/// Calculates new ratings for only two teams where each team has 1 or more players.
///
///
/// When you only have two teams, the math is still simple: no factor graphs are used yet.
///
class TwoTeamTrueSkillCalculator extends SkillCalculator
{
public function __construct()
{
parent::__construct(SkillCalculatorSupportedOptions::NONE, TeamsRange::exactly(2), PlayersRange::atLeast(1));
}
public function calculateNewRatings($gameInfo,
array $teams,
array $teamRanks)
{
Guard::argumentNotNull($gameInfo, "gameInfo");
$this->validateTeamCountAndPlayersCountPerTeam($teams);
RankSorter::sort($teams, $teamRanks);
$team1 = $teams[0];
$team2 = $teams[1];
$wasDraw = ($teamRanks[0] == $teamRanks[1]);
$results = new RatingContainer();
self::updatePlayerRatings($gameInfo,
$results,
$team1,
$team2,
$wasDraw ? PairwiseComparison::DRAW : PairwiseComparison::WIN);
self::updatePlayerRatings($gameInfo,
$results,
$team2,
$team1,
$wasDraw ? PairwiseComparison::DRAW : PairwiseComparison::LOSE);
return $results;
}
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);
$rankMultiplier = 1;
}
foreach ($selfTeam->getAllPlayers() as $selfTeamCurrentPlayer)
{
$previousPlayerRating = $selfTeam->getRating($selfTeamCurrentPlayer);
$meanMultiplier = (square($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));
$newPlayerRatings->setRating($selfTeamCurrentPlayer, new Rating($newMean, $newStdDev));
}
}
///
public function calculateMatchQuality($gameInfo, array $teams)
{
Guard::argumentNotNull($gameInfo, "gameInfo");
$this->validateTeamCountAndPlayersCountPerTeam($teams);
// We've verified that there's just two teams
$team1Ratings = $teams[0]->getAllRatings();
$team1Count = count($team1Ratings);
$team2Ratings = $teams[1]->getAllRatings();
$team2Count = count($team2Ratings);
$totalPlayers = $team1Count + $team2Count;
$betaSquared = square($gameInfo->getBeta());
$meanGetter =
function($currentRating)
{
return $currentRating->getMean();
};
$varianceGetter =
function($currentRating)
{
return square($currentRating->getStandardDeviation());
};
$team1MeanSum = sum($team1Ratings, $meanGetter);
$team1StdDevSquared = sum($team1Ratings, $varianceGetter);
$team2MeanSum = sum($team2Ratings, $meanGetter);
$team2SigmaSquared = sum($team2Ratings, $varianceGetter);
// This comes from equation 4.1 in the TrueSkill paper on page 8
// The equation was broken up into the part under the square root sign and
// the exponential part to make the code easier to read.
$sqrtPart
= sqrt(
($totalPlayers*$betaSquared)
/
($totalPlayers*$betaSquared + $team1StdDevSquared + $team2SigmaSquared)
);
$expPart
= exp(
(-1*square($team1MeanSum - $team2MeanSum))
/
(2*($totalPlayers*$betaSquared + $team1StdDevSquared + $team2SigmaSquared))
);
return $expPart*$sqrtPart;
}
}
?>