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<?php |
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namespace GeminiLabs\SiteReviews\Modules; |
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class Rating |
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{ |
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public const CONFIDENCE_LEVEL_Z_SCORES = [ |
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50 => 0.67449, |
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70 => 1.04, |
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75 => 1.15035, |
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80 => 1.282, |
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85 => 1.44, |
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90 => 1.64485, |
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92 => 1.75, |
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95 => 1.95996, |
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96 => 2.05, |
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97 => 2.17009, |
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98 => 2.326, |
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99 => 2.57583, |
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'99.5' => 2.81, |
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'99.8' => 3.08, |
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'99.9' => 3.29053, |
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]; |
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public const MAX_RATING = 5; |
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public const MIN_RATING = 0; |
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/** |
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* @param int[] $ratingCounts |
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*/ |
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public function average(array $ratingCounts, ?int $roundBy = null): float |
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{ |
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$average = 0; |
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$total = $this->totalCount($ratingCounts); |
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if ($total > 0) { |
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$average = $this->totalSum($ratingCounts) / $total; |
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} |
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if (is_null($roundBy)) { |
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$roundBy = glsr()->filterInt('rating/round-by', 1); |
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} |
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$roundedAverage = round($average, intval($roundBy)); |
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return glsr()->filterFloat('rating/average', $roundedAverage, $average, $ratingCounts); |
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} |
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public function emptyArray(): array |
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{ |
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return array_fill_keys(range(0, static::max()), 0); |
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} |
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public function format(float $rating): string |
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{ |
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$roundBy = $rating > 0 ? 1 : 0; |
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$roundBy = glsr()->filterInt('rating/round-by', $roundBy, $rating); |
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return (string) number_format_i18n($rating, $roundBy); |
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} |
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public function isValid(int $rating): bool |
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{ |
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return array_key_exists($rating, $this->emptyArray()); |
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} |
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public static function labels(): array |
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{ |
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$labels = [ |
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__('Excellent', 'site-reviews'), |
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__('Very good', 'site-reviews'), |
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__('Average', 'site-reviews'), |
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__('Poor', 'site-reviews'), |
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__('Terrible', 'site-reviews'), |
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]; |
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$max = static::max(); |
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if (5 !== $max) { |
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$labels = array_map( |
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fn ($stars) => sprintf(_n('%d star', '%d stars', $stars, 'site-reviews'), $stars), |
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range($max, 1) |
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); |
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} |
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return array_combine(range($max, 1), $labels); |
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} |
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/** |
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* Get the lower bound for up/down ratings |
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* Method receives an up/down ratings array: [1, -1, -1, 1, 1, -1]. |
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* |
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* @see http://www.evanmiller.org/how-not-to-sort-by-average-rating.html |
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* @see https://news.ycombinator.com/item?id=10481507 |
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* @see https://dataorigami.net/blogs/napkin-folding/79030467-an-algorithm-to-sort-top-comments |
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* @see http://julesjacobs.github.io/2015/08/17/bayesian-scoring-of-ratings.html |
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*/ |
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public function lowerBound(array $upDownCounts = [0, 0], int $confidencePercentage = 95): float |
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{ |
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$numRatings = array_sum($upDownCounts); |
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if ($numRatings < 1) { |
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return 0; |
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} |
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$z = static::CONFIDENCE_LEVEL_Z_SCORES[$confidencePercentage]; |
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$phat = 1 * $upDownCounts[1] / $numRatings; |
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return (float) ($phat + $z * $z / (2 * $numRatings) - $z * sqrt(($phat * (1 - $phat) + $z * $z / (4 * $numRatings)) / $numRatings)) / (1 + $z * $z / $numRatings); |
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} |
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public static function max(): int |
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{ |
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return max(1, glsr()->filterInt('const/MAX_RATING', static::MAX_RATING)); |
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} |
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public static function min(): int |
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{ |
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return max(0, glsr()->filterInt('const/MIN_RATING', static::MIN_RATING)); |
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} |
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/** |
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* @param array $noopedPlural The result of _n_noop() |
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*/ |
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public function optionsArray(array $noopedPlural = [], int $minRating = 1): array |
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{ |
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$options = []; |
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if (empty($noopedPlural)) { |
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$noopedPlural = _n_noop('%s Star', '%s Stars', 'site-reviews'); |
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} |
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$min = max($minRating, static::min()); |
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foreach (range(static::max(), $min) as $rating) { |
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$title = translate_nooped_plural($noopedPlural, $rating, 'site-reviews'); |
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if (!str_contains($title, '%s')) { |
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$title = "%s {$title}"; // because Arr::unique() is used for array values when defaults are merged. |
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} |
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$options[$rating] = wp_sprintf($title, $rating); |
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} |
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return $options; |
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} |
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/** |
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* @param int[] $ratingCounts |
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*/ |
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public function overallPercentage(array $ratingCounts): float |
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{ |
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return round($this->average($ratingCounts) * 100 / static::max(), 2); |
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} |
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/** |
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* @param int[] $ratingCounts |
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*/ |
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public function percentages(array $ratingCounts): array |
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{ |
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if (empty($ratingCounts)) { |
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$ratingCounts = $this->emptyArray(); |
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} |
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$percentages = []; |
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$total = array_sum($ratingCounts); |
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foreach ($ratingCounts as $index => $count) { |
