1) Meaning

Cumulative Uplift is the running total of the incremental effect (extra responses, conversions, or purchases) gained from targeting customers ranked by uplift score.

It tells you how much total benefit you’ve achieved up to a given proportion of the population.
It’s the Y-axis of the Qini curve (with population proportion on the X-axis).

2) Formula

For top $k\%$ of customers ranked by uplift score:

$\text{Cumulative Uplift}(k) = \sum_{i=1}^{kN} \Big( y_i^{\text{treatment}} – y_i^{\text{control}} \Big)$

Where:

  • $N$ = total number of customers
  • $y_i^{\text{treatment}}$​ = observed outcome if treated
  • $y_i^{\text{control}}$​ = expected outcome if not treated

3) Step-by-Step Example

Suppose we target 1,000 customers, split equally into treatment vs. control.

We rank customers by uplift score and check each decile (10%).

  • Top 10% (100 customers):
    • Treatment = 18 conversions
    • Control = 12 conversions
    • Incremental = +6
    • Cumulative Uplift = 6
  • Top 20% (200 customers):
    • Treatment = 32 conversions
    • Control = 24 conversions
    • Incremental = +8
    • Cumulative Uplift = 6 + 8 = 14
  • Top 30% (300 customers):
    • Incremental = +10
    • Cumulative Uplift = 24

…and so on until the full population.

At 100%, the final cumulative uplift = total incremental benefit of the campaign.

4) Why It Matters

  • Shows where uplift is concentrated (e.g., top 20% of customers may give most benefit).
  • Helps decide optimal targeting cutoff (stop where cumulative uplift flattens).
  • Used to evaluate uplift models:
    • A good model: steep cumulative uplift early (finds Persuadables first).
    • A bad model: curve looks like random baseline.

5) Relation to Other Metrics

  • Incremental Gain: step-by-step added benefit in each group.
  • Cumulative Uplift: running sum of all incremental gains.
  • Total Incremental Benefit: final cumulative uplift at 100% of population.
  • Qini Curve: graphical plot of cumulative uplift vs. population proportion.

Bottom line:
Cumulative Uplift is the running total of incremental responses from an uplift model as you target more customers. It is essential for Qini curve analysis, model evaluation, and campaign optimization.