compute_wilson_score.py

# Objective: compute the Wilson score given the numbers of positive and negative reviews

from math import sqrt

# Quantiles of the normal distribution
# Reference: https://en.wikipedia.org/wiki/Normal_distribution
quantile_normal_dist_dict = {
    0.80: 1.281551565545,
    0.90: 1.644853626951,
    0.95: 1.959963984540,
    0.98: 2.326347874041,
    0.99: 2.575829303549,
    0.995: 2.807033768344,
    0.998: 3.090232306168,
    0.999: 3.290526731492,
    0.9999: 3.890591886413,
    0.99999: 4.417173413469,
    0.999999: 4.891638475699,
    0.9999999: 5.326723886384,
    0.99999999: 5.730728868236,
    0.999999999: 6.109410204869,
}


def compute_wilson_score(num_pos, num_neg, confidence=0.95):
    # Reference: https://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval#Wilson_score_interval

    if not (num_pos >= 0):
        raise AssertionError()
    if not (num_neg >= 0):
        raise AssertionError()

    if confidence in quantile_normal_dist_dict:
        tabulated_confidence = confidence
    else:
        tabulated_confidence_list = list(quantile_normal_dist_dict.keys())
        sorted(tabulated_confidence_list)
        confidence = min(confidence, tabulated_confidence_list[-1])
        diff_list = [(c - confidence) for c in tabulated_confidence_list]
        index = min(i for i in range(len(diff_list)) if diff_list[i] >= 0)
        tabulated_confidence = tabulated_confidence_list[index]
        print(tabulated_confidence)

    z_quantile = quantile_normal_dist_dict[tabulated_confidence]

    z2 = pow(z_quantile, 2)
    den = num_pos + num_neg + z2

    mean = (num_pos + z2 / 2) / den

    try:
        inside_sqrt = num_pos * num_neg / (num_pos + num_neg) + z2 / 4
        delta = (z_quantile * sqrt(inside_sqrt)) / den
        wilson_score_value = mean - delta
    except ZeroDivisionError:
        if not (num_pos == 0):
            raise AssertionError()
        if not (num_neg == 0):
            raise AssertionError()
        wilson_score_value = None

    return wilson_score_value


def main():
    # Loop over the number of reviews
    for num_reviews in [pow(10, n) for n in range(5)]:
        # Display the Wilson score of a game with as many positive and negative reviews
        wilson_score = compute_wilson_score(num_reviews / 2, num_reviews / 2, 0.95)
        print(
            "#reviews = " + str(num_reviews) + "\tWilson score = " + str(wilson_score),
        )

    return True


if __name__ == "__main__":
    main()