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, $newStdDev);
}
protected function updateMessageVariable(Message &$message, Variable &$variable)
{
$oldMarginal = clone $variable->getValue();
$oldMessage = clone $message->getValue();
$messageFromVariable = GaussianDistribution::divide($oldMarginal, $oldMessage);
$c = $messageFromVariable->getPrecision();
$d = $messageFromVariable->getPrecisionMean();
$sqrtC = sqrt($c);
$dOnSqrtC = $d / $sqrtC;
$epsilonTimesSqrtC = $this->_epsilon * $sqrtC;
$d = $messageFromVariable->getPrecisionMean();
$denominator = 1.0 - TruncatedGaussianCorrectionFunctions::wWithinMargin($dOnSqrtC, $epsilonTimesSqrtC);
$newPrecision = $c / $denominator;
$newPrecisionMean = ($d + $sqrtC * TruncatedGaussianCorrectionFunctions::vWithinMargin($dOnSqrtC, $epsilonTimesSqrtC)) / $denominator;
$newMarginal = GaussianDistribution::fromPrecisionMean($newPrecisionMean, $newPrecision);
$newMessage = GaussianDistribution::divide(GaussianDistribution::multiply($oldMessage, $newMarginal), $oldMarginal);
// Update the message and marginal
$message->setValue($newMessage);
$variable->setValue($newMarginal);
// Return the difference in the new marginal
return GaussianDistribution::subtract($newMarginal, $oldMarginal);
}
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));
}
}