Setup & Data
10K
Daily installs/variant
$0.50
ARPDAU (baseline)
5
Data points given
Log
Trendline model
| Day | Variant A | Variant B | Difference |
|---|---|---|---|
| 1 | 41.00% | 46.00% | B +5.00% |
| 3 | 39.46% | 41.28% | B +1.82% |
| 7 | 38.28% | 37.63% | A +0.65% |
| 14 | 37.31% | 34.65% | A +2.66% |
| 28 | 36.33% | 31.67% | A +4.66% |
Variant A
R(d) = 0.41 − 0.014 × ln(d)
Slow start, flat decay — “the steady one”
Variant B
R(d) = 0.46 − 0.043 × ln(d)
High start, fast decay — “the flashy one”
Crossover at Day ~5.6: Before this day, B retains more users. After this day, A takes over and the gap keeps widening.
Results
Question A
Maximize DAU on Day 15
Variant A
Older cohorts (6–14 days) dominate the Day-15 DAU calculation, and A is superior in all of them.
Question B
Maximize cumulative revenue (15d)
Variant B
Stronger early retention creates more total “user-days” in the first 15 days, generating $4,599 more revenue.
Question C
ARPDAU spike ($0.70 → $0.50, Day 15–25)
Variant A
Higher ARPDAU × growing DAU gap = multiplier effect. A’s long-tail retention wins by $7,562.
The Bottom Line
Short-term campaign? Choose B. Its strong early retention generates more revenue in a 15-day window.
Long-term game? Choose A. My model shows A overtakes B at Day ~5.6 and never looks back. By Day 15, A leads by 307 DAU; by Day 30 the gap reaches thousands. Combined with $4,599 higher cumulative revenue (15d) and a $7,562 advantage under the ARPDAU spike scenario, A is the clear choice for any product built to last.
