Bayesian modelling of football outcomes: using the Skellam's distribution for the goal difference

Modelling football match outcomes is becoming increasingly popular nowadays for both team managers and betting funs. Most of the existing literature deals with modelling the number of goals scored by each team. In this paper, we work in a different direction. Instead of modelling the number of goals directly, we focus on the difference of the number of goals, i.e. the margin of victory. Modelling the differences instead of the scores themselves has some major advantages. Firstly, we eliminate correlation imposed by the fact that the two opponent teams compete each other, and secondly, we do not assume that the scored goals by each team are marginally Poisson distributed. Application of the Bayesian methodology for the Skellam's distribution using covariates is discussed. Illustrations using real data from the English Premiership for the season 2006-2007 are provided. The advantages of the proposed approach are also discussed.