Why do N-day, rolling and bracket retention give three different numbers for one cohort?

## The three rules Fix an acquisition cohort — say everyone who installed a mobile game on the same day, with install day labelled day 0. Retention always means "share of that cohort that satisfies an activity rule", and the three common rules are: - **N-day retention** (also called day-N or classic retention): the share of the cohort active on **exactly** day N. Day-7 retention counts a user only if they opened the game somewhere in day 7's window, regardless of what they did on days 1-6 or day 8. - **Rolling retention** (also called unbounded retention): the share of the cohort active on day N **or any day after**. A user who was silent for a month and came back on day 45 counts toward day-7 rolling retention. - **Bracket retention** (also called range or window retention): the share active at least once **within a day range**, such as days 1-7. It is the rule behind statements like "55% of installs came back during their first week". Vendor and team vocabulary for these is inconsistent, so the first move in any conversation about a retention number is to ask which rule produced it. ## Why the numbers differ, and by how much Each rule admits a different set of users, and the sets nest in a way you can reason about: - Being active exactly on day N implies being active on day N or later. So for the same cohort and the same N, `N-day(N) <= rolling(N)`. The gap is the share of users who skipped day N but returned later, which is large for products with irregular cadence and small for daily-habit products. - Bracket over days 1-7 admits anyone active on any of those seven days, so it is at least as large as N-day retention for any single day inside the bracket. It is not directly comparable to rolling at day 7, since the two conditions cover different time spans. A product with a weekly rhythm can easily report day-7 N-day retention of 18%, bracket days 1-7 retention of 46%, and rolling day-7 retention of 31% — all correct, all describing the same cohort. ## Monotonicity, and the day-7 bump **Rolling retention is non-increasing in N.** The set of users active on day N or later shrinks as N grows, because the qualifying window only gets shorter. A rolling curve that goes up as N increases is a bug. **N-day retention is not monotone.** It is a per-day snapshot, so it inherits every rhythm in the underlying behaviour. Day-7, day-14 and day-30 values often sit above their neighbours because people return on the same weekday, on payday, or when a weekly event resets. Reading that bump as a data error is a common mistake; so is cherry-picking day 7 as "the" retention number because it happens to be a local peak. **Bracket retention is non-decreasing as the bracket widens**, since a wider window can only admit more users. ## The maturity problem N-day and bracket retention are **final once the cohort has aged past the window**: after day 7 has fully elapsed for that cohort, day-7 retention will never change. Rolling retention is different. "Day 7 or later" has no end date, so the number you compute today is a lower bound on the true value — a dormant user who returns next quarter will retroactively raise the day-7 rolling retention of a cohort from last year. In practice teams cut it off at the data boundary, which means rolling numbers for young cohorts are systematically understated relative to old ones. Comparing a 3-month-old cohort's rolling retention with a 2-year-old cohort's is comparing an unfinished measurement with a finished one. ## Which rule to use when - **N-day** is the right choice when the product has a genuine daily expectation and you want a sharp, comparable, final number. It is also the rule whose curve you sum to get expected active days per user. - **Bracket** suits products with a natural period — a weekly or monthly cadence — where asking "did they come back this week?" is the honest question and per-day snapshots are mostly noise. - **Rolling** suits low-frequency products where dormancy is normal and you want to know whether a user is gone for good rather than gone this Tuesday. Its cost is that it never settles. ## What a good answer adds Always quote the rule, the value of N, the cohort definition and the activity definition together. "Retention is 31%" is not a fact; "day-7 rolling retention for the June install cohort, where active means opening the app, is 31% as of today" is. Most disagreements about whether retention improved are two people using different rules on the same data.