TrueSkill

TrueSkill is a skill-based ranking system developed by Microsoft for use with video game matchmaking on Xbox Live. Unlike the popular Elo rating system, which was initially designed for chess, TrueSkill is designed to support games with more than two players.

A player's skill is represented as a normal distribution ${\displaystyle {\mathcal {N}}}$ characterized by a mean value of ${\displaystyle \mu }$ (mu, representing perceived skill) and a variance of ${\displaystyle \sigma }$ (sigma, representing how "unconfident" the system is in the player's ${\displaystyle \mu }$ value). As such ${\displaystyle {\mathcal {N}}(x)}$ can be interpreted as the probability that the player's "true" skill is ${\displaystyle x}$.

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