Showcasing how LTV curves are dependent on Retention Curves

LTV_and_Retention_Curves.py

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()