// My original:
//public static double VWithinMargin(double teamPerformanceDifference, double drawMargin)
//{
// var teamPerformanceDifferenceAbsoluteValue = Math.Abs(teamPerformanceDifference);
// return (GaussianDistribution.At(-drawMargin - teamPerformanceDifferenceAbsoluteValue) - GaussianDistribution.At(drawMargin - teamPerformanceDifferenceAbsoluteValue))
// /
// (GaussianDistribution.CumulativeTo(drawMargin - teamPerformanceDifferenceAbsoluteValue) - GaussianDistribution.CumulativeTo(-drawMargin - teamPerformanceDifferenceAbsoluteValue));
//}
// from F#:
public static double VWithinMargin(double teamPerformanceDifference, double drawMargin)
{
double teamPerformanceDifferenceAbsoluteValue = Math.Abs(teamPerformanceDifference);
double denominator =
GaussianDistribution.CumulativeTo(drawMargin - teamPerformanceDifferenceAbsoluteValue) -
GaussianDistribution.CumulativeTo(-drawMargin - teamPerformanceDifferenceAbsoluteValue);
if (denominator < 2.222758749e-162)
{
if (teamPerformanceDifference < 0.0)
{
return(-teamPerformanceDifference - drawMargin);
}
return(-teamPerformanceDifference + drawMargin);
}
double numerator = GaussianDistribution.At(-drawMargin - teamPerformanceDifferenceAbsoluteValue) -
GaussianDistribution.At(drawMargin - teamPerformanceDifferenceAbsoluteValue);
if (teamPerformanceDifference < 0.0)
{
return(-numerator / denominator);
}
return(numerator / denominator);
}
protected override double GetPlayerWinProbability(GameInfo gameInfo, double playerRating, double opponentRating)
{
double ratingDifference = playerRating - opponentRating;
// See equation 1.1 in the TrueSkill paper
return(GaussianDistribution.CumulativeTo(
ratingDifference
/
(Math.Sqrt(2) * gameInfo.Beta)));
}
private double VExceedsMargin(double drawMargin, double performanceDiff)
{
var denominator = GaussianDistribution.CumulativeTo(performanceDiff - drawMargin);
if (denominator < 2.222758749e-162)
{
return(-performanceDiff + drawMargin);
}
return(GaussianDistribution.At(performanceDiff - drawMargin) / denominator);
}
public static double VExceedsMargin(double teamPerformanceDifference, double drawMargin)
{
double denominator = GaussianDistribution.CumulativeTo(teamPerformanceDifference - drawMargin);
if (denominator < 2.222758749e-162)
{
return(-teamPerformanceDifference + drawMargin);
}
return(GaussianDistribution.At(teamPerformanceDifference - drawMargin) / denominator);
}
private double WExceedsMargin(double drawMargin, double performanceDiff)
{
var denominator = GaussianDistribution.CumulativeTo(performanceDiff - drawMargin);
if (denominator < 2.222758749e-162)
{
return(performanceDiff < 0 ? 1 : 0);
}
var vWin = VExceedsMargin(performanceDiff, drawMargin);
return(vWin * (vWin + performanceDiff - drawMargin));
}
private double VWithinMargin(double drawMargin, double performanceDiff)
{
var performanceDiffAbsoluteValue = Math.Abs(performanceDiff);
var denominator = GaussianDistribution.CumulativeTo(drawMargin - performanceDiffAbsoluteValue) - GaussianDistribution.CumulativeTo(-drawMargin - performanceDiffAbsoluteValue);
if (denominator < 2.222758749e-162)
{
return(performanceDiff < 0 ? -performanceDiff - drawMargin : -performanceDiff + drawMargin);
}
var numerator = GaussianDistribution.At(-drawMargin - performanceDiffAbsoluteValue) - GaussianDistribution.At(drawMargin - performanceDiffAbsoluteValue);
return(performanceDiff < 0 ? -numerator / denominator : numerator / denominator);
}
public static double WExceedsMargin(double teamPerformanceDifference, double drawMargin)
