/cohort-analysis

name: Cohort Analysis
description: Track and analyze user cohorts over time, calculate retention rates, and identify behavioral patterns for customer lifecycle and retention analysis

Cohort Analysis

Overview

Cohort analysis tracks groups of users with shared characteristics over time, revealing patterns in retention, engagement, and lifetime value.

When to Use

• Measuring user retention rates and identifying when users churn
• Analyzing customer lifetime value (LTV) and payback periods
• Comparing performance across different user acquisition channels or campaigns
• Understanding how product changes affect different user groups over time
• Tracking engagement patterns and identifying early warning signs of churn
• Evaluating the long-term impact of onboarding improvements or feature releases

Core Concepts

• **Cohort**: Group of users sharing a characteristic (signup date, region, etc.)
• **Cohort Size**: Initial group size
• **Retention Rate**: Percentage remaining active
• **Churn Rate**: Percentage who left
• **Retention Curve**: How cohort degrades over time

Cohort Types

• **Acquisition Date**: Users grouped by signup period
• **Behavioral**: Users grouped by actions taken
• **Revenue**: Users grouped by purchase value
• **Geographic**: Users grouped by location
• **Demographic**: Users grouped by characteristics

Implementation with Python

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns

# Create sample user lifecycle data
np.random.seed(42)

# Generate user data
n_users = 5000
users = []

for user_id in range(n_users):
    signup_month = np.random.choice(range(1, 13))
    lifetime_months = np.random.poisson(6) + 1

    for month in range(1, lifetime_months + 1):
        users.append({
            'user_id': user_id,
            'signup_month': signup_month,
            'month': month,
            'active': 1,
        })

df = pd.DataFrame(users)

# Add derived columns
df['cohort_month'] = df['signup_month']
df['cohort_age'] = df['month']  # Could be day, week, etc.
df['date'] = pd.to_datetime('2023-01-01') + pd.to_timedelta(df['signup_month'] * 30, unit='D')

print("User Data Summary:")
print(df.head(10))

# 1. Cohort Table (Retention Matrix)
cohort_data = df.groupby(['cohort_month', 'cohort_age']).agg({
    'user_id': 'nunique'
}).reset_index()
cohort_data.columns = ['cohort_month', 'cohort_age', 'unique_users']

# Create pivot table
cohort_pivot = cohort_data.pivot(index='cohort_month', columns='cohort_age', values='unique_users')

print("\nCohort Sizes (Raw User Counts):")
print(cohort_pivot)

# 2. Cohort Retention (as percentage of cohort size)
cohort_size = cohort_pivot.iloc[:, 0]
retention_table = cohort_pivot.divide(cohort_size, axis=0) * 100

print("\nCohort Retention Rate (%):")
print(retention_table.round(1))

# 3. Visualize Retention Matrix
fig, axes = plt.subplots(2, 1, figsize=(14, 8))

# Heatmap of raw counts
sns.heatmap(cohort_pivot, annot=True, fmt='g', cmap='YlOrRd', ax=axes[0],
            cbar_kws={'label': 'User Count'})
axes[0].set_title('Cohort Sizes - User Counts')
axes[0].set_xlabel('Cohort Age (Months)')
axes[0].set_ylabel('Cohort Month')

# Heatmap of retention rates
sns.heatmap(retention_table, annot=True, fmt='.0f', cmap='RdYlGn', vmin=0, vmax=100,
            ax=axes[1], cbar_kws={'label': 'Retention %'})
axes[1].set_title('Cohort Retention Rates (%)')
axes[1].set_xlabel('Cohort Age (Months)')
axes[1].set_ylabel('Cohort Month')

plt.tight_layout()
plt.show()

# 4. Retention Curve
fig, ax = plt.subplots(figsize=(12, 6))

# Plot retention curves for each cohort
for cohort_month in cohort_pivot.index[:8]:  # First 8 cohorts
    cohort_retention = retention_table.loc[cohort_month]
    ax.plot(cohort_retention.index, cohort_retention.values, marker='o', label=f'Cohort {cohort_month}')

ax.set_xlabel('Cohort Age (Months)')
ax.set_ylabel('Retention Rate (%)')
ax.set_title('Retention Curves by Cohort')
ax.legend(bbox_to_anchor=(1.05, 1), loc='upper left')
ax.grid(True, alpha=0.3)
ax.set_ylim([0, 105])

plt.tight_layout()
plt.show()

# 5. Average Retention Curve
fig, ax = plt.subplots(figsize=(10, 6))

# Calculate average retention at each age
avg_retention = retention_table.mean()
ax.plot(avg_retention.index, avg_retention.values, marker='o', linewidth=2, markersize=8, color='navy')
ax.fill_between(avg_retention.index, avg_retention.values, alpha=0.3, color='navy')

# Add confidence interval
std_retention = retention_table.std()
ax.fill_between(std_retention.index,
                avg_retention - std_retention,
                avg_retention + std_retention,
                alpha=0.2, color='navy', label='±1 Std Dev')

ax.set_xlabel('Cohort Age (Months)')
ax.set_ylabel('Retention Rate (%)')
ax.set_title('Average Retention Curve with Confidence Band')
ax.legend()
ax.grid(True, alpha=0.3)
ax.set_ylim([0, 105])

plt.tight_layout()
plt.show()

# 6. Churn Rate
churn_rate = 100 - retention_table
print("\nChurn Rates (%):")
print(churn_rate.round(1).head())

# 7. Revenue Cohort Analysis
# Add revenue data
np.random.seed(42)
df['revenue'] = np.random.exponential(50, len(df))

# Revenue by cohort
revenue_data = df.groupby(['cohort_month', 'cohort_age']).agg({
    'revenue': 'sum',
    'user_id': 'nunique'
}).reset_index()
revenue_data['revenue_per_user'] = revenue_data['revenue'] / revenue_data['user_id']

revenue_pivot = revenue_data.pivot(index='cohort_month', columns='cohort_age', values='revenue')
rpu_pivot = revenue_data.pivot(index='cohort_month', columns='cohort_age', values='revenue_per_user')

# Visualize revenue
fig, axes = plt.subplots(2, 1, figsize=(14, 8))

sns.heatmap(revenue_pivot, annot=True, fmt='.0f', cmap='YlGnBu', ax=axes[0],
            cbar_kws={'label': 'Total Revenue ($)'})
axes[0].set_title('Total Revenue by Cohort')
axes[0].set_xlabel('Cohort Age (Months)')
axes[0].set_ylabel('Cohort Month')

sns.heatmap(rpu_pivot, annot=True, fmt='.2f', cmap='YlGnBu', ax=ax