Thread: Bayes weighted average with example

1. Bayes weighted average with example

Hello. I have 2 movies which need to be compared. Movie 1 - Mean score 92/100 from 2000 votes. Movie 2 - Mean score 80/100 from 4000 votes.
Currently Movie is ranked 1 and Movie 2 is ranked 2. Shoudln't it be the other way round since movie 2 has more votes despite having a low score.
I used bayes weighted average to normalize the ratings and recalculate the grades using the following formula. b(r) = [ W(a) * a + W(r) * r ] / (W(a) + W(r)]
where r = average rating for an item W(r) = weight of that rating, which is the number of ratings a = average rating for the entire data set of 5 products. W(a) = weight of that average, which is the average number of ratings for all the 5 products, and Bayes(r) = new bayesian rating
For the above example , a = 0.84 i.e weighted mean of movie 1 and 2. W(a) is 3000 i.e (2000+4000)/2.
The results are as follows. Movie 1 Bayes r : 87/100---- RANK 1 Movie 2 bayes r : 82/100---- RANK 2
Despite the normalization movie 1 still continues to rank higher than movie2 .
Thoughts anyone ?

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