A decaying lift settling near 2 percent

Question

A redesign's weekly lift on clicks is decaying as novelty wears off: week 1 = 10%, week 2 = 6%, week 3 = 4%, week 4 = 3%. The team wants the durable long-run lift.

Estimate the steady-state lift this is heading toward.

Accepted Answer

Model: floor plus fading bonus. Write each week as 	ext{lift}t = L + A \cdot r^{\,t}, with L the durable lift and A \cdot r^{t} the shrinking novelty bonus. Find the ratio from the weekly drops. - Week 1 to 2: 10 	o 6, drop of 4. - Week 2 to 3: 6 	o 4, drop of 2. - Week 3 to 4: 4 	o 3, drop of 1. The drops (4, 2, 1) halve each week, so r = 1/2. Solve for the floor. The excess above L should halve. Test L = 2: the excesses are 10-2, 6-2, 4-2, 3-2 = 8, 4, 2, 1, which halve perfectly. So the lift is converging to L = 2\%. Interpretation. The 10% first week was mostly novelty. The durable cli…

A decaying lift settling near 2 percent

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