How To Normalize Reviews Based On Score

Question

What is the best way to normalize reviews? I.E. lets assume we have products that users can vote from 1-5 stars.

Simply taking the average is not a good way, because it does not account for the number of reviews.

For example, if a product only has one review of a 5 star, it should not be ahead of a product with 10000 reviews, simply because the only review gave it 5 stars.

Essentially how do I normalize the score based on the number of reviews as well?

Answer 1

I am sorry if my answer looks crazy. But when I first saw your question, the following answer came to my mind.

The formula for calculating the Top Rated 250 Titles gives a true Bayesian estimate:

weighted rating (WR) = (v ÷ (v+m)) × R + (m ÷ (v+m)) × C 

where:

R = average for the movie (mean) = (Rating)

v = number of votes for the movie = (votes)

m = minimum votes required to be listed in the Top 250 (currently 3000)

C = the mean vote across the whole report (currently 6.9)

(This is how IMDB ranks their top films according to user reviews and votes. Below is a link to the page where I got the above passage: http://www.imdb.com/chart/top.)