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import numpy as np
from scipy.stats import norm

def score_to_elo(score):
    return -400 * np.log(1 / score - 1) / np.log(10)

def elo_to_score(elo):
    return (1 / (1 + 10 ** (-elo / 400)))

Pentanomial = [1, 3, 4, 7, 2]
double_wins = Pentanomial[4]
single_wins = Pentanomial[3]
double_draws = Pentanomial[2]
single_loss = Pentanomial[1]
double_loss = Pentanomial[0]

total_pairs = double_wins + single_wins + double_draws + single_loss + double_loss
score = (double_wins + single_wins * 0.75 + double_draws * 0.5 + single_loss * 0.25 + double_loss * 0) / total_pairs

double_wins_p = double_wins / total_pairs
single_wins_p = single_wins / total_pairs
double_draws_p = double_draws / total_pairs
single_loss_p = single_loss / total_pairs
double_loss_p = double_loss / total_pairs

double_wins_dev = double_wins_p * (1 - score) ** 2
single_wins_dev = single_wins_p * (0.75 - score) ** 2
double_draws_dev = double_draws_p * (0.5 - score) ** 2
single_loss_dev = single_loss_p * (0.25 - score) ** 2
double_loss_dev = double_loss_p * (0 - score) ** 2
std_deviation = np.sqrt((double_wins_dev + single_wins_dev + double_draws_dev + single_loss_dev + double_loss_dev) / total_pairs)

confidence_p = 0.95
min_confidence_p = (1 - confidence_p) / 2
max_confidence_p = 1 - min_confidence_p
score_lower_bound = score + norm.ppf(min_confidence_p) * std_deviation
score_upper_bound = score + norm.ppf(max_confidence_p) * std_deviation

elo = score_to_elo(score)
elo_upper_bound = score_to_elo(score_upper_bound)
elo_lower_bound = score_to_elo(score_lower_bound)
error_margin = (elo_upper_bound - elo_lower_bound) / 2