private static function calculateNewRating(GameInfo $gameInfo, Rating $selfRating, Rating $opponentRating, $comparison)
{
$drawMargin = DrawMargin::getDrawMarginFromDrawProbability($gameInfo->getDrawProbability(), $gameInfo->getBeta());
$c = sqrt(square($selfRating->getStandardDeviation()) + square($opponentRating->getStandardDeviation()) + 2 * square($gameInfo->getBeta()));
$winningMean = $selfRating->getMean();
$losingMean = $opponentRating->getMean();
switch ($comparison) {
case PairwiseComparison::WIN:
case PairwiseComparison::DRAW:
// NOP
break;
case PairwiseComparison::LOSE:
$winningMean = $opponentRating->getMean();
$losingMean = $selfRating->getMean();
break;
}
$meanDelta = $winningMean - $losingMean;
if ($comparison != PairwiseComparison::DRAW) {
// non-draw case
$v = TruncatedGaussianCorrectionFunctions::vExceedsMarginScaled($meanDelta, $drawMargin, $c);
$w = TruncatedGaussianCorrectionFunctions::wExceedsMarginScaled($meanDelta, $drawMargin, $c);
$rankMultiplier = (int) $comparison;
} else {
$v = TruncatedGaussianCorrectionFunctions::vWithinMarginScaled($meanDelta, $drawMargin, $c);
$w = TruncatedGaussianCorrectionFunctions::wWithinMarginScaled($meanDelta, $drawMargin, $c);
$rankMultiplier = 1;
}
$meanMultiplier = (square($selfRating->getStandardDeviation()) + square($gameInfo->getDynamicsFactor())) / $c;
$varianceWithDynamics = square($selfRating->getStandardDeviation()) + square($gameInfo->getDynamicsFactor());
$stdDevMultiplier = $varianceWithDynamics / square($c);
$newMean = $selfRating->getMean() + $rankMultiplier * $meanMultiplier * $v;
$newStdDev = sqrt($varianceWithDynamics * (1 - $w * $stdDevMultiplier));
return new Rating($newMean, $newStdDev);
}
private static function updatePlayerRatings(GameInfo $gameInfo, RatingContainer &$newPlayerRatings, Team $selfTeam, Team $otherTeam, $selfToOtherTeamComparison)
{
$drawMargin = DrawMargin::getDrawMarginFromDrawProbability($gameInfo->getDrawProbability(), $gameInfo->getBeta());
$betaSquared = square($gameInfo->getBeta());
$tauSquared = square($gameInfo->getDynamicsFactor());
$totalPlayers = $selfTeam->count() + $otherTeam->count();
$meanGetter = function ($currentRating) {
return $currentRating->getMean();
};
$selfMeanSum = sum($selfTeam->getAllRatings(), $meanGetter);
$otherTeamMeanSum = sum($otherTeam->getAllRatings(), $meanGetter);
$varianceGetter = function ($currentRating) {
return square($currentRating->getStandardDeviation());
};
$c = sqrt(sum($selfTeam->getAllRatings(), $varianceGetter) + sum($otherTeam->getAllRatings(), $varianceGetter) + $totalPlayers * $betaSquared);
$winningMean = $selfMeanSum;
$losingMean = $otherTeamMeanSum;
switch ($selfToOtherTeamComparison) {
case PairwiseComparison::WIN:
case PairwiseComparison::DRAW:
// NOP
break;
case PairwiseComparison::LOSE:
$winningMean = $otherTeamMeanSum;
$losingMean = $selfMeanSum;
break;
}
$meanDelta = $winningMean - $losingMean;
if ($selfToOtherTeamComparison != PairwiseComparison::DRAW) {
// non-draw case
$v = TruncatedGaussianCorrectionFunctions::vExceedsMarginScaled($meanDelta, $drawMargin, $c);
$w = TruncatedGaussianCorrectionFunctions::wExceedsMarginScaled($meanDelta, $drawMargin, $c);
$rankMultiplier = (int) $selfToOtherTeamComparison;
} else {
// assume draw
$v = TruncatedGaussianCorrectionFunctions::vWithinMarginScaled($meanDelta, $drawMargin, $c);
$w = TruncatedGaussianCorrectionFunctions::wWithinMarginScaled($meanDelta, $drawMargin, $c);
$rankMultiplier = 1;
}
$selfTeamAllPlayers =& $selfTeam->getAllPlayers();
foreach ($selfTeamAllPlayers as &$selfTeamCurrentPlayer) {
$localSelfTeamCurrentPlayer =& $selfTeamCurrentPlayer;
$previousPlayerRating = $selfTeam->getRating($localSelfTeamCurrentPlayer);
$meanMultiplier = (square($previousPlayerRating->getStandardDeviation()) + $tauSquared) / $c;
$stdDevMultiplier = (square($previousPlayerRating->getStandardDeviation()) + $tauSquared) / square($c);
$playerMeanDelta = $rankMultiplier * $meanMultiplier * $v;
$newMean = $previousPlayerRating->getMean() + $playerMeanDelta;
$newStdDev = sqrt((square($previousPlayerRating->getStandardDeviation()) + $tauSquared) * (1 - $w * $stdDevMultiplier));
$newPlayerRatings->setRating($localSelfTeamCurrentPlayer, new Rating($newMean, $newStdDev));
}
}
public function calculateMatchQuality(GameInfo $gameInfo, array $teams)
{
// We need to create the A matrix which is the player team assigments.
