Predicting match outcomes in football by an Ordered Forest estimator

Predicting the outcome of football (i.e. soccer) games based on past information is a non-standard predictive task because of the nature of the game outcome, as well as because of the importance of uncertainty (luck and unobservables). The game outcome consists of the scores of the two teams that are usually either collapsed into a goal-difference or further aggregated to reflect whether the game ended as a win for the home or away team, or as a draw. From a statistical perspective, such outcomes have bounded support and, thus, standard linear modelling can be expected to perform poorly. The large amount of uncertainty in the game outcomes due to just luck or due to game- or team-specific unobservables (e.g. hidden injuries of players, etc.) makes it imperative to use prediction methods that fully exploit the potential of the available information, as well as to uncover the uncertainty of a match outcome. The latter is also relevant when interest is not only in single games but also in a league table at the end of the season. Obviously, such league tables should capture the uncertainty for the single games accumulated over a season to be useful guides on what to expect. Recently, machine learning methods have shown their power in all sorts of prediction problems, in particular in situations where the relation of the variables capturing the information used to predict with the target of the prediction, i.e. here the outcome of the game, is non-linear. However, so far there has been only little development in gearing these methods explicitly towards the estimation of the probabilities of ordered outcomes, such as score differences and points, or just wins, draws, and losses. Lechner and Okasa (2019) propose adapting classical random forest estimation, which is known to have excellent predictive performance (e.g. Biau and Scornet (2016), Fernández-Delgado et al. (2014)) to the problem of predicting probabilities of ordered categorical outcomes, such as the win-draw-loss problem of a football game. In this chapter, we use their approach to predict game outcomes of the German Bundesliga 1 (BL1) based on more than ten years' data on game outcomes as well as extensive information about teams, their players, and their environment. These predictions are then used to obtain the final season rankings in a way that reflects and shows the magnitude of the inherent uncertainty of football games.