Causal Forest — model output

What we start with

User	Account age	W	watch	subs	search	niche	Ŷ
User 1	New	1	22	3	8	1	0.871
User 2	New	1	18	2	6	1	0.782
User 3	New	0	10	1	3	0	0.433
User 4	Established	1	24	3	9	1	0.921
User 5	Established	0	20	2	7	1	0.861

Model output

Leaf: New Users 1, 2, 3

avg treated = (0.871 + 0.782)/2 = 0.827 avg control = 0.433 = 0.433 τ̂ = 0.827 − 0.433

+0.394 retention

Leaf: Established Users 4, 5

avg treated = 0.921 = 0.921 avg control = 0.861 = 0.861 τ̂ = 0.921 − 0.861

+0.060 retention

Average the effect across everyone

Each user gets a score Γ = their leaf's effect + a correction for how far their own Ŷ sat from the leaf-arm average. Treatment was 50/50, so the correction divides by 0.5.

User 1 (New, treated): leaf effect (New) = 0.827 − 0.433 = 0.394 correction = (0.871 − 0.827)/0.5 = +0.088 Γ = 0.394 + 0.088 = 0.482

Similarly, Γ = +0.305 for User 2, +0.394 for User 3, +0.060 for User 4, and +0.060 for User 5.

ATE = (0.482 + 0.305 + 0.394 + 0.060 + 0.060)/5 = 1.301/5

ATE = +0.260

cross-check · size-weighted leaves = (0.394×3 + 0.060×2)/5 = +0.260 ✓

The new algorithm lifts 12-month retention — but not evenly.

+39 ppnew accounts

+6 ppestablished accounts

+26 ppeveryone (ATE)