A bivariate Weibull count model for forecasting association football scores

Abstract

The paper presents a forecasting model for association football scores. The model uses a Weibullinter-arrival times based count process and a copula to produce a bivariate distribution for the number of goals scored by the home and away teams in a match. We test it against a variety of alternatives, including the simpler Poisson distribution-based model and an independent version of our model. The out-of-sample performance of our methodology is illustrated first using calibration curves and then in a Kelly-type betting strategy that is applied to the pre-match win/draw/loss market and to the over-under 2.5 goals market. The new model provides an improved fit to data compared to previous models and results in positive returns to betting.

A Bayesian In-Play Prediction Model for Association Football Outcomes

“…Ref. [12] used a Weibull inter-arrival-times-based count process and a copula to produce a bivariate distribution of the numbers of goals acored by the home and away teams in a match.…”

“…A player based model proposed by [19], which is one of the state of the art model, is chosen as a comparator pre-match forecasting model. Their basic model for the scoreline in a football match is a bivariate Weibull count model described by [12]. In addition, the dynamic nature of team strengths are also incorporated into the player-based model.…”

“…Calibration can be intuitively seen as a way to visualise how often a model is right or wrong [12]. In this section, we directly evaluate the calibration of the approximation Bayesian model's posterior prediction distribution using 1520 matches from from August 2013 to May 2017.…”

“…In addition, because the Poisson count model only applies in instances where the data are time-homogeneous and equi-dispersed, McShane [11] proposed the count model based on Weibull interarrival times, which were capable of managing both under and over-dispersed data. Boshnakov et al [12] applied the Weibull model for forecasting association football scores, and the results demonstrated it performed better than the Poisson count model. Recently, Ref.…”

“…[19] presented a player-based model for football scores which takes into account the abilities of the players on each team. In addition, their basic model for the scoreline in a football match is a bivariate Weibull count model proposed by [12].…”