Incremental Gain

1) Meaning

Incremental Gain is the extra positive outcome (e.g., conversions, sales, sign-ups, purchases) achieved by applying a treatment (like a marketing campaign, discount, or medical intervention) compared to not applying it, for a specific portion of the population.

It’s the building block of cumulative incremental gain and the Qini curve.
While total incremental benefit is the overall effect, incremental gain shows the step-by-step added value as you target more people.

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2) Formula

For a given segment of population:

$\text{Incremental Gain} = \text{Responses}_{\text{treatment}} – \text{Responses}_{\text{control}}$

Where:

• $\text{Responses}_{\text{treatment}}$​ = number of positive outcomes in treatment group
• $\text{Responses}_{\text{control}}$ = expected number of outcomes if same group were not treated

If expressed in probability terms:

$\text{Incremental Gain} = \big(P(\text{Outcome | Treatment}) – P(\text{Outcome | Control})\big) \times n$

Where $n$ = number of targeted individuals in that segment.

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3) Example

A company runs a campaign on 2,000 customers ranked by uplift score and splits into deciles (10 groups of 200 customers each):

• Top 10% (200 customers):
  • Treatment conversion rate = 18% (36 purchases)
  • Control conversion rate = 10% (20 purchases)
  • Incremental Gain = 36 – 20 = 16 extra purchases
• Next 10% (200 customers):
  • Treatment = 14% (28 purchases)
  • Control = 12% (24 purchases)
  • Incremental Gain = 28 – 24 = 4 extra purchases

So:

• First decile contributed 16 extra purchases
• Second decile added 4 more
• Cumulative incremental gain after top 20% = 16 + 4 = 20 purchases

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4) Relation to Other Metrics

• Incremental Gain: local (step-by-step) effect in each segment.
• Cumulative Incremental Gain (CIG): running sum of all incremental gains up to a given segment.
• Total Incremental Benefit: the final CIG when 100% of the population is considered.
• Qini Curve: plots CIG vs. proportion of population targeted.

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5) Why It Matters

• Identifies where uplift is strongest (e.g., top deciles).
• Helps choose targeting thresholds (stop targeting when incremental gain flattens or turns negative).
• Provides business insight: which customer groups truly respond to interventions.

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Bottom line:
Incremental Gain measures the additional outcomes produced by a treatment in a given segment of the population. It’s the step-by-step value add that builds up to cumulative incremental gain and the total incremental benefit.