public static function getDrawMarginFromDrawProbability($drawProbability, $beta)
{
// Derived from TrueSkill technical report (MSR-TR-2006-80), page 6
// draw probability = 2 * CDF(margin/(sqrt(n1+n2)*beta)) -1
// implies
//
// margin = inversecdf((draw probability + 1)/2) * sqrt(n1+n2) * beta
// n1 and n2 are the number of players on each team
$margin = GaussianDistribution::inverseCumulativeTo(0.5 * ($drawProbability + 1), 0, 1) * sqrt(1 + 1) * $beta;
return $margin;
}
