/// Calculates the new ratings for only two players.
///
///
/// When you only have two players, a lot of the math simplifies. The main purpose of this class
/// is to show the bare minimum of what a TrueSkill implementation should have.
///
class TwoPlayerTrueSkillCalculator extends SkillCalculator
{
public function __construct()
{
parent::__construct(SkillCalculatorSupportedOptions::NONE, TeamsRange::exactly(2), PlayersRange::exactly(1));
}
public function calculateNewRatings(GameInfo &$gameInfo,
array $teams,
array $teamRanks)
{
// Basic argument checking
Guard::argumentNotNull($gameInfo, "gameInfo");
$this->validateTeamCountAndPlayersCountPerTeam($teams);
// Make sure things are in order
RankSorter::sort($teams, $teamRanks);
// Since we verified that each team has one player, we know the player is the first one
$winningTeamPlayers = $teams[0]->getAllPlayers();
$winner = $winningTeamPlayers[0];
$winnerPreviousRating = $teams[0]->getRating($winner);
$losingTeamPlayers = $teams[1]->getAllPlayers();
$loser = $losingTeamPlayers[0];
$loserPreviousRating = $teams[1]->getRating($loser);
$wasDraw = ($teamRanks[0] == $teamRanks[1]);
$results = new RatingContainer();
$results->setRating($winner, self::calculateNewRating($gameInfo,
$winnerPreviousRating,
$loserPreviousRating,
$wasDraw ? PairwiseComparison::DRAW
: PairwiseComparison::WIN));
$results->setRating($loser, self::calculateNewRating($gameInfo,
$loserPreviousRating,
$winnerPreviousRating,
$wasDraw ? PairwiseComparison::DRAW
: PairwiseComparison::LOSE));
// And we're done!
return $results;
}
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);
}
///
public function calculateMatchQuality(GameInfo $gameInfo, array $teams)
{
Guard::argumentNotNull($gameInfo, "gameInfo");
$this->validateTeamCountAndPlayersCountPerTeam($teams);
$team1 = $teams[0];
$team2 = $teams[1];
$team1Ratings = $team1->getAllRatings();
$team2Ratings = $team2->getAllRatings();
$player1Rating = $team1Ratings[0];
$player2Rating = $team2Ratings[0];
// We just use equation 4.1 found on page 8 of the TrueSkill 2006 paper:
$betaSquared = square($gameInfo->getBeta());
$player1SigmaSquared = square($player1Rating->getStandardDeviation());
$player2SigmaSquared = square($player2Rating->getStandardDeviation());
// This is the square root part of the equation:
$sqrtPart =
sqrt(
(2*$betaSquared)
/
(2*$betaSquared + $player1SigmaSquared + $player2SigmaSquared));
// This is the exponent part of the equation:
$expPart =
exp(
(-1*square($player1Rating->getMean() - $player2Rating->getMean()))
/
(2*(2*$betaSquared + $player1SigmaSquared + $player2SigmaSquared)));
return $sqrtPart*$expPart;
}
}
?>