{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Weighted Rating\n", "\n", "I was looking for an algorithm that takes into account the number of votes and not just the average rating. For example a 4 star review with 100 reviewers should account for more that 5 star review from 3 people.\n", "\n", "A bit of googling found [an answer on mathexchange](http://math.stackexchange.com/questions/942738/algorithm-to-calculate-rating-based-on-multiple-reviews-using-both-review-score). The formula given there is:\n", "\n", "$score = 5p/10 + 5(1 -e^{-q/Q})$\n", "\n", "Where\n", "* `p` is the rating\n", "* `q` is the number of votes\n", "* `Q` is the weight of number of votes\n", "\n", "This looked good but I wanted to have a quick look on how this behaves. " ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "%matplotlib inline\n", "plt.style.use('seaborn-whitegrid')" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def weighted_score(rating, votes, weight=10):\n", " return (5 * rating/10.0) + (5 * (1 - np.e**(-votes/weight)))" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "rating of 5 from 10 people = 5.66\n", "rating of 4 from 1000 people = 7.00\n" ] } ], "source": [ "for rating, votes in [(5, 10), (4, 1000)]:\n", " s = weighted_score(rating, votes)\n", " print('rating of %d from %d people = %.2f' % (rating, votes, s))" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { 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xDvUHh04f4skNT/Jx6sd0bd6VZUOW0bZhW//cvBrgk56EvDw4ccLYjh8vsd/6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/2VRUVFsfPnz3NjysrK2BNPPMFu3Ljh9n3T6Y//unLlCtRqNSZMmIA33ngDjY2ND+R+zGYzLBYL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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ratings = [5, 4, 3, 2, 1]\n", "votes = range(5, 101, 5)\n", "for rating in ratings:\n", " scores = [weighted_score(rating, vote) for vote in votes]\n", " plt.plot(votes, scores, '-o', label='%d stars' % rating)\n", "\n", "plt.xticks(votes)\n", "plt.xlabel('Vores')\n", "plt.ylabel('Score')\n", "plt.legend(loc='best');" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "We can see for example that 3 stars with 15 votes gets more than 5 stars with 5 votes. I might play a bit with the weight to tweak the scores but looks like it's the right solution." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 1 }