1) Meaning

Cumulative Incremental Gain (CIG) is a performance measure in uplift modeling that shows the total additional positive outcomes (e.g., purchases, sign-ups, conversions) achieved by targeting customers ranked by uplift score.

It represents the extra benefit from using the model compared to random or no targeting.
Plotted as the Y-axis of a Qini curve.

2) How It Works

  1. Rank customers by predicted uplift score (highest → lowest).
  2. Divide population into deciles (or percentiles).
  3. For each segment:
    • Compare outcomes of treatment vs. control groups.
    • Compute incremental gain = (Response_treatment – Response_control).
  4. Cumulative incremental gain = sum of incremental gains up to that segment.

3) Formula

For a given proportion ppp of targeted population:

$\text{CIG}(p) = \sum_{i=1}^{pN} \left( y_i^{\text{treat}} – y_i^{\text{control}} \right)$

Where:

  • $y_i^{\text{treat}}$ = observed outcome if treated.
  • $y_i^{\text{control}}$ = expected outcome if not treated.
  • $N$ = total population size.

4) Example

  • Total customers = 10,000
  • Campaign run with treatment + control groups.
  • Uplift model ranks customers.

Target top 20% (2,000 customers):

  • Treatment conversions = 400
  • Control conversions = 300
  • Incremental gain = 400 – 300 = 100 extra conversions

Target top 40% (4,000 customers):

  • Treatment conversions = 750
  • Control conversions = 550
  • Incremental gain = 750 – 550 = 200 extra conversions

Cumulative Incremental Gain at 40% = 100 + 200 = 300 conversions.

5) Relation to Qini Curve

  • The Qini Curve plots Cumulative Incremental Gain (Y-axis) against % of population targeted (X-axis).
  • A steeper initial slope = model is good at finding Persuadables early.
  • A flat curve = poor uplift model (not better than random).

6) Why It Matters

  • Directly shows business impact of targeting strategy.
  • Helps determine optimal targeting percentage (where gain stops increasing significantly).
  • Allows comparison of models (which produces more incremental gains).

Bottom line:
Cumulative Incremental Gain (CIG) measures the total additional outcomes generated by targeting customers ranked by uplift score, and it’s the backbone of the Qini curve. It quantifies how many more conversions/revenue the uplift model actually delivers.