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

Jose M. Calabuig, César Catalán, Luis M. García-Raffi () and Enrique A. Sánchez-Pérez
Additional contact information
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

Mathematics, 2024, vol. 12, issue 23, 1-18

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.

Keywords: mathematical modeling; approximation functions; football metrics; pressure model; tracking data analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/23/3854/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/23/3854/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:23:p:3854-:d:1538756

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().