Created
January 14, 2019 16:44
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Showcasing how LTV curves are dependent on Retention Curves
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| import matplotlib.pyplot as plt | |
| import matplotlib.ticker as ticker | |
| import pandas as pd | |
| import numpy as np | |
| import random | |
| def build_userbase( n, payer_percentage ): | |
| users = pd.DataFrame( columns=[ "user", "payer", "payment_probability", "payment" ] ) | |
| for x in range( 1, n + 1 ): | |
| payer = True if random.randint( 1, 100 ) <= ( payer_percentage * 100 ) else 0 | |
| payment_probability = 0 | |
| payment = 0 | |
| churn_probability = float( random.randint( 1, 10 ) ) / 100 | |
| if payer: | |
| payment_probability = float( random.randint( 1, 25 ) ) / 100 | |
| payment = float( random.randint( 1, 100 ) ) | |
| users = users.append( | |
| { "user": x, "payer": payer, | |
| "payment_probability": payment_probability, "payment": payment, | |
| "churn_probability": churn_probability, "churned": 0 }, ignore_index=True ) | |
| return users | |
| def build_cumulative_revenue( users, days ): | |
| payers = users[ users[ 'payer' ] == 1 ] | |
| daily_revenue = [ 0 ] * ( days + 1 ) | |
| daily_cumulative_revenue = [ 0 ] * ( days + 1 ) | |
| for x in range( 1, days + 1 ): | |
| daily_revenue[ x ] = 0 | |
| daily_cumulative_revenue[ x ] = 0 | |
| this_daily_revenue = 0 | |
| for index, p in payers.iterrows(): | |
| this_payment_probability = float( random.randint( 1, 100 ) ) / 100 | |
| this_payment = p[ "payment" ] if this_payment_probability <= p[ "payment_probability" ] else 0 | |
| this_daily_revenue += this_payment | |
| daily_revenue[ x ] = this_daily_revenue | |
| daily_cumulative_revenue[ x ] = ( daily_cumulative_revenue[ x - 1 ] + daily_revenue[ x ] ) if x > 1 else daily_revenue[ x ] | |
| return daily_revenue, daily_cumulative_revenue | |
| def build_cumulative_revenue_with_churn( users, days ): | |
| payers = users[ users[ 'payer' ] == 1 ] | |
| daily_revenue = [ 0 ] * ( days + 1 ) | |
| daily_cumulative_revenue = [ 0 ] * ( days + 1 ) | |
| for x in range( 1, days + 1 ): | |
| daily_revenue[ x ] = 0 | |
| daily_cumulative_revenue[ x ] = 0 | |
| this_daily_revenue = 0 | |
| for index, p in payers.iterrows(): | |
| if( not p[ "churned" ] ): | |
| #if they didn't churn out | |
| this_churn_probability = float( random.randint( 1, 100 ) ) / 100 | |
| if this_churn_probability > p[ "churn_probability" ]: | |
| #if this isn't their day to churn | |
| this_payment_probability = float( random.randint( 1, 100 ) ) / 100 | |
| this_payment = p[ "payment" ] if this_payment_probability <= p[ "payment_probability" ] else 0 | |
| this_daily_revenue += this_payment | |
| else: | |
| #they are churning | |
| payers.loc[ index, "churned" ] = True | |
| daily_revenue[ x ] = this_daily_revenue | |
| daily_cumulative_revenue[ x ] = ( daily_cumulative_revenue[ x - 1 ] + daily_revenue[ x ] ) if x > 1 else daily_revenue[ x ] | |
| users.loc[ users[ "payer" ] == True ] = payers | |
| return daily_revenue, daily_cumulative_revenue | |
| def build_DAU_with_churn( users, days ): | |
| DAU = [ 0 ] * ( days + 1 ) | |
| churn = [ 0 ] * ( days + 1 ) | |
| for x in range( 1, days + 1 ): | |
| for index, u in users.iterrows(): | |
| if( not u[ "churned" ] ): | |
| #if the user has not yet churned | |
| this_churn_probability = float( random.randint( 1, 100 ) ) / 100 | |
| if this_churn_probability > u[ "churn_probability" ]: | |
| #if this user is not churning on this day | |
