Mobile Cohort Retention Heatmap (2D)

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

—

D7 retention

—

D30 retention

—

Est. 90-day LTV

—

DAU today

—

Cumulative installs

—

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)

The top panel is a live cohort retention heatmap — one row per daily install cohort, one column per "days since install" — exactly the staircase-shaped grid analysts read in a Mixpanel/Amplitude retention report. Only the diagonal actually observed so far (cohort age ≤ elapsed time) is lit; drag to pan the grid and scroll/pinch to zoom, just like panning a real cohort table. The lower-left panel plots the retention curve itself so you can see r₁ and b bend its shape directly; the lower-right panel tracks DAU and cumulative installs over time.

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

Drag heatmap to pan · scroll to zoom