Investigating Efficiency of Free-for-All Models in a Matchmaking Context

We explore several popular (and unpopular) systems for matchmaking and ranking in free-for-all environments. The commonplace existing methods involve the reinterpretation of established two-player ranking systems (i.e., Elo/Glicko) and decomposing multiplayer games into a set of multiple one-versus-one pairings. This decomposition, while commonplace, is not part of the intended use-case of these two-player ranking systems. We are the first to formally explore this ad-hoc usage and reassuringly find evidence that it converges to correct values. Second, we identify a method that appears to dominate what appears to be the most common publicly used method. At the same time, this novel method maintains fidelity to many games for which there is no “second place,” whereas in other systems, second place winners are given a large boost in rankings. Third, some idiosyncrasies about the reward structure and distribution of each of the systems are identified, which may affect user experience and satisfaction. This system was tested by simulation and deployment in a real world matchmaking system with over 135 000 games played. Our tests suggest it converges on appropriate player rank at a similar or better rate as the most popular alternative.