged. Compared to the initial formation of players, the efficiency time gains in the unconditioned layouts are between 3 and 6.8%. Also, when the manager claims that his three forwards shouldn’t shift positions with the midfielders, the efficiency gains in these restricted layouts is about 14´´ to 74´´, which is about 1 to 3% of the approximately 40´ effective time spent into passes and markings from both teams.

Suggested Citation

  • Papahristodoulou, Christos, 2009. "The optimal layout of football players: A case study for AC Milan," MPRA Paper 20102, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:20102
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    References listed on IDEAS

    as
    1. Loiola, Eliane Maria & de Abreu, Nair Maria Maia & Boaventura-Netto, Paulo Oswaldo & Hahn, Peter & Querido, Tania, 2007. "A survey for the quadratic assignment problem," European Journal of Operational Research, Elsevier, vol. 176(2), pages 657-690, January.
    2. Papahristodoulou, Christos, 1999. "A Pure Binary LP Model to the Facility Layout Problem," Working Paper Series 1999:13, Uppsala University, Department of Economics.
    3. Yang, Taho & Kuo, Chunwei, 2003. "A hierarchical AHP/DEA methodology for the facilities layout design problem," European Journal of Operational Research, Elsevier, vol. 147(1), pages 128-136, May.
    4. Hahn, Peter M. & Kim, Bum-Jin & Stutzle, Thomas & Kanthak, Sebastian & Hightower, William L. & Samra, Harvind & Ding, Zhi & Guignard, Monique, 2008. "The quadratic three-dimensional assignment problem: Exact and approximate solution methods," European Journal of Operational Research, Elsevier, vol. 184(2), pages 416-428, January.
    5. Papahristodoulou, Christos, 2007. "An analysis of Champions League match statistics," MPRA Paper 3605, University Library of Munich, Germany.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Papahristodoulou, Christos, 2012. "Optimal football strategies: AC Milan versus FC Barcelona," MPRA Paper 35940, University Library of Munich, Germany.

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    More about this item

    Keywords

    sports; layout; assignment; football players; passes; markings; time;
    All these keywords.

    JEL classification:

    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • L83 - Industrial Organization - - Industry Studies: Services - - - Sports; Gambling; Restaurants; Recreation; Tourism
    • C81 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Microeconomic Data; Data Access

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