I am figuring out how to build a ranking system for movies using IMDB data. My own dataset related exclusively to "art movies", so they would tend to have fewer reviews than the average IMDB movie (the mean is 3,000 for my own dataset). In particular, I've considered using the IMDB "Bayesian estimator" for its Top 250 list (shown below). The problem is that I don't understand how the $m$ (minimum votes) constant is calculated. I read somewhere that it is a rather arbitrary constant but it could be thought as the minimum number of reviews needed to "expect" a rating similar to a "true rating" (assuming all reviewers actually rated a given movie). But it is not entirely clear to me how to think about this $m$ constant for my own case.
Would choosing $m$ to be the average number of votes in my dataset a valid choice?
There are a lot of interesting discussions regarding Bayesian ratings here on CV, which themselves link to (what looks like it could be) great reading material to better understand Bayesian ratings (for example, a blog entry by Andrew Gelman), but most of the links are dead, so I can't read them.
Could you please recommend any good material on Bayesian ratings for me to get a better grasp of how to build one for my own? I have a good grasp of statistics and basic Bayesian probability, but I would prefer introductory material.
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 25,000)
* C = the mean vote across the whole report (currently 6.9)
Best Answer
The Bayesian rating formula looks very simple to me.
Let me break it down and present an alternate view of the parameters involved.
WR = $\frac{v}{v+m}*R+\frac{m}{v+m}*C$
=P(enough evidence)*[Rating based on evidence]+P(no evidence)*[best guess when no evidence]
Say, a movie got v ratings and you have empiracally chosen m based on what you think is a good number of votes to rely on the rating based on votes.
Observe that the second term ($\frac{m}{v+m}*C$) in the sum goes to zero when v is large. The best guess for the rating, when there is no evidence is the average rating of all the movies.
I think choosing m as the average number of votes in the dataset is over-kill. I would start with the first quartile of the number of votes.
Thanks