Cinder: A fast and fair matchmaking system

A fair and fast matchmaking system is an important component of modern multiplayer online games, directly impacting player retention and satisfaction. However, creating fair matches between lobbies (pre-made teams) of heterogeneous skill levels presents a significant challenge. Matching based simply on average team skill metrics, such as mean or median rating or rank, often results in unbalanced and one-sided games, particularly when skill distributions are wide or skewed. This paper introduces Cinder, a two-stage matchmaking system designed to provide fast and fair matches. Cinder first employs a rapid preliminary filter by comparing the "non-outlier" skill range of lobbies using the Ruzicka similarity index. Lobbies that pass this initial check are then evaluated using a more precise fairness metric. This second stage involves mapping player ranks to a non-linear set of skill buckets, generated from an inverted normal distribution, to provide higher granularity at average skill levels. The fairness of a potential match is then quantified using the Kantorovich distance on the lobbies' sorted bucket indices, producing a "Sanction Score." We demonstrate the system's viability by analyzing the distribution of Sanction Scores from 140 million simulated lobby pairings, providing a robust foundation for fair matchmaking thresholds.