Cinder通过双阶段匹配，提升异质团队公平性与速度。
Cinder: A fast and fair matchmaking system
- 先用鲁齐卡相似度快速筛选非异常技能范围的队伍
- 再用非线性技能桶与坎托罗维奇距离计算公平得分
- 适用于对匹配公平性要求高的多人在线游戏
公平高效的匹配系统是现代多人在线游戏的关键，直接影响玩家留存与满意度。然而，将技能水平各异的队伍进行公平匹配面临挑战。仅依据平均分或中位数等指标匹配，常导致游戏失衡，尤其在技能分布宽或偏斜时更为明显。本文提出Cinder，一种两阶段匹配系统，兼顾速度与公平。第一阶段使用鲁齐卡相似度，基于队伍的非异常技能范围进行快速预筛选；通过该筛选的队伍进入第二阶段，采用逆正态分布生成非线性技能桶，实现平均技能区间的更高粒度划分。匹配公平性通过坎托罗维奇距离在排序后的技能桶索引上计算，生成“制裁分”（Sanction Score）。我们通过1.4亿次模拟队列配对分析了制裁分分布，为公平匹配阈值提供了坚实基础。
原文摘要 · Abstract (English)
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.
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