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119 lines
2.8 KiB
PHP
119 lines
2.8 KiB
PHP
<?php
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/**
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* Jingga
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*
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* PHP Version 8.1
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*
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* @package phpOMS\Algorithm\Rating
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* @copyright Dennis Eichhorn
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* @license OMS License 2.0
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* @version 1.0.0
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* @link https://jingga.app
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*/
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declare(strict_types=1);
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namespace phpOMS\Algorithm\Rating;
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use phpOMS\Math\Solver\Root\Bisection;
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/**
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* Elo rating calculation using Glicko-2
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*
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* @package phpOMS\Algorithm\Rating
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* @license OMS License 2.0
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* @link https://jingga.app
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* @since 1.0.0
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* @see https://en.wikipedia.org/wiki/Glicko_rating_system
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* @see http://www.glicko.net/glicko/glicko2.pdf
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*
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* @todo: implement
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*/
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final class Glicko2
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{
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public float $tau = 0.5;
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public int $DEFAULT_ELO = 1500;
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public int $DEFAULT_RD = 350;
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public float $DEFAULT_VOLATILITY = 0.06;
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public int $MIN_ELO = 100;
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public int $MIN_RD = 50;
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/**
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* @example $glicko->elo(1500, 200, 0.06, [1,0,0], [1400,1550,1700], [30,100,300]) // 1464, 151, 0.059
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*/
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public function rating(
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int $eloOld = 1500,
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int $rdOld = 50,
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float $volOld = 0.06,
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array $s = [],
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array $oElo = [],
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array $oRd = []
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) : array
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{
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$tau = $this->tau;
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// Step 0:
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$rdOld = $rdOld / 173.7178;
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$eloOld = ($eloOld - $this->DEFAULT_ELO) / 173.7178;
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foreach ($oElo as $idx => $value) {
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$oElo[$idx] = ($value - $this->DEFAULT_ELO) / 173.7178;
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}
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foreach ($oRd as $idx => $value) {
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$oRd[$idx] = $value / 173.7178;
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}
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// Step 1:
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$g = [];
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foreach ($oRd as $rd) {
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$g[] = 1 / \sqrt(1 + 3 * $rd * $rd / (\M_PI * \M_PI));
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}
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$E = [];
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foreach ($oElo as $idx => $elo) {
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$E[] = 1 / (1 + \exp(-$g[$idx] * ($eloOld - $elo)));
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}
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$v = 0;
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foreach ($g as $idx => $t) {
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$v += $t * $t * $E[$idx] * (1 - $E[$idx]);
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}
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$v = 1 / $v;
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$tDelta = 0;
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foreach ($g as $idx => $t) {
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$tDelta += $t * ($s[$idx] - $E[$idx]);
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}
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$Delta = $v * $tDelta;
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// Step 2:
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$fn = function($x) use ($Delta, $rdOld, $v, $tau, $volOld)
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{
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return 0.5 * (\exp($x) * ($Delta ** 2 - $rdOld ** 2 - $v - \exp($x))) / (($rdOld ** 2 + $v + \exp($x)) ** 2)
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- ($x - \log($volOld ** 2)) / ($tau ** 2);
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};
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$root = Bisection::bisection($fn, -100, 100, 1000);
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$vol = \exp($root / 2);
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// Step 3:
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$RD = 1 / \sqrt(1 / ($rdOld ** 2 + $vol ** 2) + 1 / $v);
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$r = $eloOld + $RD ** 2 * $tDelta;
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// Undo step 0:
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$RD = 173.7178 * $RD;
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$r = 173.7178 * $r + $this->DEFAULT_ELO;
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return [
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'elo' => (int) \max($r, $this->MIN_ELO),
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'rd' => (int) \max($RD, $this->MIN_RD),
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'vol' => $vol,
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];
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}
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}
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