cr_formulas.py

def calculate_weight(constant, index):
    return constant ** index

def base_curve(accuracy, curve_data):
    accuracy = min(accuracy, 100)
    
    # https://www.desmos.com/calculator/bkyq4lsq2l
    # baseline: z
    # cutoff: w
    # exponential: v

    # apply default values
    defaults = {
        'baseline': 0.78,
        'cutoff': 0.5,
        'exponential': 2.5,
    }
    defaults.update(curve_data)
    curve_data = defaults

    baseline = curve_data['baseline'] * 100
    cutoff = curve_data['cutoff']
    exponential = curve_data['exponential']
    if accuracy < baseline:
        return accuracy / 100 * cutoff
    else:
        return accuracy / 100 * cutoff + (1 - cutoff) * ((accuracy - baseline)/(100 - baseline)) ** exponential

def linear_curve(accuracy, curve_data):
    accuracy = min(accuracy, 100)

    defaults = {'points': [[0, 0], [0.8, 0.5], [1, 1]]}
    defaults.update(curve_data)
    curve_data = defaults

    accuracy = accuracy / 100

    for i in range(len(curve_data['points'])):
        if accuracy < curve_data['points'][i][0]:
            break

    if i == 0:
        i = 1

    middle_dis = (accuracy - curve_data['points'][i - 1][0]) / (curve_data['points'][i][0] - curve_data['points'][i - 1][0])

    return curve_data['points'][i - 1][1] + middle_dis * (curve_data['points'][i][1] - curve_data['points'][i - 1][1])

curves = {
    'basic': base_curve,
    'linear': linear_curve,
}

def cr_score_curve(accuracy, curve_data):
    return curves[curve_data['type']](accuracy, curve_data)

def calculate_cr(accuracy, difficulty, curve_data):
    return difficulty * 50 * cr_score_curve(accuracy, curve_data)

def cr_accumulation_curve(index, accumulation_constant=0.94):
    return accumulation_constant ** index