Retention curves: read the cohort, not the total
What a cohort is. The word is Latin: a Roman legion (about 5,000 men) was divided into 10 cohorts of about 480 men each, a unit that marched together. Analytics borrows exactly that sense: a cohort is a batch of users sharing one starting point, such as registering in the same week. Cohort analysis watches one batch over time.
Why cohorts, not totals. A total mixes batches, and new inflow masks outflow. Illustrative numbers, not any product's actuals: week 1 brings 100 users, week 2 keeps 40 of them reading, week 3 keeps 30, so the batch lost 70%. But if 100 new users arrive each week, the total reads 140, then 170, and looks healthy while the first batch bled out. A total cannot tell retention apart from replacement. The denominator of a cohort curve is the batch's initial size, and the numerator each week is how many of that batch are still active.
Shapes, and what each one indicts. A steep drop that then flattens means the early leavers were never the target audience (wrong acquisition, curious passersby) and the flat tail is a core that found value: the problem is targeting and filtering, not the product's core. A curve that keeps declining without flattening means even the survivors keep leaving: the product itself has no stickiness, and buying traffic pours water into a leaky bucket. A single-week cliff (a whole block dropping at, say, week 4) points at one mechanism (trial ends, content runs out, paywall hits): investigate that point, not stickiness in general. Flat then steep is the fourth shape: the core held for a while and then eroded. The flat part proves a core existed; the steep part proves the core's reason to stay expired or was broken: content exhausted with no next step, a change that drove core users away (paywall, price, bad update), or the cohort's natural lifecycle ending (exam over, semester over). Find what changed at the bend week, and for a reading product the classic case is finishing a book with no next book catching the reader.
Denominator traps. Registration versus activation denominators answer different questions: registration covers the whole funnel (acquisition quality plus onboarding plus product); activation covers only people who experienced the product. An active definition must be behavioral and event-instrumented, not "opened the app": opened-app definitions inflate the curve, over-strict ones deflate it. Frequency must match the product: weekly is the honest window for a low-frequency product like reading, daily would misjudge it as sticky-less. And batches must be cut, not pooled: by channel (different channels bring different-quality users) and by key-action completion (for example, whether the user imported a first book).
Derivation: the area under the curve is expected lifetime. Let weekly churn be c. Week 1 has 100% of the batch, week 2 has 1-c, week 3 has (1-c) squared, and so on. Summing the geometric series gives expected lifetime in weeks:
Weekly churn of 20% means an expected lifetime of 5 weeks; 10% means 10 weeks. This is where the division by churn in the LTV formula comes from.
Lucerna worked conclusions (decided 2026-10-26). Weekly retention uses activated users as the denominator, not registered users: churn after activation is what indicts the product. Weekly active means at least one valid reading session in the week, defined by event instrumentation with a duration threshold. Per-user average events are tracked separately as engagement depth, not mixed into the retention numerator. The duration threshold must be set from the actual reading-duration distribution, not guessed; the duration is reading time, not app foreground time (screen-off and backgrounded time excluded); and depth is read with the median and the distribution alongside the mean, since a few heavy users pull the mean up.