PHP/MySQL - algorithm for "Top Rated"

Question

So I just built a star-rating system and and trying to come up with an algorithm to list the "Top Rated" items. For simplicity, here are the columns:

item_name
average_rating (a decimal from 1 to 5)
num_votes

I'm trying to determine the "sweet spot" between number of votes and rating. For example...

• An item rated (4.6 / 20 votes) should be higher on the list than an item that's (5.0 / 2 votes)
• An item rated (2.5 / 100 votes) should be below an item that's (4.5 / 2 votes)

So in other words, num_votes plays a factor in what's "Top".

Anyone know of an algorithm that is pretty good at determining this "sweet spot"?

Thanks in advance.

Answer 1

How about you give each 10 votes a weight of 1 so 20 votes gives the item 2 weight. Then if the item has 0 weight it will loose 0.5 from the average

4.6/20 = 20/10: 2 weight
5.0/2 = 2/10: 0 weight

(4.6 * 0.02) + 4.6 = 4.692
(5.0 * 0.00) + 5.0 = 5 - 0.5 = 4.5

2.5/100 = 100/10: 10 weight
4.5/2 = 2/10: 0 weight

(2.5 * 0.1) + 2.5 = 2.75
(4.5 * 0.0) + 4.5 = 4.5 - 0.5 = 4

Answer 2

here's another, statistically sound good way: http://www.thebroth.com/blog/118/bayesian-rating

Answer 3

The question is, how much higher the 4.6/20 shall be rated than the 5.0/2...

An idea not to take items in consideration that do not have at least x votes.

Another idea is to fill up with "medium" votes. Decide that 10votes shall be the minimum. The 5.0/2 must be filled with 8 virtual votes of 2.5

5.0/2 means 2 votes with 5.0, add 8 with 2.5 you'll get 30/10 -> 3.0 ;)

Now, you have to decide how many votes an item shall at least have. For those that already have the minimum votes, a direct comparation shall be done.

4.5/20 > 4.4/100
5.0/2  < 3.1/20  (as 5.0/2 is, as we calculated, 3.0/10)