Player ranking and matchmaking for team-based multiplayer games.

Player ranking is based on the Weng-Lin Bayesian ranking algorithm which (unlike Elo) is suitable for multiplayer games. The algorithm assumes the rating of each player is a random variable following a normal distribution with mean μ, and standard deviation σ. Initially μ = 25 and σ = 25/3. Each game updates those values so the mean (μ) converges to the actual strength of each player. The actual strength of a player is within 2 standard deviations (σ) of the mean (μ) with probability 95%. For example if μ = 29 and σ = 3 we can say we are 95% confident that the player's actual strength is between 23 and 35.

Matchmaking works by trying all possible teams of equal number of players. The strength of a team is calculated by adding the ratings of all the players.

Create a text file like this:

alice john mary > bob elisa thomas
alice bob mary < john elisa thomas
elisa john mary > bob thomas alice
elisa alice mary = bob thomas john

Each line represents a game. A > B means team A beat team B. A = B means the game was a draw.

Save the file as games.txt

Run the following command to get ratings:

openmmr rank games.txt

output:

john    29.80  7.91
elisa   26.34  7.91
mary    26.14  7.91
thomas  23.86  7.91
alice   23.47  7.91
bob     20.39  7.91

The 2nd column is the mean (μ), and the 3rd column is the standard deviation (σ).

Run the following command to get all the possible teams sorted from the most balanced to the most imbalanced.

openmmr teams games.txt

output:

[john thomas bob]  vs  [elisa mary alice]  74.05 vs 75.95  -1.90
[john mary bob]  vs  [elisa thomas alice]  76.32 vs 73.68  2.65
[john alice bob]  vs  [elisa mary thomas]  73.66 vs 76.34  -2.68
[john elisa bob]  vs  [mary thomas alice]  76.53 vs 73.47  3.06
[john thomas alice]  vs  [elisa mary bob]  77.13 vs 72.87  4.26
[john mary alice]  vs  [elisa thomas bob]  79.41 vs 70.59  8.81
[john elisa alice]  vs  [mary thomas bob]  79.61 vs 70.39  9.22
[john mary thomas]  vs  [elisa alice bob]  79.80 vs 70.20  9.59
[john elisa thomas]  vs  [mary alice bob]  80.00 vs 70.00  10.00
[john elisa mary]  vs  [thomas alice bob]  82.27 vs 67.73  14.55

This command won't work if the file games.txt contains an odd number of players. In that case you can exclude one or more players like this:

openmmr teams --exclude john,elisa games.txt
openmmr teams --include alice,bob,thomas,mary games.txt

You can also generate teams by using as input a file that contains ratings (instead of games) like this:

openmmr rank games.txt > ratings.txt
openmmr teams-from-rank ratings.txt

Or you can use "-" to read from the standard input like this:

openmmr rank games.txt | openmmr teams-from-rank -

Linux, Windows 8.1+, macOS 10.13+

Download the latest release and run it. No installation is required.

On macOS you have to remove the application from quarantine by following the instructions here, or by running the following command:

xattr -d com.apple.quarantine /path/to/openmmr

Requires Zig v0.9.0

Run zig build at the root of the repository.

Copyright (C) 2021 Charalampos Mitsakis

openMMR is licensed under the EUPL-1.2-or-later.

The implementation of the Weng-Lin Bayesian ranking algorithm in the file weng_lin/rank.c is licensed under the terms of the BSD-3-Clause license.