{
double denominator = GaussianDistribution.CumulativeTo(teamPerformanceDifference - drawMargin);
if (denominator < 2.222758749e-162)
{
if (teamPerformanceDifference < 0.0)
{
return(1.0);
}
return(0.0);
}
double vWin = VExceedsMargin(teamPerformanceDifference, drawMargin);
return(vWin * (vWin + teamPerformanceDifference - drawMargin));
}
private double WWithinMargin(double drawMargin, double performanceDiff)
{
var performanceDiffAbsoluteValue = Math.Abs(performanceDiff);
var denominator = GaussianDistribution.CumulativeTo(drawMargin - performanceDiffAbsoluteValue) - GaussianDistribution.CumulativeTo(-drawMargin - performanceDiffAbsoluteValue);
if (denominator < 2.222758749e-162)
{
return(1);
}
var vt = VWithinMargin(drawMargin, performanceDiff);
// Separating large return math shown in original work for readability
var factor1 = drawMargin - performanceDiffAbsoluteValue;
var factor2 = GaussianDistribution.At(drawMargin - performanceDiffAbsoluteValue);
var factor3 = -drawMargin - performanceDiffAbsoluteValue;
var factor4 = GaussianDistribution.At(-drawMargin - performanceDiffAbsoluteValue);
var numerator = (factor1 * factor2) - (factor3 * factor4);
return((vt * vt) + (numerator / denominator));
}
// My original:
//public static double WWithinMargin(double teamPerformanceDifference, double drawMargin)
//{
// var teamPerformanceDifferenceAbsoluteValue = Math.Abs(teamPerformanceDifference);
// var vDraw = VWithinMargin(teamPerformanceDifferenceAbsoluteValue, drawMargin);
// return (vDraw * vDraw)
// +
// (
// ((drawMargin - teamPerformanceDifferenceAbsoluteValue) * GaussianDistribution.At(drawMargin - teamPerformanceDifferenceAbsoluteValue) + (drawMargin + teamPerformanceDifferenceAbsoluteValue) * GaussianDistribution.At(drawMargin + teamPerformanceDifferenceAbsoluteValue))
// /
// (GaussianDistribution.CumulativeTo(drawMargin - teamPerformanceDifferenceAbsoluteValue) - GaussianDistribution.CumulativeTo(-drawMargin - teamPerformanceDifferenceAbsoluteValue))
// );
//}
// From F#:
public static double WWithinMargin(double teamPerformanceDifference, double drawMargin)
{
double teamPerformanceDifferenceAbsoluteValue = Math.Abs(teamPerformanceDifference);
double denominator = GaussianDistribution.CumulativeTo(drawMargin - teamPerformanceDifferenceAbsoluteValue)
-
GaussianDistribution.CumulativeTo(-drawMargin - teamPerformanceDifferenceAbsoluteValue);
if (denominator < 2.222758749e-162)
{
return(1.0);
}
double vt = VWithinMargin(teamPerformanceDifferenceAbsoluteValue, drawMargin);
return(vt * vt +
(
(drawMargin - teamPerformanceDifferenceAbsoluteValue)
*
GaussianDistribution.At(
drawMargin - teamPerformanceDifferenceAbsoluteValue)
- (-drawMargin - teamPerformanceDifferenceAbsoluteValue)
*
GaussianDistribution.At(-drawMargin - teamPerformanceDifferenceAbsoluteValue)) / denominator);
}
public void CumulativeToTests()
{
// Verified with WolframAlpha
// (e.g. http://www.wolframalpha.com/input/?i=CDF%5BNormalDistribution%5B0%2C1%5D%2C+0.5%5D )
Assert.AreEqual(0.691462, GaussianDistribution.CumulativeTo(0.5), ErrorTolerance);
}
public void CumulativeToTests()
{
Assert.AreEqual(0.691462, GaussianDistribution.CumulativeTo(0.5), ErrorTolerance);
}
/// <summary>
/// Given a difficulty, return the chance of success for it.
/// </summary>
/// <param name="difficulty"></param>
/// <returns>Higher means easier</returns>
public static double ChanceOfSuccess(double difficulty)
{
return(GaussianDistribution.CumulativeTo(difficulty, World.Mean, World.StandardDeviation));
}