A common problem with a website is how to sort things by their rating. Evan Miller describes it well in his 2009 post, How Not To Sort By Average Rating.
Here is a Python snippet that implements his method:
import math from scipy import stats def ci_lower_bound(positive_ratings, total_ratings, confidence): """ Following http://www.evanmiller.org/how-not-to-sort-by-average-rating.html#changes :return: the lower bound of the confidence interval """ n = total_ratings z = stats.norm.ppf(1 - (1 - confidence) / 2) p_hat = 1.0 * positive_ratings / n result = ( ( p_hat + z * z / (2 * n) - z * math.sqrt( (p_hat * (1 - p_hat) + z * z / (4 * n)) / n ) ) / (1 + z * z / n) ) return result
Note that this assumes you have the python package
scipy installed. You can find it
As Evan Miller notes, your z value will be constant so you can also hardcode it, for example to
1.96 if you want a 95% confidence interval.
You can interpret the output of this function as a corrected rating, which ‘punishes’ items with a low number of votes.