openskill

An implementation of the Open Skill rating system in Go.

Key Features:

• Any number of teams (>1)
• Uneven team sizes
• Predict outcomes before playing
• Per player contribution
• Accuracy on par with TrueSkill, but faster and open source
• No 3rd party dependencies

Example

	player1 := openskill.Rating{Mu: 25, Sigma: 3}
	player2 := openskill.Rating{Mu: 10, Sigma: 2.5}
	player3 := openskill.Rating{Mu: 5, Sigma: 2}
	player4 := openskill.Rating{Mu: 17, Sigma: 2}
	teams := [][]openskill.Rating{{player1}, {player2, player3}, {player4}}

	m := openskill.DefaultPlackettLuceModel()
	p := openskill.DefaultPredictor()

	// Predict the outcome of a match
	drawChance, _ := p.ChanceOfDraw(teams)                     // 0.18...
	winChance, _ := p.ChanceOfWinning(teams)                   // [0.59... 0.15... 0.24...]
	predictedRanks, probabilities, _ := p.ChanceOfRanks(teams) // [1 3 2] [0.59... 0.15... 0.24...]

	// Update the ratings based on a match where the first team won
	ranks := []int{1, 2, 3}
	teams, _ = m.Rate(teams, ranks, nil, nil)

	// Update the ratings based on a match where the first team won 10-5-3
	scores := []int{10, 5, 3}
	teams, _ = m.Rate(teams, nil, scores, nil)

	// Update the ratings based on a match where the second team won, but player 2 should get more credit
	ranks = []int{2, 1, 3}
	weights := [][]float64{{1}, {0.8, 0.2}, {1}}
	teams, _ = m.Rate(teams, ranks, nil, weights)

Description

The package provides a simple interface which all of the models implement allowing for easy mocking or extension:

type Rater interface {
	Rate(teams [][]Rating, ranks, scores []int, weights [][]float64) (updatedRatings [][]Rating, err error)
}

Use the Default...Model() methods to get started quickly or New...Model(...) if you want to tune the parameters yourself.

If you do not (want to) understand how the models work, DefaultPlackettLuceModel() is the recommended model, but feel free to experiment with what type of model or parameters works best for your type of matches.

The package also provides a way to predict the outcome of matches between teams using the Predictor interface:

type Predictor interface {
	ChanceOfWinning(teams [][]Rating) ([]float64, error)
	ChanceOfDraw(teams [][]Rating) (float64, error)
	ChanceOfRanks(teams [][]Rating) ([]int, []float64, error)
}

Use DefaultPredictor() to get started quickly or NewPredictor(...) if you want to tune the parameters yourself. If you are using a custom model with New...Model(...), your Predictor should be initialized with the same parameter values.

Implementations in other languages

• Elixir
• Kotlin
• Lua
• Javascript
• Java
• Python

References

This project is originally based on the openskill.py package. All of the models are based on the work in this paper or are the derivatives of algorithms found in it.

• Julia Ibstedt, Elsa Rådahl, Erik Turesson, and Magdalena vande Voorde. Application and further development of trueskill™ ranking in sports. 2019. URL: https://www.diva-portal.org/smash/get/diva2:1322103/FULLTEXT01.pdf.
• Ruby C. Weng and Chih-Jen Lin. A bayesian approximation method for online ranking. Journal of Machine Learning Research, 12(9):267–300, 2011. URL: http://jmlr.org/papers/v12/weng11a.html.