horaceho / ers

ERS (EGF Rating System)

The rating algorithm was updated starting 2021. The whole database from back in 1996 was recalculated with this algorithm. You can find the old algorithm here.

• Ratings are updated by: r' = r + con * (Sa - Se) + bonus
• r is the old EGD rating (GoR) of the player
• r' is the new EGD rating of the player
• Sa is the actual game result (1.0 = win, 0.5 = jigo, 0.0 = loss)
• Se is the expected game result as a winning probability (1.0 = 100%, 0.5 = 50%, 0.0 = 0%). See further below for its computation.
• con is a factor that determines rating volatility (similar to K in regular Elo rating systems): con = ((3300 - r) / 200) ^ 1.6
• bonus (not found in regular Elo rating systems) is a term included to counter rating deflation: bonus = ln(1 + exp((2300 - rating) / 80)) / 5
• Se is computed by the Bradley-Terry formula: Se = 1 / (1 + exp(β(r2) - β(r1)))
• r1 is the EGD rating of the player
• r2 is the EGD rating of the opponent
• β is a mapping function for EGD ratings: β = -7 * ln(3300 - r)

EGF Official ratings system

Usage

composer require horaceho/ers

<?php

require_once __DIR__ . '/../vendor/autoload.php';

use Horaceho\Ers;

$ers = new Ers\Ers();

$player = 2100.0;
$opponent = 2100.0;
$win = 1.0;
$loss = 0.0;

$win_update = $ers->update($player, $opponent, $win);
assert ($win_update == 2109.306);
echo $win_update . PHP_EOL;

Test

git clone [e-mail]:horaceho/ers.git
cd ers
php test/ers.php
php test/about.php