Rating::getRankingUsingImdb() - Code Metrics - Inspection of "CountsManager" - pryley/site-reviews - Measure and Improve Code Quality continuously with Scrutinizer

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by Paul

created 2018-07-18 17:18 UTC

Rating::getRankingUsingImdb() A

↳ Parent: Rating

Complexity

Conditions	2
Paths	2

Size

Total Lines	12
Code Lines	6

Duplication

Lines	0
Ratio	0 %

Code Coverage

Tests	0
CRAP Score	6

Importance

Changes

Metric	Value
cc	2
eloc	6
nc	2
nop	2
dl	0
loc	12
ccs	0
cts	9
cp	0
crap	6
rs	10
c	0
b	0
f	0

<?php

namespace GeminiLabs\SiteReviews\Modules;

class Rating
{
	/**
	 * The more sure we are of the confidence interval (the higher the confidence level), the less
	 * precise the estimation will be as the margin for error will be higher.
	 * @see http://homepages.math.uic.edu/~bpower6/stat101/Confidence%20Intervals.pdf
	 * @see https://www.thecalculator.co/math/Confidence-Interval-Calculator-210.html
	 * @see https://www.youtube.com/watch?v=grodoLzThy4
	 * @see https://en.wikipedia.org/wiki/Standard_score
	 * @var array
	 */
	const CONFIDENCE_LEVEL_Z_SCORES = [
		50 => 0.67449,
		70 => 1.04,
		75 => 1.15035,
		80 => 1.282,
		85 => 1.44,
		90 => 1.64485,
		92 => 1.75,
		95 => 1.95996,
		96 => 2.05,
		97 => 2.17009,
		98 => 2.326,
		99 => 2.57583,
		'99.5' => 2.81,
		'99.8' => 3.08,
		'99.9' => 3.29053,
	];

	/**
	 * @var int
	 */
	const MAX_RATING = 5;

	/**
	 * @var int
	 */
	const MIN_RATING = 1;

	/**
	 * @param int $roundBy
	 * @return float
	 */
	public function getAverage( array $ratingCounts, $roundBy = 1 )
	{
		$average = array_sum( $ratingCounts );
		if( $average > 0 ) {
			$average = round( $this->getTotalSum( $ratingCounts ) / $average, intval( $roundBy ));
		}
		return floatval( apply_filters( 'site-reviews/rating/average', $average, $ratingCounts ));
	}

	/**
	 * Get the lower bound for up/down ratings
	 * Method receives an up/down ratings array: [1, -1, -1, 1, 1, -1]
	 * @see http://www.evanmiller.org/how-not-to-sort-by-average-rating.html
	 * @see https://news.ycombinator.com/item?id=10481507
	 * @see https://dataorigami.net/blogs/napkin-folding/79030467-an-algorithm-to-sort-top-comments
	 * @see http://julesjacobs.github.io/2015/08/17/bayesian-scoring-of-ratings.html
	 * @param int $confidencePercentage
	 * @return int|float
	 */
	public function getLowerBound( array $upDownCounts = [0, 0], $confidencePercentage = 95 )
	{
		$numRatings = array_sum( $upDownCounts );
		if( $numRatings < 1 ) {
			return 0;
		}
		$z = static::CONFIDENCE_LEVEL_Z_SCORES[$confidencePercentage];
		$phat = 1 * $upDownCounts[1] / $numRatings;
		return ( $phat + $z * $z / ( 2 * $numRatings ) - $z * sqrt(( $phat * ( 1 - $phat ) + $z * $z / ( 4 * $numRatings )) / $numRatings )) / ( 1 + $z * $z / $numRatings );
	}

	/**
	 * @return int|float
	 */
	public function getOverallPercentage( array $ratingCounts )
	{
		return round( $this->getAverage( $ratingCounts ) * 100 / static::MAX_RATING, 2 );
	}

	/**
	 * @return array
	 */
	public function getPercentages( array $ratingCounts )
	{
		$total = array_sum( $ratingCounts );
		foreach( $ratingCounts as $index => $count ) {
			if( empty( $count ))continue;
			$ratingCounts[$index] = $count / $total * 100;
		}
		return $this->getRoundedPercentages( $ratingCounts );
	}

	/**
	 * @return float
	 */
	public function getRanking( array $ratingCounts )
	{
		return floatval( apply_filters( 'site-reviews/bayesian/ranking',
			$this->getRankingUsingImdb( $ratingCounts ),
			$ratingCounts,
			$this
		));
	}

