Domain-Driven Identification of Football Probabilities

Obtaining accurate estimates of the true probabilities of sporting events remains a long-standing problem in sports analytics. In this paper we propose a new domain-driven approach that infers true probabilities from betting odds. This task is not trivial, as betting odds are noisy because of bookmaker margins (vig), insider bets, and model imperfections. In this study, we present a novel approach that integrates estimates across multiple groups of betting markets to obtain more robust estimates of true probability. Our method takes market structure into account and constructs a constrained optimisation problem that is solved using the Dixon–Coles model of a football match. We compare our approach with a wide range of existing methods, using a large dataset of 359035 matches from more than 6000 leagues. The proposed method achieves the lowest log-loss and the best probability calibration among all tested approaches. It also performs the best in terms of expected profit convergence in Monte Carlo simulations, outperforming its competitors in terms of MSE and bias. This study contributes both to a new margin-removal (devig) method and provides a comprehensive comparative analysis of other known methods. Beyond football, this approach has potential applications in other sports with discrete scoring systems and potentially in other areas involving stochastic processes and market inference, such as prediction markets, finance, reliability engineering, and social prediction systems.