I'm implementing a rating system to be used on my website, and I think the Bayesian average is the best way to go about it. Every item will be rated in six different categories by the users. I don't want items with only one high rating to shoot to the top though, which is why I want to implement a Bayesian system.
Here is the formula:
Bayesian Rating = ( (avg_num_votes * avg_rating) + (this_num_votes * this_rating) ) / (avg_num_votes + this_num_votes)
Because the items will be rated in 6 different categories, should I use the average of the sums of those categories as "this_rating" for the Bayesian system? For instance, take one item with two ratings (scale of 0-5):
Rating 1: Category A: 3 Category B: 1 Category C: 2 Category D: 4 Category E: 5 Category F: 3 Sum: 18 Rating 2: Category A: 2 Category B: 3 Category C: 3 Category D: 5 Category E: 0 Category F: 1 Sum: 14
Should "this_rating" be simply the average of the sums listed above? Is my thinking correct, or should a Bayesian system be implemented for each category as well (or is that overthinking it)?