Package glicko implements the player's strength estimate based on the Glicko-2
rating system.

Originally designed as an improvement over existing rating systems, Glicko-2 has
become a popular choice among game developers.

One potential caveat when using the stock Glicko-2 system is that it expects
a collection of games within a rating period to apply the rating algorithm.

This implementation aims to address that limitation by allowing the player's
rating to be estimated sequentially based on individual match outcomes rather
than in batches. To achieve this, the periodFraction parameter was introduced
into the Estimate function. As a result, rating, deviation, and volatility
evolve smoothly when matches occur at arbitrary moments instead of being
grouped into fixed rating periods.

Another notable modification is the introduction of bounds on the player's rating,
deviation, and volatility. All system parameters are user-defined, making the
system both flexible and safe.

Usage

To install glicko, run go get:

go get github.com/treepeck/glicko

Here is a simple example (based on the original Glicko-2 paper):

package main

import (
	"fmt"

	"github.com/treepeck/glicko"
)

func main() {
	c := glicko.Converter{
		Rating:    glicko.DefaultRating,
		Deviation: glicko.DefaultDeviation,
		Factor:    glicko.DefaultFactor,
	}

	// Initial player's strength.
	s := glicko.Strength{
		Mu:    c.Rating2Mu(glicko.DefaultRating),
		Phi:   c.Deviation2Phi(200),
		Sigma: glicko.DefaultVolatility,
	}

	// Match outcomes.
	outcomes := []glicko.Outcome{
		{Mu: c.Rating2Mu(1400), Phi: c.Deviation2Phi(30), Score: 1},
		{Mu: c.Rating2Mu(1550), Phi: c.Deviation2Phi(100), Score: 0},
		{Mu: c.Rating2Mu(1700), Phi: c.Deviation2Phi(300), Score: 0},
	}

	// Initialize the strength estimator.
	e := glicko.Estimator{
		MinMu: c.Rating2Mu(10), MaxMu: c.Rating2Mu(5000),
		MinPhi:   c.Deviation2Phi(30),
		MaxPhi:   c.Deviation2Phi(glicko.DefaultDeviation),
		MinSigma: 0.04, MaxSigma: 0.08,
		Tau: glicko.DefaultTau, Epsilon: glicko.DefaultEpsilon,
	}

	// Estimate player's rating based on game outcomes sequantially.
	// New rating can be calculated immediately after each match.
	for i := range outcomes {
		e.Estimate(&s, outcomes[i], 1)
	}

	// Those values slighly (+- 1 rating point) differ from the original
	// Glicko-2 example.  This is because the implementation processes each
	// game sequentially and the original algorithm is not linear.  The
	// difference is negligable is most cases.

	// Prints "1463.7884049111285"
	fmt.Println(int(c.Mu2Rating(s.Mu)))
	// Prints "151.87316169372073"
	fmt.Println(c.Phi2Deviation(s.Phi))
	// Prints "0.05999440707992557"
	fmt.Println(s.Sigma)
}

Acknowledgments

https://www.glicko.net/glicko/glicko2.pdf

https://blog.hypersect.com/the-online-skill-ranking-of-inversus-deluxe/