true_rate_me_so_called_objective_scoring_rubric.py

import numpy as np

np.set_printoptions(suppress=True)

stdevs = [i / 2 for i in range(1, 24 + 1)]
TRIALS = 1_000
WOMEN = 500_000

trial_results = {k: list() for k in stdevs}

np.random.seed(69420)

for t in range(TRIALS):
    true_attractiveness_norm = np.random.normal(0, 1, size=WOMEN)
    for std in stdevs:
        true_attractiveness = (true_attractiveness_norm * std) + 5
        bound_attractiveness = np.maximum(np.minimum(np.round(true_attractiveness, 0), 10), 0)
        mse = np.mean(((true_attractiveness - bound_attractiveness) / std) ** 2)
        trial_results[std].append(mse)

for std, mse_list in trial_results.items():
    print(f"{std=} --> {np.mean(mse_list)}")