Code Coverage |
||||||||||
Lines |
Functions and Methods |
Classes and Traits |
||||||||
| Total | |
0.00% |
0 / 45 |
|
0.00% |
0 / 13 |
CRAP | |
0.00% |
0 / 1 |
| TrueSkill | |
0.00% |
0 / 45 |
|
0.00% |
0 / 13 |
182 | |
0.00% |
0 / 1 |
| __construct | |
0.00% |
0 / 1 |
|
0.00% |
0 / 1 |
2 | |||
| drawProbability | |
0.00% |
0 / 1 |
|
0.00% |
0 / 1 |
2 | |||
| drawMargin | |
0.00% |
0 / 1 |
|
0.00% |
0 / 1 |
2 | |||
| vWin | |
0.00% |
0 / 1 |
|
0.00% |
0 / 1 |
2 | |||
| vDraw | |
0.00% |
0 / 10 |
|
0.00% |
0 / 1 |
2 | |||
| wWin | |
0.00% |
0 / 2 |
|
0.00% |
0 / 1 |
2 | |||
| wDraw | |
0.00% |
0 / 5 |
|
0.00% |
0 / 1 |
2 | |||
| buildRatingLayer | |
0.00% |
0 / 1 |
|
0.00% |
0 / 1 |
2 | |||
| buildPerformanceLayer | |
0.00% |
0 / 1 |
|
0.00% |
0 / 1 |
2 | |||
| buildTeamPerformanceLayer | |
0.00% |
0 / 1 |
|
0.00% |
0 / 1 |
2 | |||
| buildTruncLayer | |
0.00% |
0 / 1 |
|
0.00% |
0 / 1 |
2 | |||
| factorGraphBuilders | |
0.00% |
0 / 6 |
|
0.00% |
0 / 1 |
2 | |||
| rating | |
0.00% |
0 / 14 |
|
0.00% |
0 / 1 |
2 | |||
| 1 | <?php |
| 2 | /** |
| 3 | * Jingga |
| 4 | * |
| 5 | * PHP Version 8.1 |
| 6 | * |
| 7 | * @package phpOMS\Algorithm\Rating |
| 8 | * @copyright Microsoft |
| 9 | * @license This algorithm may be patented by Microsoft, verify and acquire a license if necessary |
| 10 | * @version 1.0.0 |
| 11 | * @link https://jingga.app |
| 12 | */ |
| 13 | declare(strict_types=1); |
| 14 | |
| 15 | namespace phpOMS\Algorithm\Rating; |
| 16 | |
| 17 | use phpOMS\Math\Stochastic\Distribution\NormalDistribution; |
| 18 | |
| 19 | /** |
| 20 | * Elo rating calculation using Elo rating |
| 21 | * |
| 22 | * @package phpOMS\Algorithm\Rating |
| 23 | * @license OMS License 2.0 |
| 24 | * @link https://jingga.app |
| 25 | * @since 1.0.0 |
| 26 | * @see https://www.moserware.com/assets/computing-your-skill/The%20Math%20Behind%20TrueSkill.pdf |
| 27 | * |
| 28 | * @todo implement https://github.com/sublee/trueskill/blob/master/trueskill/__init__.py |
| 29 | */ |
| 30 | class TrueSkill |
| 31 | { |
| 32 | public int $DEFAULT_MU = 25; |
| 33 | |
| 34 | public float $DEFAULT_SIGMA = 25 / 3; |
| 35 | |
| 36 | public float $DEFAULT_BETA = 25 / 3 / 2; |
| 37 | |
| 38 | public float $DEFAULT_TAU = 25 / 3 / 100; |
| 39 | |
| 40 | public float $DEFAULT_DRAW_PROBABILITY = 0.1; |
| 41 | |
| 42 | public function __construct() |
| 43 | { |
| 44 | } |
| 45 | |
| 46 | // Draw margin = epsilon |
| 47 | /** |
| 48 | * P_{draw} = 2\Phi\left(\dfrac{\epsilon}{\sqrt{n_1 + n_2} * \beta}\right) - 1 |
| 49 | */ |
| 50 | public function drawProbability(float $drawMargin, int $n1, int $n2, float $beta) |
| 51 | { |
| 52 | return 2 * NormalDistribution::getCdf($drawMargin / (\sqrt($n1 + $n2) * $beta), 0.0, 1.0) - 1; |
| 53 | } |
| 54 | |
| 55 | /** |
| 56 | * \epsilon = \Phi^{-1}\left(\dfrac{P_{draw} + 1}{2}\right) * \sqrt{n_1 + n_2} * \beta |
| 57 | */ |
| 58 | public function drawMargin(float $drawProbability, int $n1, int $n2, float $beta) |
| 59 | { |
