wilson.rb

# A solution to "how do I sort by average rating, while taking into account the fact that some things have more ratings than others and this provides more Bayesian evidence about their quality? See https://www.evanmiller.org/how-not-to-sort-by-average-rating.html

def ci_lower_bound(pos, n)
    if n == 0
        return 0
    end
    z = 1.96 # hardcoded confidence level of 0.95
    phat = 1.0*pos/n

    midpoint = phat + z*z/(2*n)
    half_width = z * Math.sqrt((phat*(1-phat)+z*z/(4*n))/n)
    [(midpoint - half_width)/(1+z*z/n), (midpoint + half_width)/(1+z*z/n)]
end

p ci_lower_bound(81.83, 92.67)
p ci_lower_bound(48, 59)
p ci_lower_bound(152, 157)