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A Mathematical Model to Study Defensive Metrics in Football: Individual, Collective and Game Pressures

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  • Jose M. Calabuig

    (InstitutoUniversitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camí de Vera s/n, 46022 Valencia, Spain)

  • César Catalán

    (InstitutoUniversitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camí de Vera s/n, 46022 Valencia, Spain)

  • Luis M. García-Raffi

    (InstitutoUniversitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camí de Vera s/n, 46022 Valencia, Spain)

  • Enrique A. Sánchez-Pérez

    (InstitutoUniversitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camí de Vera s/n, 46022 Valencia, Spain)

Abstract

Performance analysis, utilizing video technology and recent technological advancements in soccer stadiums, provides a wealth of data, including player trajectories and real-time game statistics, which are crucial for tactical evaluation and decision-making by coaches and players. These data allow for the definition of metrics that not only enrich the experience for soccer fans through enhanced visual displays but also empower coaching staff and managers to make informed, real-time decisions that directly impact match outcomes. Ultimately, these data serve as a pivotal tool for improving team strategy based on comprehensive post-match data analysis. In this article, we present a mathematical model to study the concept of pressure between players and, subsequently, between teams. We first explore the concept in a fixed frame of a match, determining what we call influence areas between players. We introduce the unit pressure function and analyze the total number of pressure interactions. Then, we apply these concepts to football matches, considering various factors such as players and the radius of the area of influence and examining pressure efficiency through mean unitary pressure. Lastly, a real case study is presented, showcasing visualizations like a heatmap matrix displaying individual and collective pressure, as well as the team pressure balance.

Suggested Citation

  • Jose M. Calabuig & César Catalán & Luis M. García-Raffi & Enrique A. Sánchez-Pérez, 2024. "A Mathematical Model to Study Defensive Metrics in Football: Individual, Collective and Game Pressures," Mathematics, MDPI, vol. 12(23), pages 1-18, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3854-:d:1538756
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    References listed on IDEAS

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    1. Adam Hewitt & Grace Greenham & Kevin Norton, 2016. "Game style in soccer: what is it and can we quantify it?," International Journal of Performance Analysis in Sport, Taylor & Francis Journals, vol. 16(1), pages 355-372, April.
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