Forecasting Outcomes Using Multi-Option, Advantage-Sensitive Thurstone-Motivated Models

In this paper, multi-option probabilistic paired comparison models are presented and applied for prediction. As these models operate on the basis of probabilities, they can estimate the likelihood of future outcomes and thus predict future events. The aim of the paper is to demonstrate that these models have strong predictive capabilities when the information embedded into the data is properly utilized. To this end, we incorporate the degree (e.g., large or small) of the differences between the compared objects. By refining the usual three-option model, we define a five-option model capable of leveraging information derived from the goal differences. To incorporate additional information, the model is further extended to account for potential advantages in the comparisons. As a further refinement, temporal weighting is also introduced. These models are applied to forecasting football match outcomes in the top five European leagues (Premier League, La Liga, Serie A, Bundesliga, and Ligue 1), and their predictive performance is evaluated using various metrics. Based on the most recent football seasons, this model consistently delivers better predictive metrics, on average, than those of the already strong benchmark model. The effect of a home-field advantage is statistically supported across all five leagues. The model fits are illustrated using confidence intervals, and, as an interesting insight, we also present the evolution of the team strengths for the top four English clubs during the 2023/24 season.