https://chess.stackexchange.com/a/37515/23230

37515_23230.py

import numpy as np
from scipy import stats

def wilson_cont(n1, n2, alpha=0.05):
    '''
    Wilson score interval with continuity correction.
    Two-tail interval is assumed.

    Parameters:
        n1 (int): Count of outcome 1.
        n2 (int): Count of outcome 2.
        alpha (float):

    Source:
        https://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval
    '''
    assert type(n1) == int and type(n2) == int
    assert 0 < alpha < 1
    z = stats.norm.ppf(1 - alpha / 2)
    n = n1 + n2
    phat = n1 / n
    num1 = 2 * n * phat + z**2
    num2 = z * np.sqrt(z**2 - 1 / n + 4 * n * phat * (1 - phat) + 4 * phat - 2) + 1
    num3 = z * np.sqrt(z**2 + 1 / n + 4 * n * phat * (1 - phat) - 4 * phat - 2) + 1
    denom = 2 * (n + z **2)
    return max(0, (num1 - num2) / denom), min(1, (num1 + num3) / denom)