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Plus–minus player ratings for soccer

Author

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  • Kharrat, Tarak
  • McHale, Ian G.
  • Peña, Javier López

Abstract

The paper presents plus–minus ratings for use in association football (soccer). We first describe the general plus–minus methodology as used in basketball and ice-hockey and then adapt it for use in soccer. The usual goal-differential plus–minus is considered before two new variations are proposed. For the first variation, we present a methodology to calculate an expected goals plus–minus rating. The second variation makes use of in-play probabilities of match outcome to evaluate an expected points plus–minus rating. We use the ratings to examine who are the best players in European football, and demonstrate how the players’ ratings evolve over time. Finally, we shed light on the debate regarding which is the strongest league. The model suggests the English Premier League is the strongest, with the German Bundesliga a close runner-up.

Suggested Citation

  • Kharrat, Tarak & McHale, Ian G. & Peña, Javier López, 2020. "Plus–minus player ratings for soccer," European Journal of Operational Research, Elsevier, vol. 283(2), pages 726-736.
    • Handle: RePEc:eee:ejores:v:283:y:2020:i:2:p:726-736
    DOI: 10.1016/j.ejor.2019.11.026
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    References listed on IDEAS

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    10. Ian G. McHale & Philip A. Scarf & David E. Folker, 2012. "On the Development of a Soccer Player Performance Rating System for the English Premier League," Interfaces, INFORMS, vol. 42(4), pages 339-351, August.
    11. Ian G. McHale & Łukasz Szczepański, 2014. "A mixed effects model for identifying goal scoring ability of footballers," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 177(2), pages 397-417, February.
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    2. Buraimo, Babatunde & Forrest, David & McHale, Ian G. & Tena, J.D., 2022. "Armchair fans: Modelling audience size for televised football matches," European Journal of Operational Research, Elsevier, vol. 298(2), pages 644-655.
    3. Butler, David & Butler, Robert & Farnell, Alex & Simmons, Robert, 2024. "COVID-19 infections and short-run worker performance: Evidence from European football," European Journal of Operational Research, Elsevier, vol. 315(2), pages 750-763.
    4. McHale, Ian G. & Holmes, Benjamin, 2023. "Estimating transfer fees of professional footballers using advanced performance metrics and machine learning," European Journal of Operational Research, Elsevier, vol. 306(1), pages 389-399.
    5. Babatunde Buraimo & David Forrest & Ian G. McHale & J.D. Tena, 2020. "Armchair Fans: New Insights Into The Demand For Televised Soccer," Working Papers 202020, University of Liverpool, Department of Economics.
    6. Antonio Avila-Cano & Amparo Ruiz-Sepulveda & Francisco Triguero-Ruiz, 2021. "Identifying the Maximum Concentration of Results in Bilateral Sports Competitions," Mathematics, MDPI, vol. 9(11), pages 1-19, June.
    7. Kaori Narita & Benjamin Holmes & Ian McHale, 2022. "Managerial Contribution to Firm Success: Evidence from Professional Football Leagues," Working Papers 202224, University of Liverpool, Department of Economics.
    8. Joost Bosker & Marc Gürtler, 2024. "The impact of cultural differences on the success of elite labor migration—Evidence from professional soccer," Annals of Operations Research, Springer, vol. 341(2), pages 781-824, October.

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