| #increment the DAU | |
| DAU[ x ] += 1 | |
| else: | |
| churn[ x ] += 1 | |
| users.loc[ index, "churned" ] = True | |
| return DAU, churn | |
| # | |
| # Build initial userbase | |
| # | |
| users = build_userbase( 1000, payer_percentage=0.05 ) | |
| users[ "churned" ] = users[ "churned" ].astype('bool') | |
| # | |
| # Get daily revenue values | |
| # | |
| dr_users = users | |
| daily_revenue, daily_cumulative_revenue = build_cumulative_revenue( dr_users, 365 ) | |
| # | |
| # Get daily revenue values with churn | |
| # | |
| drc_users = users | |
| daily_revenue_with_churn, daily_cumulative_revenue_with_churn = build_cumulative_revenue_with_churn( drc_users, 365 ) | |
| # | |
| # Get DAU and Churn | |
| # | |
| dau_users = users | |
| DAU, churn = build_DAU_with_churn( dau_users, 365 ) | |
| # | |
| # Print Revenue Graph | |
| # | |
| fig, ax = plt.subplots() | |
| plt.rcParams['figure.figsize'] = [10, 5] | |
| plt.plot( daily_cumulative_revenue, '-g', label='Cumulative Revenue', linewidth=3 ) | |
| plt.plot( daily_revenue, '-r', label='Daily Revenue', linewidth=3 ) | |
| plt.legend(loc='upper left') | |
| plt.ylabel( 'Revenue' ) | |
| fmt = '${x:,.0f}' | |
| tick = ticker.StrMethodFormatter( fmt ) | |
| ax.yaxis.set_major_formatter( tick ) | |
| plt.xticks( rotation=25 ) | |
| fig.suptitle( 'Cumulative and Daily Revenue, No Churn', fontsize=14 ) | |
| plt.show() | |
| # | |
| # Print Revenue with Churn Graph | |
| # | |
| fig, ax = plt.subplots() | |
| plt.rcParams['figure.figsize'] = [10, 5] | |
| plt.plot( daily_cumulative_revenue_with_churn, '-g', label='Cumulative Revenue (with Churn)', linewidth=3 ) | |
| plt.plot( daily_revenue_with_churn, '-r', label='Daily Revenue (with Churn)', linewidth=3 ) | |
| plt.legend(loc='center right') | |
| plt.ylabel( 'Revenue' ) | |
| fmt = '${x:,.0f}' | |
| tick = ticker.StrMethodFormatter( fmt ) | |
| ax.yaxis.set_major_formatter( tick ) | |
| plt.xticks( rotation=25 ) | |
| fig.suptitle( 'Cumulative and Daily Revenue with Churn', fontsize=14 ) | |
| plt.show() | |
| # | |
| # Print DAU and Churn Graph | |
| # | |
| fig, ax1 = plt.subplots() | |
| plt.rcParams['figure.figsize'] = [10, 5] | |
| ax1.plot( DAU, '-r', label='Cohort DAU', linewidth=3 ) | |
| ax1.set_ylabel( 'DAU' ) | |
| ax1.plot( churn , '-y', label='Daily Cohort Churn', linewidth=3 ) | |
| ax1.legend( loc='upper right' ) | |
| fig.suptitle( 'DAU and Daily Churn Values', fontsize=14 ) | |
| plt.show() | |
| x = np.arange( 1, 365, 1 ) | |
| # | |
| # Print a random LTV graph | |
| # | |
| ltv = np.log( x ) | |
| fig, ax1 = plt.subplots() | |
| plt.rcParams['figure.figsize'] = [10, 5] | |
| ax1.set_ylabel( 'LTV' ) | |
| ax1.plot( ltv, '-g', label='LTV Curve (Arbitrary)', linewidth=3 ) | |
| ax1.legend( loc='center right' ) | |
| fig.suptitle( 'An Arbitrary LTV Curve', fontsize=14 ) | |
| fmt = '${x:,.0f}' | |
| tick = ticker.StrMethodFormatter( fmt ) | |
| ax1.yaxis.set_major_formatter( tick ) | |
| plt.show() | |
| # | |
| # Print a random retention graph | |
| # | |
| retention = np.exp( -.05 * x ) | |
| fig, ax1 = plt.subplots() | |
| plt.rcParams[ 'figure.figsize' ] = [ 10, 5 ] | |
| ax1.set_ylabel( 'Retention' ) | |
| ax1.plot( retention, '-r', label='Retention Curve (Arbitrary)', linewidth=3 ) | |
| ax1.legend( loc='center right' ) | |
| fig.suptitle( 'An Arbitrary Retention Curve', fontsize=14 ) | |
| vals = ax1.get_yticks() | |
| ax1.set_yticklabels(['%1.2f%%' %i for i in vals]) | |
| plt.show() | |
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