| 60 | return NormalDistribution::getIcdf(($drawProbability + 1) / 2.0, 0.0, 1.0) * \sqrt($n1 + $n2) * $beta; |
| 61 | } |
| 62 | |
| 63 | /** |
| 64 | * Mean additive truncated gaussion function "v" for wins |
| 65 | * |
| 66 | * @latex c = \sqrt{2 * \beta^2 + \sigma_{winner}^2 + \sigma_{loser}^2} |
| 67 | * @latex \mu_{winner} = \mu_{winner} + \dfrac{\sigma_{winner}^2}{c} * \nu \left(\dfrac{\mu_{winner} - \mu_{loser}}{c}, \dfrac{\epsilon}{c}\right) |
| 68 | * @latex \mu_{loser} = \mu_{loser} + \dfrac{\sigma_{loser}^2}{c} * \nu \left(\dfrac{\mu_{winner} - \mu_{loser}}{c}, \dfrac{\epsilon}{c}\right) |
| 69 | * @latex t = \dfrac{\mu_{winner} - \mu_{loser}}{c} |
| 70 | * |
| 71 | * @latex \nu = \dfrac{\mathcal{N}(t - \epsilon)}{\Phi(t - \epsilon)} |
| 72 | * |
| 73 | * @param float $t Difference winner and loser mu |
| 74 | * @param float $epsilon Draw margin |
| 75 | * |
| 76 | * @return float |
| 77 | * |
| 78 | * @since 1.0.0 |
| 79 | */ |
| 80 | private function vWin(float $t, float $epsilon) : float |
| 81 | { |
| 82 | return NormalDistribution::getPdf($t - $epsilon, 0, 1.0) / NormalDistribution::getCdf($t - $epsilon, 0.0, 1.0); |
| 83 | } |
| 84 | |
| 85 | /** |
| 86 | * Mean additive truncated gaussion function "v" for draws |
| 87 | * |
| 88 | * @latex c = \sqrt{2 * \beta^2 + \sigma_{winner}^2 + \sigma_{loser}^2} |
| 89 | * @latex \mu_{winner} = \mu_{winner} + \dfrac{\sigma_{winner}^2}{c} * \nu \left(\dfrac{\mu_{winner} - \mu_{loser}}{c}, \dfrac{\epsilon}{c}\right) |
| 90 | * @latex \mu_{loser} = \mu_{loser} + \dfrac{\sigma_{loser}^2}{c} * \nu \left(\dfrac{\mu_{winner} - \mu_{loser}}{c}, \dfrac{\epsilon}{c}\right) |
| 91 | * @latex t = \dfrac{\mu_{winner} - \mu_{loser}}{c} |
| 92 | * @latex \dfrac{\mathcal{N}(t - \epsilon)}{\Phi(t - \epsilon)} |
| 93 | * |
| 94 | * @latex \nu = \dfrac{\mathcal{N}(-\epsilon - t) - \mathcal{N}(\epsilon - t)}{\Phi(\epsilon - t) - \Phi(-\epsilon - t)} |
| 95 | * |
| 96 | * @param float $t Difference winner and loser mu |
| 97 | * @param float $epsilon Draw margin |
| 98 | * |
| 99 | * @return float |
| 100 | * |
| 101 | * @since 1.0.0 |
| 102 | */ |
| 103 | private function vDraw(float $t, float $epsilon) : float |
| 104 | { |
| 105 | $tAbs = \abs($t); |
| 106 | $a = $epsilon - $tAbs; |
| 107 | $b = -$epsilon - $tAbs; |
| 108 | |
| 109 | $aPdf = NormalDistribution::getPdf($a, 0.0, 1.0); |
| 110 | $bPdf = NormalDistribution::getPdf($b, 0.0, 1.0); |
| 111 | $numer = $bPdf - $aPdf; |
| 112 | |
| 113 | $aCdf = NormalDistribution::getCdf($a, 0.0, 1.0); |
| 114 | $bCdf = NormalDistribution::getCdf($b, 0.0, 1.0); |
| 115 | $denom = $aCdf - $bCdf; |
| 116 | |
| 117 | return $numer / $denom; |
| 118 | } |
| 119 | |
| 120 | /** |
| 121 | * Variance multiplicative function "w" for draws |
| 122 | * |
| 123 | * @latex w = \nu * (\nu + t - \epsilon) |
| 124 | * |
| 125 | * @param float $t Difference winner and loser mu |
| 126 | * @param float $epsilon Draw margin |
| 127 | * |
| 128 | * @return float |
