mmo-modeling-responsecurve.py

def get_response_curve(channel, start_time, end_time):
    
    def hill_transform(x, alpha, gamma):
        return 1 / (1 + (x/gamma)**-alpha)
    
    # parameters
    coefficient = model.query("variable == @channel")['coefficient'].iloc[0]
    alpha = model.query("variable == @channel")['alpha'].iloc[0]
    gamma = model.query("variable == @channel")['gamma'].iloc[0]
    
    # means for inverse scaling
    spend_mean = media.query("DATE >= @start_time and DATE <= @end_time")[channel].mean()
    revenue_mean = media.query("DATE >= @start_time and DATE <= @end_time")['REVENUE'].mean()
    
    # actual spend and contribution
    spend = media.query("DATE >= @start_time and DATE <= @end_time")[channel].sum()
    revenue = hill_transform(spend / spend_mean, alpha, gamma) * coefficient * revenue_mean
    
    spend_axis = np.arange(spend/10, spend*2, 1e03)
    revenue_axis = hill_transform(spend_axis / spend_mean, alpha, gamma) * coefficient * revenue_mean
    
    return spend_axis, revenue_axis, spend, revenue
    
spend_axis, revenue_axis, spend, revenue = get_response_curve('PAID_SEARCH', '2022-11-01', '2023-01-01')
plt.plot(spend_axis, revenue_axis)
x0, y0 = spend, revenue
plt.plot(x0, y0, "s");
plt.xlabel('Spend');
plt.ylabel('Revenue');
plt.title('Paid Search Response Curve');