TrueSkill is a skill-based ranking system developed by

Microsoft Microsoft Corporation is an American multinational corporation, multinational technology company, technology corporation producing Software, computer software, consumer electronics, personal computers, and related services headquartered at th ...

for use with video game matchmaking on

Xbox Live The Xbox network, formerly and still sometimes branded as Xbox Live, is an online multiplayer gaming and digital media delivery service created and operated by Microsoft. It was first made available to the Xbox system on November 15, 2002. An u ...

. Unlike the popular

Elo rating system The Elo rating system is a method for calculating the relative skill levels of players in zero-sum games such as chess. It is named after its creator Arpad Elo, a Hungarian-American physics professor. The Elo system was invented as an improved ...

, which was initially designed for

chess Chess is a board game for two players, called White and Black, each controlling an army of chess pieces in their color, with the objective to checkmate the opponent's king. It is sometimes called international chess or Western chess to dist ...

, TrueSkill is designed to support games with more than two players. In 2018, Microsoft published details about an extended version of TrueSkill, named TrueSkill2.

Calculation

A player's skill is represented as a

normal distribution In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is : f(x) = \frac e^ The parameter \mu i ...

\mathcal

characterized by a mean value of

\mu

(mu, representing perceived skill) and a variance of

\sigma

(sigma, representing how "unconfident" the system is in the player's

\mu

value). As such

\mathcal(x)

can be interpreted as the probability that the player's "true" skill is

x

. On Xbox Live, players start with

\mu = 25

and

\sigma = 25/3

;

\mu

always increases after a win and always decreases after a loss. The extent of actual updates depends on each player's

\sigma

and on how "surprising" the outcome is to the system. Unbalanced games, for example, result in either negligible updates when the favorite wins, or huge updates when the favorite loses surprisingly. Factor graphs and

expectation propagation Expectation propagation (EP) is a technique in Bayesian machine learning. EP finds approximations to a probability distribution. It uses an iterative approach that uses the factorization structure of the target distribution. It differs from ot ...

via moment matching are used to compute the message passing equations which in turn compute the skills for the players. Player ranks are displayed as the conservative estimate of their skill,

R = \mu - 3 \times \sigma

. This is conservative, because the system is 99% sure that the player's skill is actually higher than what is displayed as their rank. The system can be used with arbitrary scales, but Microsoft uses a scale from 0 to 50 for Xbox Live. Hence, players start with a rank of

R = 25 - 3 \cdot \frac = 0

. This means that a new player's defeat results in a large sigma loss, which partially or completely compensates their mu loss. This explains why people may gain ranks from losses.

Use in other projects

TrueSkill is patented, and the name is trademarked, so it is limited to Microsoft projects and commercial projects that obtain a license to use the algorithm.

References

External links

Microsoft Research's TrueSkill homepage

Microsoft Research's TrueSkill paper

{{Microsoft Research Rating systems Games for Windows Xbox network

Calculation

Use in other projects

See also

References

External links