Predicting sports outcomes : Investigating adaptive learning rates in the Elo rating system

Details

Supervisors

Absil, Pierre-Antoine ; Hendrickx, Julien

Faculty

Ecole polytechnique de Louvain

Degree label

Master [120] : ingénieur civil en mathématiques appliquées, à finalité spécialisée

Abstract

enThis thesis investigates the prediction of sports outcomes through rating systems. Usually, these systems use a constant parameter, denoted as K, to update the ratings. In a standard rating system, the K parameter determines how strongly ratings react to new observations (i.e. result of a new game). Although it is generally chosen as a fixed constant, such a specification may be poorly suited to environments in which players' underlying abilities evolve over time. Such a choice also overlooks the uncertainty associated with the start of the season compared to the end of the season. The aim of this work is to improve prediction abilities of existing systems by proposing adaptive methods where this K parameter is not fixed anymore, with a particular emphasis on the Elo Rating System. Several adaptive K parameter methods are therefore proposed and compared. These include optimisation-based approaches that select K according to past rating trajectories, terminal rating estimates, or predictive performance, as well as analytical rules based on uncertainty, outcome variance, persistent prediction errors, empirical rating volatility, and change-point detection. The methods are evaluated against a constant-K baseline, a decreasing K parameter, and an oracle benchmark. Their performance is studied through experimental simulations involving a wide range of dynamic ability profiles and through an application to real basketball data. The comparison relies on predictive accuracy, the Brier score, and a centred measure of rating estimation error. The results assess whether allowing the K parameter to respond to observed information can improve both outcome prediction and the tracking of time-varying player abilities. The experiments show that, although some scenarios are favorable to adaptive methods, their performance remains too unstable to constitute a reliable alternative to a constant-K rule. Results on real basketball data reinforce this finding, suggesting that the additional flexibility offered by adaptive K factors does not translate into sufficiently consistent predictive improvements to outweigh the robustness of a well-calibrated constant K.