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$percentage = empty($count) ? 0 : $count / $total * 100; |
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$percentages[$index] = (float) $percentage; |
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} |
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return $this->roundedPercentages($percentages); |
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} |
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/** |
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* @param int[] $ratingCounts |
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*/ |
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public function ranking(array $ratingCounts): float |
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{ |
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return glsr()->filterFloat('rating/ranking', |
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$this->rankingUsingImdb($ratingCounts), |
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$ratingCounts, |
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$this |
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); |
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} |
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/** |
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* Get the bayesian ranking for an array of reviews |
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* This formula is the same one used by IMDB to rank their top 250 films. |
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* |
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* @see https://www.xkcd.com/937/ |
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* @see https://districtdatalabs.silvrback.com/computing-a-bayesian-estimate-of-star-rating-means |
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* @see http://fulmicoton.com/posts/bayesian_rating/ |
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* @see https://stats.stackexchange.com/questions/93974/is-there-an-equivalent-to-lower-bound-of-wilson-score-confidence-interval-for-va |
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*/ |
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public function rankingUsingImdb(array $ratingCounts, int $confidencePercentage = 70): float |
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{ |
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$avgRating = $this->average($ratingCounts); |
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// Represents a prior (your prior opinion without data) for the average star rating. A higher prior also means a higher margin for error. |
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// This could also be the average score of all items instead of a fixed value. |
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$bayesMean = ($confidencePercentage / 100) * static::max(); // prior, 70% = 3.5 |
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// Represents the number of ratings expected to begin observing a pattern that would put confidence in the prior. |
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$bayesMinimal = 10; // confidence |
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$numOfReviews = $this->totalCount($ratingCounts); |
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return $avgRating > 0 |
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? (float) (($bayesMinimal * $bayesMean) + ($avgRating * $numOfReviews)) / ($bayesMinimal + $numOfReviews) |
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: (float) 0; |
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} |
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/** |
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* The quality of a 5 star rating depends not only on the average number of stars but also on |
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* the number of reviews. This method calculates the bayesian ranking of a page by its number |
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* of reviews and their rating. |
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* |
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* @see http://www.evanmiller.org/ranking-items-with-star-ratings.html |
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* @see https://stackoverflow.com/questions/1411199/what-is-a-better-way-to-sort-by-a-5-star-rating/1411268 |
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* @see http://julesjacobs.github.io/2015/08/17/bayesian-scoring-of-ratings.html |
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* |
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* @param int[] $ratingCounts |
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*/ |
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public function rankingUsingZScores(array $ratingCounts, int $confidencePercentage = 90): float |
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{ |
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$ratingCountsSum = (float) $this->totalCount($ratingCounts) + static::max(); |
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$weight = $this->weight($ratingCounts, $ratingCountsSum); |
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$weightPow2 = $this->weight($ratingCounts, $ratingCountsSum, true); |
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$zScore = static::CONFIDENCE_LEVEL_Z_SCORES[$confidencePercentage]; |
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return $weight - $zScore * sqrt(($weightPow2 - pow($weight, 2)) / ($ratingCountsSum + 1)); |
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} |
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/** |
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* @param int[] $ratingCounts |
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*/ |
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public function totalCount(array $ratingCounts): int |
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{ |
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$values = array_filter($ratingCounts, 'is_numeric'); |
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$values = array_map('intval', $values); |
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if (isset($values[0]) && glsr()->filterBool('rating/ignore-zero-stars', true)) { |
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$values[0] = 0; // ignore 0-star ratings when calculating the average and ranking |
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} |
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return (int) array_sum($values); |
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} |
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/** |
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* Returns array sorted by key DESC. |
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* |
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* @param float[] $percentages |
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*/ |
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protected function roundedPercentages(array $percentages, int $totalPercent = 100): array |
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{ |
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array_walk($percentages, function (&$percent, $index) { |
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$percent = [ |
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'index' => $index, |
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'percent' => floor($percent), |
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'remainder' => fmod($percent, 1), |
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]; |
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}); |
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$indexes = wp_list_pluck($percentages, 'index'); |
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$remainders = wp_list_pluck($percentages, 'remainder'); |
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array_multisort($remainders, \SORT_DESC, \SORT_STRING, $indexes, \SORT_DESC, $percentages); |
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$i = 0; |
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if (array_sum(wp_list_pluck($percentages, 'percent')) > 0) { |
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while (array_sum(wp_list_pluck($percentages, 'percent')) < $totalPercent) { |
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++$percentages[$i]['percent']; |
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++$i; |
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} |
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} |
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array_multisort($indexes, \SORT_DESC, $percentages); |
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return array_combine($indexes, wp_list_pluck($percentages, 'percent')); |
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} |
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/** |
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* @param int[] $ratingCounts |
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*/ |
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protected function totalSum(array $ratingCounts): int |
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{ |
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return (int) array_reduce( |
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array_keys($ratingCounts), |
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fn ($carry, $i) => $carry + ($i * $ratingCounts[$i]), |
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0 |
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); |
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} |
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/** |
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* @param int[] $ratingCounts |
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*/ |
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protected function weight(array $ratingCounts, float $ratingCountsSum, bool $powerOf2 = false): float |
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{ |
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return (float) array_reduce(array_keys($ratingCounts), |
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function ($count, $rating) use ($ratingCounts, $ratingCountsSum, $powerOf2) { |
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$ratingLevel = $powerOf2 |
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? pow($rating, 2) |
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: $rating; |
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return $count + ($ratingLevel * ($ratingCounts[$rating] + 1)) / $ratingCountsSum; |
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}, |
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0 |
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); |
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} |
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} |
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