Two main approaches are considered when building statistical models for football outcomes: (1) the goal-based approach, where the number of goals scored by two competing teams is modelled, and (2) the result-based approach, where a three-category outcome (win–draw–loss) is modelled. The debate about which approach is preferable is still ongoing, although the general agreement is that any direct comparison between the forecasting abilities of the two approaches should be based on the quality of the forecasts. Alternatively, a greater emphasis can be given to diagnostic measures in order to judge the quality of model specifications, as is more customary in statistical modelling. In this paper, we develop a broad comparison of four possible Bayesian models, focusing on model checking and calibration and then using Markov chain Monte Carlo replications to explore the predictive performance over future matches. Although inconclusive, we believe our set of comparison tools may be beneficial for future scholars in differentiating the two approaches.
