Bayes estimator - Internet Movie Database (IMDB)

Description

In estimation theory and decision theory, a Bayes estimator or a Bayes action is an estimator or decision rule that minimizes the posterior expected value of a loss function (i.e., the posterior expected loss). The Internet Movie Database has used a formula for calculating and comparing the ratings of films by its users, including their Top Rated 250 Titles which is claimed to give “a true Bayesian estimate”. As the number of ratings surpasses m, the confidence of the average rating surpasses the confidence of the prior knowledge, and the weighted bayesian rating (W) approaches a straight average®. The closer v (the number of ratings for the film) is to zero, the closer W gets to C, where W is the weighted rating and C is the average rating of all films. So, films with very few ratings/votes will have a rating weighted towards the average across all films, while films with many ratings/votes will have a rating weighted towards its average rating.

Related formulas

Variables

WRweighted rating (dimensionless)
vnumber of votes for the movie = (votes) (dimensionless)
mminimum votes required to be listed in the Top 250 (currently 25000) (dimensionless)
Raverage for the movie as a number from 0 to 10 (mean) = (Rating) (dimensionless)
Cthe mean vote across the whole report (currently 7.0) (dimensionless)