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Modelling soccer matches using bivariate discrete distributions with general dependence structure
Author(s) -
McHale Ian,
Scarf Phil
Publication year - 2007
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.2007.00368.x
Subject(s) - bivariate analysis , copula (linguistics) , mathematics , covariate , poisson distribution , marginal distribution , tail dependence , bivariate data , invariant (physics) , joint probability distribution , projection (relational algebra) , statistics , econometrics , statistical physics , multivariate statistics , random variable , algorithm , physics , mathematical physics
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.