Modelling the dependence of goals scored by opposing teams in international soccer matches

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

Get full access to this article

View all access options for this article.

References

Dixon, MJ and Coles SG 1997) Modelling association football scores and inefficiencies in the football betting market. Applied Statistics, 46, 265–80.

Forrest DK and Simmons R 2000) Forecasting sport: the behaviour and performance of football tipsters. International Journal of Forecasting, 16, 317–31.

Genest C and Favre A-C 2007) Everything you wanted to know about copula modelling but were afraid to ask. Journal of Hydrological Engineering, 12, 347–68.

Genest C and Neslehova J 2007) A primer on copulas for count data. Astin Bulletin, 37, 475–415.

Goddard J 2005) Regression models for forecasting goals and match results in association football. International Journal of Forecasting, 21, 331–40.

Goddard J and Asimakopoulos I 2004) Forecasting football match results and the efficiency of fixed-odds betting. Journal of Forecasting, 23, 51–66.

Joe H 1997 Multivariate models and dependence concepts. London: Chapman & Hall.

Karlis D and Ntzoufras J 2003) Analysis of sports data using bivariate poisson models. The Statistician, 52, 381–93.

Koning RH 2000) Balance in competition in Dutch soccer. The Statistician, 49, 419–31.

10.

Maher MJ 1982) Modelling association football scores. Statistica Neerlandica, 36, 109–18.

11.

McHale IG and Scarf PA 2007) Modelling soccer matches using bivariate discrete distributions with general dependence structure. Statistica Neerlandica, 61, 432–45.

12.

Moroney MJ 1956 Facts from figures, 3rd edition, p. 102. London: Penguin.

13.

Nelsen RB 2006 An introduction to copulas, 2nd edition. Springer: New York.

14.

R Development Core Team 2005 R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing http://www.R-project.org.

15.

Reep R , Pollard R and Benjamin B 1971) Skill and chance in ball games. Journal of the Royal Statistical Society A, 134, 623–29.

16.

Ridder G , and Cramer JS and Hopstaken P 1994) Down to ten: estimating the effect of a red card in soccer. Journal of the American Statistical Association, 89, 1124–27.

17.

Sklar A 1959) Fonctions de répartition à n dimensions et leurs marges. Publications de I’Institut de Statistique de L’Université de Paris, 8, 229–31.