	/**
	 * Get the bayesian ranking for an array of reviews
	 * This formula is the same one used by IMDB to rank their top 250 films
	 * @see https://www.xkcd.com/937/
	 * @see https://districtdatalabs.silvrback.com/computing-a-bayesian-estimate-of-star-rating-means
	 * @see http://fulmicoton.com/posts/bayesian_rating/
	 * @see https://stats.stackexchange.com/questions/93974/is-there-an-equivalent-to-lower-bound-of-wilson-score-confidence-interval-for-va
	 * @param int $confidencePercentage
	 * @return int|float
	 */
	public function getRankingUsingImdb( array $ratingCounts, $confidencePercentage = 70 )
	{
		$avgRating = $this->getAverage( $ratingCounts );
		// Represents a prior (your prior opinion without data) for the average star rating. A higher prior also means a higher margin for error.
		// This could also be the average score of all items instead of a fixed value.
		$bayesMean = ( $confidencePercentage / 100 ) * static::MAX_RATING; // prior, 70% = 3.5
		// Represents the number of ratings expected to begin observing a pattern that would put confidence in the prior.
		$bayesMinimal = 10; // confidence
		$numOfReviews = array_sum( $ratingCounts );
		return $avgRating > 0
			? (( $bayesMinimal * $bayesMean ) + ( $avgRating * $numOfReviews )) / ( $bayesMinimal + $numOfReviews )
			: 0;
	}

	/**
	 * The quality of a 5 star rating depends not only on the average number of stars but also on
	 * the number of reviews. This method calculates the bayesian ranking of a page by its number
	 * of reviews and their rating.
	 * @see http://www.evanmiller.org/ranking-items-with-star-ratings.html
	 * @see https://stackoverflow.com/questions/1411199/what-is-a-better-way-to-sort-by-a-5-star-rating/1411268
	 * @see http://julesjacobs.github.io/2015/08/17/bayesian-scoring-of-ratings.html
	 * @param int $confidencePercentage
	 * @return float
	 */
	public function getRankingUsingZScores( array $ratingCounts, $confidencePercentage = 90 )
	{
		$ratingCountsSum = array_sum( $ratingCounts ) + static::MAX_RATING;
		$weight = $this->getWeight( $ratingCounts, $ratingCountsSum );
		$weightPow2 = $this->getWeight( $ratingCounts, $ratingCountsSum, true );
		$zScore = static::CONFIDENCE_LEVEL_Z_SCORES[$confidencePercentage];
		return $weight - $zScore * sqrt(( $weightPow2 - pow( $weight, 2 )) / ( $ratingCountsSum + 1 ));
	}

	/**
	 * @param int $target
	 * @return array
	 */
	protected function getRoundedPercentages( array $percentages, $totalPercent = 100 )
	{
		array_walk( $percentages, function( &$percent, $index ) {
			$percent = [
				'index' => $index,
				'percent' => floor( $percent ),
				'remainder' => fmod( $percent, 1 ),
			];
		});
		$indexes = array_column( $percentages, 'index' );
		$remainders = array_column( $percentages, 'remainder' );
		array_multisort( $remainders, SORT_DESC, SORT_STRING, $indexes, SORT_DESC, $percentages );
		$i = 0;
		if( array_sum( array_column( $percentages, 'percent' )) > 0 ) {
			while( array_sum( array_column( $percentages, 'percent' )) < $totalPercent ) {
				$percentages[$i]['percent']++;
				$i++;
			}
		}
		array_multisort( $indexes, SORT_DESC, $percentages );
		return array_combine( $indexes, array_column( $percentages, 'percent' ));
	}

	/**
	 * @return int
	 */
	protected function getTotalSum( array $ratingCounts )
	{
		return array_reduce( $ratingCounts, function( $carry, $count ) {
			return $carry + $count;
		});
	}

	/**
	 * @param int|double $ratingCountsSum
	 * @param bool $powerOf2
	 * @return float
	 */
	protected function getWeight( array $ratingCounts, $ratingCountsSum, $powerOf2 = false )
	{
		return array_reduce( array_keys( $ratingCounts ),
			function( $count, $rating ) use( $ratingCounts, $ratingCountsSum, $powerOf2 ) {
				$ratingLevel = $powerOf2
					? pow( $rating, 2 )
					: $rating;
				return $count + ( $ratingLevel * ( $ratingCounts[$rating] + 1 )) / $ratingCountsSum;
			}
		);
	}
}


