This project is a PHP implementation of the Glicko2 ranking system:
http://math.bu.edu/people/mg/glicko/glicko2.doc/example.html

With the example provide in the above page:

use Mkk\Game\Ranking\Glicko2 as RankingGlicko2;
use Mkk\Game\Player\Glicko2 as PlayerGlicko2;

$player1 = new PlayerGlicko2(array('id' = 1, 'rating' => 1500, 'ratingDeviation' => 200, 'volatility' => 0.06));
$player2 = new PlayerGlicko2(array('id' = 2, 'rating' => 1400, 'ratingDeviation' =>  30, 'volatility' => 0.06));
$player3 = new PlayerGlicko2(array('id' = 3, 'rating' => 1550, 'ratingDeviation' => 100, 'volatility' => 0.06));
$player4 = new PlayerGlicko2(array('id' = 4, 'rating' => 1700, 'ratingDeviation' => 300, 'volatility' => 0.06));

$game = new RankingGlicko2();
$game->addPlayers(array($player4, $player3, $player1, $player2));
$game->updateRanking();

$player = $game->getPlayerById(1);

echo $player->getNewRating();
echo $player->getNewRatingDeviation();
echo $player->getNewVolatility();