Cinder: A fast and fair matchmaking system
Saurav Pal
TL;DR
The paper addresses fair matchmaking for lobbies with heterogeneous skill by introducing Cinder, a two-stage system. The first stage performs a fast non-outlier range overlap check using the Ruzicka similarity; the second stage maps players to non-linear skill buckets and computes the Kantorovich distance (Wasserstein distance) $W_1$ between lobby distributions to produce the Sanction Score. A 140 million-sample simulation demonstrates the Sanction Score distribution is right-skewed and suitable for data-driven thresholds to balance fairness and queue time. The work also outlines avenues for live deployment and extensions, such as incorporating wait time and role preferences and optimizing bucket widths for game-specific demographics.
Abstract
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.