Every customer has two unobservable conversion probabilities: pC if left alone (control) and pT if sent the campaign (treated). The individual treatment effect â the uplift â is the difference:
Ï(x) = P(convert | treated, x) â P(convert | control, x)
= p_T(x) â p_C(x)
A real uplift model never sees both outcomes for the same customer (the fundamental problem of causal inference), so it is trained as a T-learner: one classifier fit on the historical control group predicts pĖC(x), a second fit on the historical treated group predicts pĖT(x), and the predicted uplift is ÏĖ(x) = pĖT(x) â pĖC(x). This simulator generates the ground-truth pC and pT for every synthetic customer directly, then adds Gaussian noise to mimic an imperfect model's predicted score ÏĖ(x) â the Model noise slider controls how far the score drifts from the truth.
Plotted on the scatter, x = pC and y = pT for each customer; the diagonal plane y = x is zero uplift. Four quadrants fall out automatically:
- Persuadables (above the diagonal, low pC) â only convert because of the campaign; targeting them is where budget should go.
- Sure Things (near the diagonal, high pC) â convert regardless; treating them is wasted spend.
- Lost Causes (near the diagonal, low pC) â never convert; also wasted spend.
- Sleeping Dogs (below the diagonal) â the campaign actively pushes them away (annoyance, opt-outs); treating them costs conversions.
The Predicted-uplift threshold sets the targeting rule: only customers with ÏĖ(x) above it receive the campaign. True incremental conversions sums the real Ï(x) only over targeted customers â the actual conversions the campaign caused, which can go negative if too many sleeping dogs are swept in. The Qini coefficient is the area between this policy's cumulative-uplift curve (customers ranked by ÏĖ) and the curve from targeting at random, normalized to roughly [â1, 1] â the standard metric for how much better an uplift model does than blind targeting; it collapses toward 0 as Model noise grows, because a noisier score ranks customers no better than chance.