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Two channels with the same churn number.
A thousand subscribers, five hundred from each channel, with real signup dates and real cancellations. Everything below is computed in your browser from the per-subscriber records: a Kaplan-Meier fit, hazard by lifecycle period, and a log-rank test. Nothing is hardcoded.
A growth team reads this row, concludes the two channels retain the same way, and spends the next quarter buying more of whichever is cheaper. Both numbers are correct. The conclusion is not.
The log-rank test weights every cancellation by how many subscribers were still at risk when it happened, which is the information a percentage throws away. Paid search produced 187 cancellations where equal hazard predicts 84. χ² = 225.3 on one degree of freedom.
Where in the lifecycle
The hazard curve names the window.
Hazard is the number a churn rate averages away: of the subscribers who made it to the start of this period, what fraction left during it. Read it and the retention work writes itself.
90.9% of every cancellation this channel has produced happened between day 7 and day 35. From week seven on, weekly hazard never again reaches 2%: whoever survives onboarding stays.
Near-zero hazard for five months, which is why this channel looks flawless on any 90-day retention report. 86.2% of its cancellations land between day 150 and day 330.
The other failure
The same cohort, twice, 23.2 pts apart.
These two groups are drawn from an identical lifetime distribution. Same product, same channel, same everything. The only difference is that one signed up in the last forty-five days, so most of them have not been watched long enough to churn yet. The retained percentage counts every one of them as a win.
Every cohort comparison you have ever run on a retained percentage carries this bias, and it always points the same way: newer looks better. Which means the cohort you are most anxious to evaluate is the one the number lies about hardest.