HN user
One data point is the netflix rating set from their contest. The system is 1 to 5 stars. The average movie rating was 3.4 in 1998 climbing to 3.8 in 2005.
Back to the original point -- if you used a formula with a default rating of 3 it would underestimate low-frequency movies. People don't view movies at random. They try to pick things they will like, which should be reflected in the statistical model.
It's very nice to see a mathematically motivated piece on how to sort based on users ratings. But there are two problems with the solution presented, the first minor, and the second more serious.
Minor: Distributions of ratings are not usually normal about the average possible rating -- they are usually skewed to the positive end, because people are pretty good at selecting what they read or view. The solution presented will tend to skew low-frequency ratings too far toward the average. It should be easy to calculate an expected average for your site, and use this instead of 1/2 for the formula given in the post.
Major: What you really need is a missing data point: the number of readers who haven't made any rating at all. It's pretty clear if you think of two examples:
Item 1 1,000,000 views 10 positive ratings 1 negative rating
Item 2 15 views 10 positive ratings 1 negative rating
Clearly, readers feel pretty blah about Item 1. You're much better off displaying Item 2, other things being equal, but the formula doesn't distinguish the two cases.