_mean = $mean; $this->_standardDeviation = $standardDeviation; $this->_conservativeStandardDeviationMultiplier = $conservativeStandardDeviationMultiplier; } /** * The statistical mean value of the rating (also known as �). */ public function getMean() { return $this->_mean; } /** * The standard deviation (the spread) of the rating. This is also known as s. */ public function getStandardDeviation() { return $this->_standardDeviation; } /** * A conservative estimate of skill based on the mean and standard deviation. */ public function getConservativeRating() { return $this->_mean - $this->_conservativeStandardDeviationMultiplier*$this->_standardDeviation; } public function getPartialUpdate(Rating $prior, Rating $fullPosterior, $updatePercentage) { $priorGaussian = new GaussianDistribution($prior->getMean(), $prior->getStandardDeviation()); $posteriorGaussian = new GaussianDistribution($fullPosterior->getMean(), $fullPosterior.getStandardDeviation()); // 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" $precisionDifference = $posteriorGaussian->getPrecision() - $priorGaussian->getPrecision(); $partialPrecisionDifference = $updatePercentage*$precisionDifference; $precisionMeanDifference = $posteriorGaussian->getPrecisionMean() - $priorGaussian.getPrecisionMean(); $partialPrecisionMeanDifference = $updatePercentage*$precisionMeanDifference; $partialPosteriorGaussion = GaussianDistribution::fromPrecisionMean( $priorGaussian->getPrecisionMean() + $partialPrecisionMeanDifference, $priorGaussian->getPrecision() + $partialPrecisionDifference); return new Rating($partialPosteriorGaussion->getMean(), $partialPosteriorGaussion->getStandardDeviation(), $prior->_conservativeStandardDeviationMultiplier); } public function __toString() { return 'mean=' . $this->_mean . ' standardDeviation=' . $this->_standardDeviation; } } ?>