Elo-MMR: A Rating System for Massive Multiplayer Competitions

Skill estimation mechanisms, colloquially known as rating systems, play an important role in competitive sports and games. They provide a measure of player skill, which incentivizes competitive performances and enables balanced match-ups. In this paper, we present a novel Bayesian rating system for contests with many participants. It is widely applicable to competition formats with discrete ranked matches, such as online programming competitions, obstacle courses races, and video games. The system’s simplicity allows us to prove theoretical bounds on its robustness and runtime. In addition, we show that it is incentive-compatible: a player who seeks to maximize their rating will never want to underperform. Experimentally, the rating system surpasses existing systems in prediction accuracy, and computes faster than existing systems by up to an order of magnitude.