Mobile Cohort Retention Curve

Retention Model

Day-1 retention r₁ 40%

Decay exponent b 0.55

Daily install growth g 5%

ARPDAU $0.12

Simulation Clock

Live Metrics

D1 retention

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D7 retention

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D30 retention

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Est. 90-day LTV

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DAU today

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Cumulative installs

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How it works

Mobile analytics tools (Amplitude, GameAnalytics, Firebase) fit a new cohort's early retention points to a power-law decay curve, then project it forward to estimate long-run value before 30/90-day data actually exists:

R(0) = 1
R(t) = r1 · t^(-b),  t ≥ 1
LTV(T) = ARPDAU · Σ(t=0..T) R(t)

Each grid row is one daily install cohort; each column is "days since install". The 3D bars trace that curve for every cohort simultaneously — a bar's height is the fraction of that cohort still active on that day. Because cohorts are created continuously, only the diagonal actually observed so far (cohort age ≤ elapsed time) is populated, exactly like a real cohort table's staircase shape.

r₁ — day-1 retention, the curve's starting value at t=1.
b — decay exponent; larger b means users churn faster after day 1.
g — daily install growth, compounding cohort size and driving the DAU/installs readouts.
ARPDAU — average revenue per daily active user, used to project 90-day LTV from the retention curve.

Real-world relevance: this is the same shape analysts read off a Mixpanel/Amplitude retention heatmap to decide whether a cohort's economics justify its acquisition cost (CAC vs LTV).

High retention Mid retention Low retention

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