1			<?php
2
3			namespace GeminiLabs\SiteReviews\Modules;
4
5			class Rating
6			{
7			/**
8			* The more sure we are of the confidence interval (the higher the confidence level), the less
9			* precise the estimation will be as the margin for error will be higher.
10			* @see http://homepages.math.uic.edu/~bpower6/stat101/Confidence%20Intervals.pdf
11			* @see https://www.thecalculator.co/math/Confidence-Interval-Calculator-210.html
12			* @see https://www.youtube.com/watch?v=grodoLzThy4
13			* @see https://en.wikipedia.org/wiki/Standard_score
14			* @var array
15			*/
16			const CONFIDENCE_LEVEL_Z_SCORES = [
17			50 => 0.67449,
18			70 => 1.04,
19			75 => 1.15035,
20			80 => 1.282,
21			85 => 1.44,
22			90 => 1.64485,
23			92 => 1.75,
24			95 => 1.95996,
25			96 => 2.05,
26			97 => 2.17009,
27			98 => 2.326,
28			99 => 2.57583,
29			'99.5' => 2.81,
30			'99.8' => 3.08,
31			'99.9' => 3.29053,
32			];
33
34			/**
35			* @var int
36			*/
37			const MAX_RATING = 5;
38
39			/**
40			* @var int
41			*/
42			const MIN_RATING = 1;
43
44			/**
45			* @param int $roundBy
46			* @return float
47			*/
48			public function getAverage( array $ratingCounts, $roundBy = 1 )
49			{
50			$average = array_sum( $ratingCounts );
51			if( $average > 0 ) {
52			$average = round( $this->getTotalSum( $ratingCounts ) / $average, intval( $roundBy ));
53			}
54			return floatval( apply_filters( 'site-reviews/rating/average', $average, $ratingCounts ));
55			}
56
57			/**
58			* Get the lower bound for up/down ratings
59			* Method receives an up/down ratings array: [1, -1, -1, 1, 1, -1]
60			* @see http://www.evanmiller.org/how-not-to-sort-by-average-rating.html
61			* @see https://news.ycombinator.com/item?id=10481507
62			* @see https://dataorigami.net/blogs/napkin-folding/79030467-an-algorithm-to-sort-top-comments
63			* @see http://julesjacobs.github.io/2015/08/17/bayesian-scoring-of-ratings.html
64			* @param int $confidencePercentage
65			* @return int\|float
66			*/
67			public function getLowerBound( array $upDownCounts = [0, 0], $confidencePercentage = 95 )
68			{
69			$numRatings = array_sum( $upDownCounts );
70			if( $numRatings < 1 ) {
71			return 0;
72			}
73			$z = static::CONFIDENCE_LEVEL_Z_SCORES[$confidencePercentage];
74			$phat = 1 * $upDownCounts[1] / $numRatings;
75			return ( $phat + $z * $z / ( 2 * $numRatings ) - $z * sqrt(( $phat * ( 1 - $phat ) + $z * $z / ( 4 * $numRatings )) / $numRatings )) / ( 1 + $z * $z / $numRatings );
76			}
77
78			/**
79			* @return int\|float
80			*/
81			public function getOverallPercentage( array $ratingCounts )
82			{
83			return round( $this->getAverage( $ratingCounts ) * 100 / static::MAX_RATING, 2 );
84			}
85
86			/**
87			* @return array
88			*/
89			public function getPercentages( array $ratingCounts )
90			{
91			$total = array_sum( $ratingCounts );
92			foreach( $ratingCounts as $index => $count ) {
93			if( empty( $count ))continue;
94			$ratingCounts[$index] = $count / $total * 100;
95			}
96			return $this->getRoundedPercentages( $ratingCounts );
97			}
98
99			/**
100			* @return float
101			*/
102			public function getRanking( array $ratingCounts )
103			{
104			return floatval( apply_filters( 'site-reviews/bayesian/ranking',
105			$this->getRankingUsingImdb( $ratingCounts ),
106			$ratingCounts,
107			$this
108			));
109			}
110
111			/**
112			* Get the bayesian ranking for an array of reviews
113			* This formula is the same one used by IMDB to rank their top 250 films
114			* @see https://www.xkcd.com/937/
115			* @see https://districtdatalabs.silvrback.com/computing-a-bayesian-estimate-of-star-rating-means
116			* @see http://fulmicoton.com/posts/bayesian_rating/
117			* @see https://stats.stackexchange.com/questions/93974/is-there-an-equivalent-to-lower-bound-of-wilson-score-confidence-interval-for-va
118			* @param int $confidencePercentage
119			* @return int\|float
