A fading engagement lift heading toward 4 percent

Question

A new feature shows a decaying weekly lift on engagement as its novelty fades: week 1 = 20%, week 2 = 12%, week 3 = 8%, week 4 = 6%. The team wants the durable long-run lift, not the inflated early weeks.

Estimate the steady-state lift this is settling toward.

Accepted Answer

Model: floor plus fading bonus. Write each week's lift as 	ext{lift}t = L + A \cdot r^{\,t}, where L is the durable steady-state lift and A \cdot r^{t} is the novelty bonus shrinking toward zero. Find the ratio from the weekly drops. - Week 1 to 2: 20 	o 12, drop of 8. - Week 2 to 3: 12 	o 8, drop of 4. - Week 3 to 4: 8 	o 6, drop of 2. The drops (8, 4, 2) halve each week, so r = 1/2. Solve for the floor. The excess above L should halve each week. Test L = 4: the excesses are 20-4, 12-4, 8-4, 6-4 = 16, 8, 4, 2, which halve perfectly. So the lift is converging to L = 4\%. Interpretation. T…

A fading engagement lift heading toward 4 percent

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