Question

I have an music items that are scored by users between 1 to 5, and
I need a formula to get the 5 most scored items.

But obviously an item that get 3.5 average score from 1000 different users will be more scored then an item thet get 4.9 average score from only 5 users… in other words I think that if an item get attention from people to score it, this indicates that the item is interesting. so in the calculation the votesCount parameter need to have a power. (how much power? I don’t sure, and I asking it you to get ideas).

I think that we need the following parameters in the function: votesAverage, votesCount.

Answer 1

Weighted voting for 5-star systems with lots of voters

You can use Bayesian estimates to calculate weighted voting.

IMDb (Internet Movie Database) uses this calculation to determine its IMDb Top 250. (Note: IMDb uses 10 stars but the formulas are identical using 5 stars).

The formula for calculating the Top Rated 250 Titles gives a true Bayesian estimate:

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 3000)
• C = the mean vote across the whole report (currently 6.9)

IMDb Reference

Wikipedia Reference