Modelling Association Football Scores and Inefficiencies in the Football Betting Market

Abstract

A parametric model is developed and fitted to English league and cup football data from 1992 to 1995. The model is motivated by an aim to exploit potential inefficiencies in the association football betting market, and this is examined using bookmakers' odds from 1995 to 1996. The technique is based on a Poisson regression model but is complicated by the data structure and the dynamic nature of teams' performances. Maximum likelihood estimates are shown to be computationally obtainable, and the model is shown to have a positive return when used as the basis of a betting strategy.

How efficient is the European football betting market? Evidence from arbitrage and trading strategies

“…Cain et al (2000) developed a model in which the goal-scoring processes of the home and away teams follow a Poisson and a negative binomial distribution, respectively, but found very few profi table opportunities. In contrast, Dixon and Coles (1997) and Goddard and Asimakopoulos (2004) reported substantial out-of-sample profi ts from strategies based on Poisson and ordered probit models, respectively. Both these papers test for semi-strong market ineffi ciency since they incorporate information on past match results and other publicly available explanatory variables.…”

“…It has been shown in the literature (e.g., Dixon and Coles, 1997;Cain et al, 2000) that the goalscoring processes of the home and away teams can be well approximated by independent Poisson processes. The density of the distribution of the number of occurrences of an event is given by …”

Score-Based Bayesian Skill Learning

“…This yields a quadratic equation, and we take the positive solution since exp(κ) must be non-negative (see the Supplemental material). The result gives us (16).…”

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

“…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.…”

“…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.…”