Retention Curves

A bucket with a hole in it never fills up, however fast you pour. Many companies spend a fortune on new customers, while old ones quietly leak away. A retention curve shows you the size of the hole.

• A bucket with a hole
• Pouring in new customers
• Old ones leak away

A retention table

We group customers by the month that they joined, and we count how many are left, in each month after that. Then we divide by the starting size, to make cohorts comparable. Run it. Read across a row to follow one group. Read down a column to compare groups at the same age. The March cohort kept thirty three percent after five months, and January kept sixteen. Something improved. Perhaps it was the new loyalty scheme. That's where you start asking questions.

import numpy as np
import pandas as pd

rng = np.random.default_rng(0)
rows = []
for cohort, keep in [("Jan", .70), ("Feb", .74), ("Mar", .80)]:
    users = 1000
    for month in range(6):
        rows.append((cohort, month, users))
        users = int(users * keep * rng.uniform(.97, 1.03))

t = pd.DataFrame(rows, columns=["cohort", "month", "users"]).pivot(index="cohort", columns="month", values="users")
print((t.div(t[0], axis=0) * 100).round(0).astype(int).to_string())

month     0   1   2   3   4   5
cohort
Feb     100  74  56  41  31  24
Jan     100  70  49  33  22  16
Mar     100  82  64  51  40  33

Reading the shape

What matters most is the shape. A curve that falls to zero means that you've got a leaky product, and growth can't last. A curve that flattens out means that you've found people who truly want what you sell. So look for the level at which it flattens. And if newer cohorts sit above older ones, your product is improving.

Summary