Cohort Curve Model

Retention data has a shape, and the shape is the business. This skill fits the standard consumer-retention power curve r(t) = a·t^(−b) to observed cohort data by log-log least squares — actual arithmetic run by the bundled script, not model vibes — then projects it forward and prices it.

Required Inputs

• Observed retention by period — from period 0 (100%) through at least period 3-4. Percent or fraction, either works. More periods = a trustworthy fit; 4 is the floor.
• ARPU per period (optional) — revenue per retained user per period. Without it, LTV is reported in lifetime-period multiples instead of currency.
• Projection horizon (optional, default 24 periods).

If the requester has cohort tables (rows of cohorts × months), take the average by period-age or fit the most recent complete cohort — say which you did.

Output Format

1. The fit — a (scale), b (decay), R² of the log-log fit, and the observed tail floor. Interpret b plainly: b < 0.5 = strong flattening, a habit is forming; 0.5–1 = normal decay; b > 1 = leaky bucket, the curve never accumulates a base.
2. The projection — observed vs fitted by period, marked where observation ends and projection begins.
3. The money — lifetime periods (Σ fitted retention over the horizon) and LTV = ARPU × lifetime periods.
4. The caveat that matters most — if R² < 0.9, say the power family fits poorly and the projection should be distrusted beyond the observed tail.