$teamAssignmentsList = $teams;
$skillsMatrix = $this->getPlayerCovarianceMatrix($teamAssignmentsList);
$meanVector = $this->getPlayerMeansVector($teamAssignmentsList);
$meanVectorTranspose = $meanVector->getTranspose();
$playerTeamAssignmentsMatrix = $this->createPlayerTeamAssignmentMatrix($teamAssignmentsList, $meanVector->getRowCount());
$playerTeamAssignmentsMatrixTranspose = $playerTeamAssignmentsMatrix->getTranspose();
$betaSquared = square($gameInfo->getBeta());
$start = Matrix::multiply($meanVectorTranspose, $playerTeamAssignmentsMatrix);
$aTa = Matrix::multiply(Matrix::scalarMultiply($betaSquared, $playerTeamAssignmentsMatrixTranspose), $playerTeamAssignmentsMatrix);
$aTSA = Matrix::multiply(Matrix::multiply($playerTeamAssignmentsMatrixTranspose, $skillsMatrix), $playerTeamAssignmentsMatrix);
$middle = Matrix::add($aTa, $aTSA);
$middleInverse = $middle->getInverse();
$end = Matrix::multiply($playerTeamAssignmentsMatrixTranspose, $meanVector);
$expPartMatrix = Matrix::scalarMultiply(-0.5, Matrix::multiply(Matrix::multiply($start, $middleInverse), $end));
$expPart = $expPartMatrix->getDeterminant();
$sqrtPartNumerator = $aTa->getDeterminant();
$sqrtPartDenominator = $middle->getDeterminant();
$sqrtPart = $sqrtPartNumerator / $sqrtPartDenominator;
$result = exp($expPart) * sqrt($sqrtPart);
return $result;
}
function loadRatings()
{
$stats = file_get_contents('games.stats');
$stats = explode("\n", $stats);
$ratings = array();
foreach ($stats as $stat) {
if (empty($stat)) {
continue;
}
$stat = explode("\t", $stat);
$playerId = (int) $stat[0];
$mean = (double) $stat[1];
$stddev = (double) $stat[2];
$ratings[$playerId] = new Rating($mean, $stddev);
}
$gameInfo = new GameInfo();
$players = loadPlayers();
foreach ($players as $playerId => $playerName) {
if (!isset($ratings[$playerId])) {
$ratings[$playerId] = $gameInfo->getDefaultRating();
}
}
return $ratings;
}
public function getPlayerWinProbability(GameInfo $gameInfo, $playerRating, $opponentRating)
{
$ratingDifference = $playerRating - $opponentRating;
// See equation 1.1 in the TrueSkill paper
return GaussianDistribution::cumulativeTo($ratingDifference / (sqrt(2) * $gameInfo->getBeta()));
}
private static function oneOnTwoBalancedPartialPlay($testClass, SkillCalculator $calculator)
{
$gameInfo = new GameInfo();
$p1 = new Player(1);
$team1 = new Team($p1, $gameInfo->getDefaultRating());
$p2 = new Player(2, 0.0);
$p3 = new Player(3, 1.0);
$team2 = new Team();
$team2->addPlayer($p2, $gameInfo->getDefaultRating());
$team2->addPlayer($p3, $gameInfo->getDefaultRating());
$teams = Teams::concat($team1, $team2);
$newRatings = $calculator->calculateNewRatings($gameInfo, $teams, array(1, 2));
$p1NewRating = $newRatings->getRating($p1);
$p2NewRating = $newRatings->getRating($p2);
$p3NewRating = $newRatings->getRating($p3);
// This should be roughly the same as a 1 v 1
self::assertRating($testClass, 29.39648040436841, 7.1713980703143205, $p1NewRating);
self::assertRating($testClass, 24.999560351959563, 8.333749978770932, $p2NewRating);
self::assertRating($testClass, 20.603519595631585, 7.1713980703143205, $p3NewRating);
$matchQuality = $calculator->calculateMatchQuality($gameInfo, $teams);
self::assertMatchQuality($testClass, 0.44721358745011336, $matchQuality);
}
