Causal lift

What τ measures

The quantity at issue is a difference of rates: τ equals the outcome rate a cohort achieves when treated, minus the rate that same cohort would have achieved untreated. The second term is a counterfactual. For any single lead only one of the two outcomes is ever observed, which is why causal lift cannot be read off a lead-by-lead ledger, however complete the ledger is.

Randomization resolves this at the group level. When a coin decides who is treated, assignment is independent of everything about the lead — industry, seniority, intent signals, a rep’s judgment — so the untreated group’s observed rate is an unbiased estimate of the counterfactual, and the difference between groups estimates τ. No retroactive analysis substitutes for the coin: the coin is what severs the link between who was chosen and how likely they already were to convert.

Correlational lift and selection

The common alternative computes lift after the fact: take the accounts that were exposed to a channel, take the accounts that were not, and compare their conversion rates. The exposed group, though, was never chosen at random — it was assembled by reps, targeting rules, or an optimizer, often precisely because those accounts looked more likely to convert. The measured gap then mixes two things that cannot be separated retroactively: the effect of the exposure and the selection that produced it.

Vendors in this space can be candid about the distinction. HockeyStack’s product page says its lift reports “compare exposed and unexposed accounts,” and its documentation describes multi-touch attribution as “purely directional, not incremental.” Its lift-reports documentation concedes that for a given conversion “there is no real way to know” it would not have happened anyway — only that lift measured on a large audience gets close. These are honest statements of what a non-randomized design supports: direction, not causation.

What a known propensity buys

In a randomized design the propensities — each lead’s probability of landing in each cell — are known constants fixed by the design, not quantities estimated afterward. That makes an inverse-propensity construction available: weight each observed outcome by one over its probability of being observed. The Horvitz–Thompson score for lead i is τ̂ᵢ = 1{proof}·Yᵢ/q_P − 1{holdout}·Yᵢ/q_H, where Yᵢ is the lead’s binary outcome and q_P, q_H are the known randomization propensities; its average is unbiased for τ. The score is also bounded — it lives in a known range of width 1/q_P + 1/q_H — so after rescaling into [0,1] it can feed machinery built for bounded means. An observational comparison has no q to divide by: the propensities existed, but no one recorded them, and they were correlated with the outcome.

How RevenueOS uses this

RevenueOS estimates causal lift with exactly this construction. Before a program sends its first email, leads are randomized into a never-mailed holdout and a proof cell the optimizer is firewalled from touching; the split fixes the propensities q_P and q_H by design. Each lead’s outcome becomes a per-lead score τ̂ᵢ = 1{proof}·Yᵢ/q_P − 1{holdout}·Yᵢ/q_H, rescaled into [0,1] and fed to a betting confidence sequence at α = 0.1 — a 90% band that remains valid under continuous monitoring, and that closes a claim only when it excludes zero.

When the band never excludes zero, the null publishes on the same ledger with the same recomputable arithmetic. RevenueOS is at design-partner stage as of July 2026 and claims no customer results; what it publishes is the method — the design constants q_P and q_H are known, so a partner can recompute τ̂ from the ledger rather than accept a directional number on faith.

Related terms

Incrementality · Randomized holdout · Anytime-valid confidence sequence