Duolingo 7-State Markov Growth Modeling & Lifecycle Forecasting

This skill exists to stop: debating retention by gut feel or one blended metric, instead of decomposing users into lifecycle states and finding the exact leaking transition.

📁 Source note: [sage] = upstream Sage repo (github.com/xoai/sage, public) — optional deeper reading; this skill runs fully on the rules inlined here. A step marked MUST READ points at a file in your own project (e.g. an event registry) — if it is missing, stop and ask instead of improvising.

🤖 0. HOW TO USE (agent workflow)

A. Classify users into the 7 lifecycle states from event data — define the anchor event explicitly and keep it stable; changing it mid-series is a methodology change that must be logged. B. Build the transition matrix + DAU forecast: report data window and source; label forecasts [ASSUMPTION] with a range. C. Diagnose: name the 1–2 transitions most worth improving and the initiative betting on each (hand off to okr-outcome-architect). Standard output: matrix + one bottleneck conclusion + one bet. Never return "retention looks fine" without numbers.

🧠 1. Core Mathematical Foundation: 7 Lifecycle States

Unlike traditional DAU/MAU ratios that hide churn dynamics, the 7-state model decomposes the entire user base into mutually exclusive, collectively exhaustive buckets: