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22 lines
659 B
PHP
22 lines
659 B
PHP
<?php
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namespace DNW\Skills\TrueSkill;
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use DNW\Skills\Numerics\GaussianDistribution;
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final class DrawMargin
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{
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public static function getDrawMarginFromDrawProbability(float $drawProbability, float $beta): float
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{
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// Derived from TrueSkill technical report (MSR-TR-2006-80), page 6
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// draw probability = 2 * CDF(margin/(sqrt(n1+n2)*beta)) -1
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// implies
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//
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// margin = inversecdf((draw probability + 1)/2) * sqrt(n1+n2) * beta
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// n1 and n2 are the number of players on each team
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return GaussianDistribution::inverseCumulativeTo(.5 * ($drawProbability + 1), 0, 1) * sqrt(1 + 1) * $beta;
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}
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}
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