120			*/
121			public function getRankingUsingImdb( array $ratingCounts, $confidencePercentage = 70 )
122			{
123			$avgRating = $this->getAverage( $ratingCounts );
124			// Represents a prior (your prior opinion without data) for the average star rating. A higher prior also means a higher margin for error.
125			// This could also be the average score of all items instead of a fixed value.
126			$bayesMean = ( $confidencePercentage / 100 ) * static::MAX_RATING; // prior, 70% = 3.5
127			// Represents the number of ratings expected to begin observing a pattern that would put confidence in the prior.
128			$bayesMinimal = 10; // confidence
129			$numOfReviews = array_sum( $ratingCounts );
130			return $avgRating > 0
131			? (( $bayesMinimal * $bayesMean ) + ( $avgRating * $numOfReviews )) / ( $bayesMinimal + $numOfReviews )
132			: 0;
133			}
134
135			/**
136			* The quality of a 5 star rating depends not only on the average number of stars but also on
137			* the number of reviews. This method calculates the bayesian ranking of a page by its number
138			* of reviews and their rating.
139			* @see http://www.evanmiller.org/ranking-items-with-star-ratings.html
140			* @see https://stackoverflow.com/questions/1411199/what-is-a-better-way-to-sort-by-a-5-star-rating/1411268
141			* @see http://julesjacobs.github.io/2015/08/17/bayesian-scoring-of-ratings.html
142			* @param int $confidencePercentage
143			* @return float
144			*/
145			public function getRankingUsingZScores( array $ratingCounts, $confidencePercentage = 90 )
146			{
147			$ratingCountsSum = array_sum( $ratingCounts ) + static::MAX_RATING;
148			$weight = $this->getWeight( $ratingCounts, $ratingCountsSum );
149			$weightPow2 = $this->getWeight( $ratingCounts, $ratingCountsSum, true );
150			$zScore = static::CONFIDENCE_LEVEL_Z_SCORES[$confidencePercentage];
151			return $weight - $zScore * sqrt(( $weightPow2 - pow( $weight, 2 )) / ( $ratingCountsSum + 1 ));
152			}
153
154			/**
155			* @param int $target
156			* @return array
157			*/
158			protected function getRoundedPercentages( array $percentages, $totalPercent = 100 )
159			{
160			array_walk( $percentages, function( &$percent, $index ) {
161			$percent = [
162			'index' => $index,
163			'percent' => floor( $percent ),
164			'remainder' => fmod( $percent, 1 ),
165			];
166			});
167			$indexes = array_column( $percentages, 'index' );
168			$remainders = array_column( $percentages, 'remainder' );
169			array_multisort( $remainders, SORT_DESC, SORT_STRING, $indexes, SORT_DESC, $percentages );
170			$i = 0;
171			if( array_sum( array_column( $percentages, 'percent' )) > 0 ) {
172			while( array_sum( array_column( $percentages, 'percent' )) < $totalPercent ) {
173			$percentages[$i]['percent']++;
174			$i++;
175			}
176			}
177			array_multisort( $indexes, SORT_DESC, $percentages );
178			return array_combine( $indexes, array_column( $percentages, 'percent' ));
179			}
180
181			/**
182			* @return int
183			*/
184			protected function getTotalSum( array $ratingCounts )
185			{
186			return array_reduce( $ratingCounts, function( $carry, $count ) {
187			return $carry + $count;
188			});
189			}
190
191			/**
192			* @param int\|double $ratingCountsSum
193			* @param bool $powerOf2
194			* @return float
195			*/
196			protected function getWeight( array $ratingCounts, $ratingCountsSum, $powerOf2 = false )
197			{
198			return array_reduce( array_keys( $ratingCounts ),
199			function( $count, $rating ) use( $ratingCounts, $ratingCountsSum, $powerOf2 ) {
200			$ratingLevel = $powerOf2
201			? pow( $rating, 2 )
202			: $rating;
203			return $count + ( $ratingLevel * ( $ratingCounts[$rating] + 1 )) / $ratingCountsSum;
204			}
205			);
206			}
207			}
208

pryley / site-reviews

Push — master ( 87eb8d...25783a )

Rating::getRankingUsingImdb() A

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