Statistical Modelling 11 (2011), 219236
Modelling the dependence of goals scored by opposing teams in
international soccer matches
Ian McHale
Centre for Operational Research and Applied Statistics,
and Centre for the Study of Gambling,
Salford Business School,
University of Salford
Greater manchester M5 4WT
UK
eMail: i.mchale@salford.ac.uk
Phil Scarf
Centre for the Study of Gambling,
University of Salford
UK
Abstract:
This paper presents models for the number of goals scored by opposing
teams in international soccer matches. The bivariate discrete
distributions employed are defined in terms of the marginal distributions
and a dependence copula. This copula representation allows dependence in
the bivariate distribution to be modelled in a flexible manner by
specifying a suitable family of copula functions and fitting this to the
bivariate data using maximum likelihood. Marginal means are modelled with
match covariates. The nature of the dependence in the number of goals
scored is complex, and we develop the idea that the strength of dependence
depends on the competitive balance of a match. Our analysis suggests that
for games between closely matched teams, the overall dependence is low,
and that the dependence becomes increasingly negative as the competitiveness
of a match decreases. In this way, we relate dependence to competitive
balance and suggest a method to measure the latter quantity. The models
developed here may also offer better forecasts than those offered by
match outcome models with independent marginal distributions.
Keywords:
competitive balance; copula; football; negative binomial
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