Modelling association football scores

Abstract

Previous authors have rejected the Poisson model for association football scores in favour of the Negative Binomial. This paper, however, investigates the Poisson model further. Parameters representing the teams' inherent attacking and defensive strengths are incorporated and the most appropriate model is found from a hierarchy of models. Observed and expected frequencies of scores are compared and goodness‐of‐fit tests show that although there are some small systematic differences, an independent Poisson model gives a reasonably accurate description of football scores. Improvements can be achieved by the use of a bivariate Poisson model with a correlation between scores of 0.2.

pi-football: A Bayesian network model for forecasting Association Football match outcomes

“…A common approach is the Poisson distribution goal-based data analysis whereby match results are generated by the attack and defence parameters of the two competing teams (Maher, 1982;Dixon & Coles, 1997, Lee 1997Karlis & Ntzoufras, 2003). A similar version is also reported in (Dixon & Pope, 2004) where the authors demonstrate profitability against the market only at very high levels of discrepancy, but which relies on small quantities of bets against an unspecified bookmaker.…”

Strategy selection and outcome prediction in sport using dynamic learning for stochastic processes

“…This technique was published in several articles including those by Maher (1982) and Dixon and Coles (1997). Although these papers adopt this bivariate approach for 'between-game' data, the underlying principle is the same as for 'within-game' data.…”

“…Suitable discrete candidates are the multivariate Poisson distribution, the multinomial distribution and the multivariate hypergeometric distribution. See Maher (1982) and Dixon and Coles (1997) for examples of this approach that use 'between-game' observations arising from football games. Continuous options include the multivariate normal distribution, after linear transformation of x n if required.…”

A generative model for predicting outcomes in college basketball

“…The soccer model by Maher (1982) or Dixon and Coles (1997) introduces an attack and defense coefficient for each team t = 1,…,T, denoted, respectively, by α t and β t . Given these coefficients, the number of scores obtained by the home and away sides at game m are independently distributed as …”

“…In the literature, we can find several variants of a simple model for soccer that identifies each team by its attack and defense coefficients (Baio and Blangiardo 2010;Crowder et al 2002;Dixon and Coles 1997;Heuer, Muller, and Rubner 2010;Maher 1982). In all these works, the score for the home team is drawn from a Poisson distribution, whose mean is the multiplicative contribution of the home team attack coefficient and the away team defense coefficient.…”