Streak & Retention Hazard Model
The cheapest day to save a user is almost never day one. This finds the day.
Model 7 of The Marketing Quant Python Kit. Runs entirely in your browser — nothing you type is sent anywhere.
Your streak
Share who come back after their first day. This is the hardest day.
Where daily retention settles once the habit is formed.
How fast continuation climbs toward the asymptote. Higher means the habit locks in sooner.
Percentage-point improvement in continuing, for someone who receives the reward.
With a fixed budget the ranking inverts: early days can no longer reach everyone, so the cheap late day stops being obviously best.
Where to place the reward
Cheapest day: day 29
Cost per additional survivor at the horizon.
$20.00
Baseline survivors
Reaching day 30 with no reward at all.
431.6
Users reached on that day
454
Spend
$909
Extra survivors bought
45.4
By day
| Day | Paid | Spend | $/survivor |
|---|---|---|---|
| 1 | 10,000 | $20,000 | $254.87 |
| 3 | 3,675 | $7,349 | $127.95 |
| 7 | 1,677 | $3,353 | $70.00 |
| 14 | 995 | $1,991 | $43.63 |
| 21 | 686 | $1,371 | $30.17 |
| 29 | 454 | $909 | $20.00 |
Early rewards reach everyone but most of them were going to continue anyway. Late rewards reach a small, self-selected group who are far more likely to be saved by it.
Every input here is an assumption about your product, not a benchmark. Fit day-1 continuation, asymptote and k to one real cohort before trusting the output — the shape of the curve drives the answer far more than the reward cost does.
Get the Gamification Mechanics Playbook
Streaks, leaderboards and loyalty tiers as measurable systems. Where streaks break, why global leaderboards drive off 95% of players, and the retention lift a tier has to clear.
Browse all free guides →The maths behind this
Where Streaks Break: The Hazard Rate Behind Daily Engagement Mechanics
Day 1 saves the most users. It also costs 12.7 times more per user saved than day 29. Both are true, and your budget decides which one matters. The hazard-rate model for streaks, with the Python and the counterintuitive answer.
Read →Loss Aversion Is a Number: Pricing a Streak Freeze With Prospect Theory
Prospect theory puts the loss aversion coefficient at about 2.25. That turns a streak into a computable liability in the user mind, and it says flat-priced streak freezes leave most of their value uncollected.
Read →Endowed Progress Effect: The Math and the 2006 Paper
The paper is Nunes and Dreze, Journal of Consumer Research 32(4), 504-512, DOI 10.1086/500480. Here is what it actually found, and the arithmetic for sizing artificial progress in your own product.
Read →Other tools
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Want this fitted to your actual numbers?
The defaults here are illustrative. Fitted to your own data — real hazard rates, real margins, real conversion — the same models tell you what to do next rather than what is theoretically possible.
Get it modelled properly