Normalized average

I think it is time voting got up to speed on the averaging function. It would be good to supply an option to sort and display the normalized average. This would fix the problem of items with fewer votes overpowering items with more votes. A great post about this method can be viewed here: http://www.evanmiller.org/how-not-to-sort-by-average-rating.html

I wrote a php function that should get the job done with minimal overhead:

function normalizedVotes($positive, $total)
{
  $average = $positive/$total;
  $normalized_constant = 1.92; // 95% confidence in lower bound prediction.
  $normalized_squared = $normalized_constant^2;
  return ($average + ($normalized_squared / (2*$total)) - $normalized_constant * sqrt(($average * (1 - $average) + $normalized_squared / (4 * $total)) / $total)) / (1 + $normalized_squared / $total);
}

In effect if one item has 999/1000 votes positive and another has 5/5 votes positive the item with more votes would appear on top despite the "perfect" score of the second one. It's not a perfect system but much better than a simple average.

I'll be implementing this on my copy of 5 star but it's Drupal 6 so probably won't do much good moving forward. I'll post a patch for Drupal 7 if I ever get around to updating the site.