How imbd ranks movies?
The formula for calculating the Top Rated 250 Titles gives a true Bayesian estimate:
= average for the movie (mean) = (Rating)
= number of votes for the movie = (votes)
= minimum votes required to be listed in the Top 250 (currently 1500)
= the mean vote across the whole report (currently 6.9)
- for the Top 250, only votes from regular voters are considered.* (source)
Now that’s something unexpected! Going further than the simple arithmetic mean is something exciting, right?
The formula is the well-known decomposition of the posterior mean -distributed a priori as normal- compromising the prior guess () and the data () weighted by the sample () and the pretend-to-be initial sample () under the conjugate prior setting.