public static double GetDrawMarginFromDrawProbability(double drawProbability, double 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
double margin = GaussianDistribution.InverseCumulativeTo(.5 * (drawProbability + 1), 0, 1) * Math.Sqrt(1 + 1) *
beta;
return(margin);
}
// This gets the draw margin from the Draw Probability. Formula pulled from http://www.moserware.com/assets/computing-your-skill/The%20Math%20Behind%20TrueSkill.pdf, page 15 public double GetDrawMargin() => GaussianDistribution.InverseCumulativeTo(1 / 2, 0, 1) * Math.Sqrt(2) * Beta;