Returning a ratio

Question

Hey all
I am trying to calculate the "popularity" of an item. Items can be rated using integers from 0 to 5. What I do now is that I only calculate the average of all the ratings for an item, this is of course not enough because the number of times an item has been rated should also be an important factor when deciding an item's popularity.
(An item with the average rating of 5 which has been rated 20 times should be more popular than an item which has the average rating of 5 and has been rated 10 times for example).
What is the best way for returning the avg Rating/n Ratings as a Double? I can always return the ratio as a String, but I don't know if that's the smoothest way of doing it. I am thinking of doing: avg rating * n ratings / n ratings. Is this a good way of returning the ratio as a Double or are there more accurate algorithms for doing it?
Code so far (will return Double when I've figured out which algorithm to use)
public Integer calculatePopularity(List<Integer> values) {
     if(values.size() == 0) {
          return 0;
     try {
          Integer result = 0;
          for(Integer i : values) {
          result = result + i;
          return result * values.size()/values.size();
          } catch (Exception e) {
               e.printStackTrace();
               return 0;
}

Answer 1

You need to come up with some weighting function yourself, and this function would take an average rating and put a 'reliability skew' (between 0 and 1) on it. I'm sure there is material for this online, because I'm certain that this paradigm must come up all the time, what with the wide variety of sites that support some sort of user rating or another.
Just thinking out loud, this might possibly some function on the domain [0, infinity) that zeroes at x=0, then tends exponentially to 1 as x-> inifinity. The initial steepness of the funtion would depend on you, how quickly you see a rating getting reliable as more and more people are adding to it.
Something like
rating = (1-e^(-(steepness)*raters)) * average rating
Of course, there are plenty of other functions you could use, or you could modify this exponential. You can for example round out curve that this relation gives more by adding a coefficient to the exponential term, and then adjusting the -(steepness)* raters with a +k to move the zero back to x=0.
Not being an applied mathematician or a sociologist, I don't know how to quantify and model 'reliability' but, as I say, there is no doubt material on this on the web