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I'm not an expert with mathematics so I hope I'm posting in the right place!

I've got a lot of products which can be rated good, bad and OK by a user. What I'm having trouble with is finding which is rated the "best"- similar to Amazon's sort by rating.

Getting the average rating won't work as I want a product with 99 good ratings and 1 bad rating to rank higher than a product with just 2 good ratings. Any ideas on what type of formula to use?

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ANSWER, SORT OF:

Thanks to Raskolnikov's comment I've found out what I need is either the Wilson Score Interval (which at the minute is way too complicated) or the Bayesian rating, which can be found here- http://www.thebroth.com/blog/118/bayesian-rating.

Now I know at least what the formula I want is called, I can figure out how to get what I want.

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    Relevant is [this article on How Not to Sort by Average Rating](http://www.evanmiller.org/how-not-to-sort-by-average-rating.html), which discusses a solution given in 1927 by Edwin B. Wilson. Oh, I see from your comment below that this is just what you found. I will leave the link here anyway.2014-08-28

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ANSWER, SORT OF:

Thanks to Raskolnikov's comment I've found out what I need is either the Wilson Score Interval (which at the minute is way too complicated) or the Bayesian rating, which can be found here- http://www.thebroth.com/blog/118/bayesian-rating.

Now I know at least what the formula I want is called, I can figure out how to get what I want.

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To assign a rating to a number, any polynomial with degree greater than 1 will work in your case. For example suppose $n_1$, $n_2$ and $n_3$ is no. of good, OK and bad ratings on product respectively. Then your equation will look like ${n_1^a + n_2^b - n_3^c}\over{n_1 + n_2 + n_3}$, where you can take $a = 2, b= 1.5, c = 2.$ (all are greater than 1).

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    Thank you for your answer and time. I've tried my best to understand it but unfortunately I don't think I'm anywhere near your level of maths to get my head round it! I've instead used the Bayesian Rating at the minute, which seems to be doing what I want.2012-03-25