Introduction

openskill.lua is an implementation of the Weng-Lin Bayesian ranking, a better, license-free alternative to TrueSkill.

It is a port of the amazing openskill.js module.

Firstly, get the module here and insert it into your game (preferably ServerStorage). You can also just paste this in the command bar: 

game:GetObjects("rbxassetid://8134663273")[1].Parent=game.ServerStorage


Create a script and require the module: 

local OpenSkill = require(game.ServerStorage.OpenSkill)


You can create a rating for every player, which describes their skill. Ratings are kept as an object which represent a gaussian curve, with properties where mu represents the mean, and sigma represents the spread or standard deviation. Create these with: 

local a1 = OpenSkill.Rating() --> {mu = 25, sigma = 8.333333333333334}
local a2 = OpenSkill.Rating(32.444) --> {mu = 32.444, sigma = 10.81466666666667}
local b1 = OpenSkill.Rating(nil, 2.421) --> {mu = 25, sigma = 2.421}
local b2 = OpenSkill.Rating(25.188, 6.211) --> {mu = 25.188, sigma = 6.211}


If a1 and a2 are on a team and win against a team of b1 and b2, you can update their skill ratings like this: 

OpenSkill.Rate({{a1, a2}, {b1, b2}})


When displaying a rating or sorting a list of ratings, you can use Ordinal: 

OpenSkill.Ordinal(a1) --> 0
--after updating the rating above:
OpenSkill.Ordinal(a1) --> 2.3245624871094


If your teams are listed in one order but your ranking is in a different order, you can specify a ranks option, such as: 

local a = OpenSkill.Rating()
local b = OpenSkill.Rating()
local c = OpenSkill.Rating()
local d = OpenSkill.Rating()

OpenSkill.Rate({{a}, {b}, {c}, {d}}, { --4 teams consisting of 1 player
    rank = {4, 1, 3, 2}
})
It is assumed that the lower ranks played better in the game, while higher ranks did worse. For example, the team of b would be the best of the game.


You can also provide a score instead, where lower is worse and higher is better. These can just be raw scores from the game, if you want. 

OpenSkill.Rate({{a}, {b}, {c}, {d}}, {
    score = {37, 19, 37, 42}
})
Ties should have either equivalent rank or score.


openskill.lua provides two rating models: PlackettLuce and ThurstoneMosteller.

  • Plackett-Luce is a generalized Bradley-Terry model for k ≥ 3 teams which scales best. It follows a logistic distribution over a player's skill, similar to Glicko.
  • Thurstone-Mosteller rating models follow a gaussian distribution, similar to TrueSkill. Gaussian CDF/PDF functions differ in implementation from system to system (they're all just chebyshev approximations anyway). The accuracy of this model isn't usually as great either, but tuning this with an alternative gamma function can improve the accuracy if you really want to get into it.
  • openskill.lua uses full pairing which should have more accurate ratings over partial pairing, however in high k games (like 100+ teams), Bradley-Terry and Thurston-Mosteller models need to do a calculation of joint probability which involves a k-1 dimensional integration, which is computationally expensive. Partial pairing, where players only change based on their neighbors, is not available yet.

You can change the default model by changing OpenSkill.Settings.DefaultModel. Alternatively you can pass a model option to the Rate function: 

OpenSkill.Rate({{a}, {b}, {c}, {d}}, {
    model = "ThurstoneMosteller"
})
More models are coming in the future.


Info

Contributions are greatly appreciated!