A cohort's retention curve flattens near 20% while another decays toward zero — what does each imply?

## What the shape means A retention curve plots `r(n)`, the share of an acquisition cohort active at age `n`, against `n`. Almost every real curve falls steeply at first and then bends. The interesting question is what it bends **toward**. - **Flattening at a positive level** — the curve descends to roughly 20% and stops falling in any practically meaningful way. Interpretation: a fraction of every cohort forms a durable habit and keeps coming back indefinitely. - **Decaying toward zero** — the curve keeps sliding, perhaps slowly, with no floor. Interpretation: every cohort eventually leaves; the product is a bucket with a hole in it. ## The arithmetic that makes it matter Suppose you acquire `c` new users every day and each cohort follows the same curve `r(n)`, with `r(0) = 1`. On any given day in steady state, the active users are the survivors of every past cohort: today's cohort contributes `c * r(0)`, yesterday's `c * r(1)`, and so on. So ``` steady-state daily actives = c * sum over n of r(n) ``` The sum of the retention curve is exactly the **expected number of active days per acquired user** — the area under the curve. - If `r(n)` converges to a positive constant, the sum diverges. There is no steady state: the active base keeps climbing, roughly linearly in time, for as long as acquisition continues. This is the growth mechanism people mean when they say retention compounds. - If `r(n)` decays to zero fast enough for the sum to converge, the active base plateaus at `c` times that finite area. Doubling the plateau then requires either doubling acquisition or genuinely enlarging the area under the curve. That difference — an active base that grows versus one that saturates — is why the asymptote is the single most consequential feature of the curve, far more than the day-1 number that gets quoted in decks. ## Why curves flatten even without a habit A subtlety worth raising unprompted: an aggregate curve flattens **mechanically** when users are heterogeneous. Suppose every user leaves at a constant per-day rate, but the rates differ across people. Early on, the high-churn users dominate and the curve falls fast. As days pass, the remaining mix shifts toward the low-churn users, so the aggregate curve bends and flattens — even though no individual's behaviour changed. So flattening is evidence of a **low-churn segment existing**, not evidence that the product taught anyone a habit. The actionable follow-through is to identify who that segment is and whether acquisition can be pointed at more people like them. ## What to check before you believe a flat curve **Horizon.** Thirty days is not long enough to see an asymptote. Curves that look flat at 12% over two months routinely resume falling over a year. Extend the same cohort as far as data allows, and plot on a log y-axis — a slow exponential decay looks flat on a linear axis and unmistakably straight and sloping on a log one. **Activity definition.** A floor can be manufactured. If a background refresh, an automated retry, a push-notification receipt or an internal test account counts as "active", the curve cannot fall below that noise level. Rebuild the curve with a deliberate action — a session with real interaction, a purchase, a message sent — and see whether the floor survives. **Cohort maturity and composition.** Only cohorts old enough to reach the far end of the curve contribute there, so a curve stitched from different cohorts at different ages is not one curve. Also check whether the flat portion is dominated by a single acquisition channel or a single country; "the product has a durable core" and "one channel brings durable users" have different strategic answers. ## How each shape changes what you do With a **flattening** curve, the leverage is at the top: getting more users to reach the flat part, and pointing acquisition at populations that resemble the durable segment. The long tail takes care of itself. With a **decaying** curve, the leverage is in the area under the curve. Either you find and remove the reason people leave late in life, or you accept the plateau and plan the business around continuous acquisition and its cost. Pouring money into acquisition against a curve that reaches zero buys a one-off bump, not a base. ## The sentence to land The asymptote of the retention curve, not its first point, decides whether growth compounds or has to be re-bought every day — and you have not established an asymptote until you have looked over a long horizon, on a log scale, with an activity definition that a human has to satisfy.