| 129 | * |
| 130 | * @since 1.0.0 |
| 131 | */ |
| 132 | private function wWin(float $t, float $epsilon) : float |
| 133 | { |
| 134 | $v = $this->vWin($t, $epsilon); |
| 135 | |
| 136 | return $v * ($v + $t - $epsilon); |
| 137 | } |
| 138 | |
| 139 | /** |
| 140 | * Variance multiplicative function "w" for draws |
| 141 | * |
| 142 | * @latex w = \nu^2 + \dfrac{(\epsilon - t) * \mathcal{N}(\epsilon - t) + (\epsilon + t) * \mathcal{N}(\epsilon + t)}{\Phi(\epsilon - t) - \Phi(-\epsilon - t)} |
| 143 | * |
| 144 | * @param float $t Difference winner and loser mu |
| 145 | * @param float $epsilon Draw margin |
| 146 | * |
| 147 | * @return float |
| 148 | * |
| 149 | * @since 1.0.0 |
| 150 | */ |
| 151 | private function wDraw(float $t, float $epsilon) : float |
| 152 | { |
| 153 | $tAbs = \abs($t); |
| 154 | |
| 155 | $v = $this->vDraw($t, $epsilon); |
| 156 | |
| 157 | return $v * $v |
| 158 | + (($epsilon - $t) * NormalDistribution::getPdf($epsilon - $tAbs, 0.0, 1.0) + ($epsilon + $tAbs) * NormalDistribution::getPdf($epsilon + $tAbs, 0.0, 1.0)) |
| 159 | / (NormalDistribution::getCdf($epsilon - $tAbs, 0.0, 1.0) - NormalDistribution::getCdf(-$epsilon - $tAbs, 0.0, 1.0)); |
| 160 | } |
| 161 | |
| 162 | private function buildRatingLayer() : void |
| 163 | { |
| 164 | } |
| 165 | |
| 166 | private function buildPerformanceLayer() : void |
| 167 | { |
| 168 | } |
| 169 | |
| 170 | private function buildTeamPerformanceLayer() : void |
| 171 | { |
| 172 | } |
| 173 | |
| 174 | private function buildTruncLayer() : void |
| 175 | { |
| 176 | } |
| 177 | |
| 178 | private function factorGraphBuilders() |
| 179 | { |
| 180 | // Rating layer |
| 181 | |
| 182 | // Performance layer |
| 183 | |
| 184 | // Team Performance layer |
| 185 | |
| 186 | // Trunc layer |
| 187 | |
| 188 | return [ |
| 189 | 'rating_layer' => $ratingLayer, |
| 190 | 'performance_layer' => $ratingLayer, |
| 191 | 'team_performance_layer' => $ratingLayer, |
| 192 | 'trunc_layer' => $ratingLayer, |
| 193 | ]; |
| 194 | } |
| 195 | |
| 196 | public function rating() : void |
| 197 | { |
| 198 | // Start values |
| 199 | $mu = 25; |
| 200 | $sigma = $mu / 3; |
| 201 | $beta = $sigma / 2; |
| 202 | $tau = $sigma / 100; |
| 203 | $Pdraw = 0.1; |
| 204 | |
| 205 | $alpha = 0.25; |
| 206 | |
| 207 | // Partial update |
| 208 | $sigmaPartial = $sigmaOld * $sigmaNew / \sqrt($alpha * $sigmaOld * $sigmaOld - ($alpha - 1) * $sigmaNew * $sigmaNew); |
| 209 | $muPartial = $muOld * ($alpha - 1) * $sigmaNew * $sigmaNew - $muNew * $alpha * $sigmaOld * $sigmaOld |
| 210 | / (($alpha - 1) * $sigmaNew * $sigmaNew - $alpha * $sigmaOld * $sigmaOld); |
| 211 | |
| 212 | // New |
| 213 | $tau = $pi * $mu; |
| 214 | |
| 215 | $P = NormalDistribution::getCdf(($s1 - $s2) / (\sqrt(2) * $beta)); |
| 216 | $Delta = $alpha * $beta * \sqrt($pi) * (($y + 1) / 2 - $P); |
| 217 | |
| 218 | $K = NormalDistribution::getCdf(); |
| 219 | |
| 220 | $pi = 1 / ($sigma * $sigma); |
| 221 | } |
| 222 | } |