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75 lines
2.9 KiB
PHP
75 lines
2.9 KiB
PHP
<?php
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namespace DNW\Skills;
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// Container for a player's rating.
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use DNW\Skills\Numerics\GaussianDistribution;
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class Rating implements \Stringable
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{
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final const CONSERVATIVE_STANDARD_DEVIATION_MULTIPLIER = 3;
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/**
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* Constructs a rating.
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*
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* @param float $_mean The statistical mean value of the rating (also known as mu).
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* @param float $_standardDeviation The standard deviation of the rating (also known as s).
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* @param float|int $_conservativeStandardDeviationMultiplier optional The number of standardDeviations to subtract from the mean to achieve a conservative rating.
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*/
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public function __construct(private $_mean, private $_standardDeviation, private $_conservativeStandardDeviationMultiplier = self::CONSERVATIVE_STANDARD_DEVIATION_MULTIPLIER)
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{
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}
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/**
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* The statistical mean value of the rating (also known as <20>).
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*/
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public function getMean()
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{
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return $this->_mean;
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}
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/**
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* The standard deviation (the spread) of the rating. This is also known as s.
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*/
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public function getStandardDeviation()
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{
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return $this->_standardDeviation;
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}
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/**
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* A conservative estimate of skill based on the mean and standard deviation.
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*/
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public function getConservativeRating()
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{
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return $this->_mean - $this->_conservativeStandardDeviationMultiplier * $this->_standardDeviation;
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}
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public function getPartialUpdate(Rating $prior, Rating $fullPosterior, $updatePercentage)
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{
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$priorGaussian = new GaussianDistribution($prior->getMean(), $prior->getStandardDeviation());
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$posteriorGaussian = new GaussianDistribution($fullPosterior->getMean(), $fullPosterior.getStandardDeviation());
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// From a clarification email from Ralf Herbrich:
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// "the idea is to compute a linear interpolation between the prior and posterior skills of each player
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// ... in the canonical space of parameters"
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$precisionDifference = $posteriorGaussian->getPrecision() - $priorGaussian->getPrecision();
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$partialPrecisionDifference = $updatePercentage * $precisionDifference;
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$precisionMeanDifference = $posteriorGaussian->getPrecisionMean() - $priorGaussian.getPrecisionMean();
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$partialPrecisionMeanDifference = $updatePercentage * $precisionMeanDifference;
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$partialPosteriorGaussion = GaussianDistribution::fromPrecisionMean(
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$priorGaussian->getPrecisionMean() + $partialPrecisionMeanDifference,
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$priorGaussian->getPrecision() + $partialPrecisionDifference
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);
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return new Rating($partialPosteriorGaussion->getMean(), $partialPosteriorGaussion->getStandardDeviation(), $prior->_conservativeStandardDeviationMultiplier);
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}
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public function __toString(): string
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{
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return sprintf('mean=%.4f, standardDeviation=%.4f', $this->_mean, $this->_standardDeviation);
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}
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}
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