Find the retention smile by detecting where the curve flattens

Description

Your retention chart looks like a slow leak and the team has been improving onboarding for months without moving the curve. The lever you actually need is the day or week the curve flattens (the smile point) and the user behavior that produced it. This identifies the smile, traces the behaviors that lead to it, and turns it into the next quarter's growth bet.

You are a growth PM diagnosing the retention curve for {{product_name}}. Cohort window: {{cohort_window}}. Available behavioral data: {{event_streams}}.

## Step 1. Plot the cohort retention curve
Build the curve for the last 8 weekly cohorts:
- D0, D1, D7, D14, D30, D60, D90 (or W0, W1 ... W12 for slower products)
- Same y-axis for all cohorts so you can compare shapes
- Note the cohort with the strongest shape and the cohort with the weakest

## Step 2. Detect the flatten point per cohort
For each cohort, mark the day (or week) where the slope of the curve flattens:
- The flatten point is where retention loses less than 1 percentage point per period
- Some cohorts will not flatten (the curve trends to zero)
- Some will flatten high (a true smile)

## Step 3. Define activated vs not for the smile
- Users who reached the flatten point at the high level are "smile users"
- Users whose curve trends to zero are "leak users"
- Resist the temptation to define this on a single event; let the retention shape define it

## Step 4. Identify behavioral predictors of the smile
For smile users vs leak users, look at the first 7 days:
- Which 3-5 events are over-represented in smile users?
- Which 1-2 events are absent in leak users that smile users have?
- What is the time-to-first-X for smile users vs leak users?

## Step 5. Validate the predictor with a holdout cohort
Pick the strongest behavioral predictor and check it on the most recent two cohorts:
- Does it still separate smile from leak?
- Does the predictor have a tight time bound (must happen by day N)?
- Are there confounders (user type, source channel) that you need to control for?

## Step 6. Design the experiment to bend the curve
- Hypothesis: "If we move the share of new users hitting the predictor from X percent to Y percent, retention at the flatten point rises from A percent to B percent."
- Treatment: an onboarding change or in-product nudge
- Sample size and duration that detect the smallest meaningful lift
- Pre-registered guardrails

## Output
1. Cohort retention curve plot for the last 8 cohorts
2. Flatten-point table (cohort, day/week of flatten, retention level at flatten)
3. Smile vs leak behavioral comparison
4. The strongest predictor with its time bound
5. Pre-registered experiment plan
6. The curve shape you would expect if the predictor is causal

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