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Modelling soccer matches using bivariate discrete distributions with general dependence structure

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  • Ian McHale
  • Phil Scarf

Abstract

In this paper copulas are used to generate bivariate discrete distributions. These distributions are fitted to soccer data from the English Premier League. An interesting aspect of these data is that the primary variable of interest, the discrete pair shots‐for and shots‐against, exhibits negative dependence; thus, in particular, we apply bivariate Poisson‐related distributions that allow such dependence. The paper focuses on Archimedian copulas, for which the dependence structure is fully determined by a one‐dimensional projection that is invariant under marginal transformations. Diagnostic plots for copula fit based on this projection are adapted to deal with discrete variables. Covariates relating to within‐match contributions such as numbers of passes and tackles are introduced to explain variability in shot outcomes. The results of this analysis would appear to support the notion that playing the ‘beautiful game’ is an effective strategy—more passes and crosses contribute to more effective play and more shots on the goal.

Suggested Citation

  • Ian McHale & Phil Scarf, 2007. "Modelling soccer matches using bivariate discrete distributions with general dependence structure," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 61(4), pages 432-445, November.
    • Handle: RePEc:bla:stanee:v:61:y:2007:i:4:p:432-445
    DOI: 10.1111/j.1467-9574.2007.00368.x
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    Cited by:

    1. Scarf, Philip & Yusof, Muhammad Mat & Bilbao, Mark, 2009. "A numerical study of designs for sporting contests," European Journal of Operational Research, Elsevier, vol. 198(1), pages 190-198, October.
    2. Hendrik van der Wurp & Andreas Groll, 2023. "Introducing LASSO-type penalisation to generalised joint regression modelling for count data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 107(1), pages 127-151, March.
    3. Heiner Matthew & Fellingham Gilbert W. & Thomas Camille, 2014. "Skill importance in women’s soccer," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 10(2), pages 1-16, June.
    4. Yuvraj Sunecher & Naushad Mamode Khan & Vandna Jowaheer & Marcelo Bourguignon & Mohammad Arashi, 2019. "A Primer on a Flexible Bivariate Time Series Model for Analyzing First and Second Half Football Goal Scores: The Case of the Big 3 London Rivals in the EPL," Annals of Data Science, Springer, vol. 6(3), pages 531-548, September.
    5. Scarf, Phil & Parma, Rishikesh & McHale, Ian, 2019. "On outcome uncertainty and scoring rates in sport: The case of international rugby union," European Journal of Operational Research, Elsevier, vol. 273(2), pages 721-730.
    6. 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.
    7. Cunniffe Nik J & Cook Alex R, 2009. "Cruel and Unusual Punishment? An Analysis of Point Deduction in European Association Football Leagues," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 5(4), pages 1-20, October.
    8. Jacek Osiewalski & Jerzy Marzec, 2019. "Joint modelling of two count variables when one of them can be degenerate," Computational Statistics, Springer, vol. 34(1), pages 153-171, March.
    9. Kosuke Toda & Masakiyo Teranishi & Keisuke Kushiro & Keisuke Fujii, 2022. "Evaluation of soccer team defense based on prediction models of ball recovery and being attacked: A pilot study," PLOS ONE, Public Library of Science, vol. 17(1), pages 1-14, January.
    10. Baker, Rose, 2008. "An order-statistics-based method for constructing multivariate distributions with fixed marginals," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2312-2327, November.
    11. Oberstone Joel, 2010. "Comparing English Premier League Goalkeepers: Identifying the Pitch Actions that Differentiate the Best from the Rest," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 6(1), pages 1-19, January.
    12. So, Sunha & Lee, Dong-Hee & Jung, Byoung Cheol, 2011. "An alternative bivariate zero-inflated negative binomial regression model using a copula," Economics Letters, Elsevier, vol. 113(2), pages 183-185.
    13. Oberstone Joel, 2009. "Differentiating the Top English Premier League Football Clubs from the Rest of the Pack: Identifying the Keys to Success," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 5(3), pages 1-29, July.

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