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using System;
using Moserware.Numerics;
namespace Moserware.Skills
{
/// <summary>
/// Container for a player's rating.
/// </summary>
public class Rating
{
private const int ConservativeStandardDeviationMultiplier = 3;
private readonly double _ConservativeStandardDeviationMultiplier;
private readonly double _Mean;
private readonly double _StandardDeviation;
/// <summary>
/// Constructs a rating.
/// </summary>
/// <param name="mean">The statistical mean value of the rating (also known as μ).</param>
/// <param name="standardDeviation">The standard deviation of the rating (also known as σ).</param>
public Rating(double mean, double standardDeviation)
: this(mean, standardDeviation, ConservativeStandardDeviationMultiplier)
{
}
/// <summary>
/// Constructs a rating.
/// </summary>
/// <param name="mean">The statistical mean value of the rating (also known as μ).</param>
/// <param name="standardDeviation">The standard deviation (the spread) of the rating (also known as σ).</param>
/// <param name="conservativeStandardDeviationMultiplier">The number of <paramref name="standardDeviation"/>s to subtract from the <paramref name="mean"/> to achieve a conservative rating.</param>
public Rating(double mean, double standardDeviation, double conservativeStandardDeviationMultiplier)
{
_Mean = mean;
_StandardDeviation = standardDeviation;
_ConservativeStandardDeviationMultiplier = conservativeStandardDeviationMultiplier;
}
/// <summary>
/// The statistical mean value of the rating (also known as μ).
/// </summary>
public double Mean
{
get { return _Mean; }
}
/// <summary>
/// The standard deviation (the spread) of the rating. This is also known as σ.
/// </summary>
public double StandardDeviation
{
get { return _StandardDeviation; }
}
/// <summary>
/// A conservative estimate of skill based on the mean and standard deviation.
/// </summary>
public double ConservativeRating
{
get { return _Mean - _ConservativeStandardDeviationMultiplier*_StandardDeviation; }
}
public static Rating GetPartialUpdate(Rating prior, Rating fullPosterior, double updatePercentage)
{
var priorGaussian = new GaussianDistribution(prior.Mean, prior.StandardDeviation);
var posteriorGaussian = new GaussianDistribution(fullPosterior.Mean, fullPosterior.StandardDeviation);
// From a clarification email from Ralf Herbrich:
// "the idea is to compute a linear interpolation between the prior and posterior skills of each player
// ... in the canonical space of parameters"
double precisionDifference = posteriorGaussian.Precision - priorGaussian.Precision;
double partialPrecisionDifference = updatePercentage*precisionDifference;
double precisionMeanDifference = posteriorGaussian.PrecisionMean - priorGaussian.PrecisionMean;
double partialPrecisionMeanDifference = updatePercentage*precisionMeanDifference;
GaussianDistribution partialPosteriorGaussion = GaussianDistribution.FromPrecisionMean(
priorGaussian.PrecisionMean + partialPrecisionMeanDifference,
priorGaussian.Precision + partialPrecisionDifference);
return new Rating(partialPosteriorGaussion.Mean, partialPosteriorGaussion.StandardDeviation,
prior._ConservativeStandardDeviationMultiplier);
}
public override string ToString()
{
// As a debug helper, display a localized rating:
return String.Format(
"μ={0:0.0000}, σ={1:0.0000}",
Mean, StandardDeviation);
}
}
}
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