Author kose-y
3 Stars
Updated Last
1 Year Ago
Started In
July 2020


TrueSkill, the video game rating system

Julia translation of the Python TrueSkill project.


This TrueSkill project is opened under the BSD license but the TrueSkill(TM) brand is not. Microsoft permits only Xbox Live games or non-commercial projects to use TrueSkill(TM). If your project is commercial, you should find another rating system.

What is TrueSkill?

TrueSkill is a rating system among game players. It was developed by Microsoft Research and has been used on Xbox LIVE for ranking and matchmaking service. This system quantifies players’ TRUE skill points by the Bayesian inference algorithm. It also works well with any type of match rule including N:N team game or free-for-all.

This project is a Julia package which implements the TrueSkill rating system.


using Pkg


Rating, the model for skill

In TrueSkill, rating is a Gaussian distribution which starts from N(25,2532). μ is an average skill of player, and σ is a confidence of the guessed rating. A real skill of player is between μ±2σ with 95% confidence.

using TrueSkill
Rating(mu=25.0, sigma=8.333333333333334)

If some player’s rating is higher β than another player’s, the player may have about a 76% chance to beat the other player. The default value of β is 25/6.

Ratings will approach real skills through few times of the TrueSkill's Bayesian inference algorithm. How many matches TrueSkill needs to estimate real skills? It depends on the game rule. See the below table:

Rule Matches
16P free-for-all 3
8P free-for-all 3
4P free-for-all 5
2P free-for-all 12
2:2:2:2 10
4:4:4:4 20
4:4 46
8:8 91

Head-to-head (1 vs. 1) match rule

r1 = Rating()
r2 = Rating()
new_r1, new_r2 = rate(r1, r2)
(Rating(mu=29.39583169299151, sigma=7.17147580700922), Rating(mu=20.604168307008482, sigma=7.17147580700922))

User should put the winner first. After the game, TrueSkill recalculates their ratings by the game rseult. You can also handle a tie game:

r1 = Rating()
r2 = Rating()
new_r1, new_r2 = rate(r1, r2; drawn=true)
(Rating(mu=24.999999999999993, sigma=6.457515683245051), Rating(mu=24.999999999999993, sigma=6.457515683245051))

Other match rules

4-player free-for-all:

r1 = Rating()
r2 = Rating()
r3 = Rating()
r4 = Rating()
new_r1, new_r2, new_r3, new_r4 = rate([r1, r2, r3, r4])
4-element Array{Rating,1}:
 Rating(mu=33.20668089498382, sigma=6.348109386291753)
 Rating(mu=27.40145515734498, sigma=5.7871628096649355)
 Rating(mu=22.598544842686724, sigma=5.787162809661523)
 Rating(mu=16.793319105008695, sigma=6.348109386298544)

4-player free-for-all with ties:

r1 = Rating()
r2 = Rating()
r3 = Rating()
r4 = Rating()
new_r1, new_r2, new_r3, new_r4 = rate([r1, r2, r3, r4]; ranks=[1, 2, 2, 4])
4-element Array{Rating,1}:
 Rating(mu=31.56397232349745, sigma=6.4047036446727095)
 Rating(mu=24.993092934523535, sigma=5.559362333660422)
 Rating(mu=25.006907065417195, sigma=5.559362333660494)
 Rating(mu=18.436027676561814, sigma=6.404703644728995)

2:2:2 match:

r1 = Rating()
r2 = Rating()
r3 = Rating()
r4 = Rating()
r5 = Rating()
r6 = Rating()
(r1, r2), (r3, r4), (r5, r6) = rate([[r1, r2], [r3, r4], [r5, r6]])
3-element Array{Array{Rating,1},1}:
 [Rating(mu=29.72018660358779, sigma=7.541668779519052), Rating(mu=29.720186603587795, sigma=7.541668779519052)]
 [Rating(mu=25.000000000002768, sigma=7.34810769389046), Rating(mu=25.000000000002764, sigma=7.34810769389046)]
 [Rating(mu=20.279813396409434, sigma=7.541668779519555), Rating(mu=20.279813396409434, sigma=7.541668779519555)]

2:1 match:

r1 = Rating()
r2 = Rating()
r3 = Rating()
t1 = [r1]
t2 = [r2, r3]
t1, t2 = rate([t1, t2]) # t1 defeats t2
2-element Array{Array{Rating,1},1}:
 [Rating(mu=33.73067114899642, sigma=7.317365362867211)]
 [Rating(mu=16.269328851003575, sigma=7.317365362867211), Rating(mu=16.269328851003575, sigma=7.317365362867211)]


The core ideas used in this project were described in "TrueSkill (TM): A Bayesian Skill Rating System" available at

Some concepts were based on Jeff Moser's code and documents, available at

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