1. Definition

  • The Qini coefficient is a performance metric for uplift models.
  • It measures how well the model separates customers who are positively influenced by a treatment (e.g., campaign responders) from those who are not.
  • Think of it as the uplift-model equivalent of AUC (Area Under the ROC Curve) in classification.

2. Key Idea

  • In normal classification, we care about predicting who will buy.
  • In uplift modeling, we care about predicting who will buy because of the treatment.
  • The Qini coefficient evaluates how well the model ranks individuals in terms of incremental effect of treatment.

3. How It’s Computed (Conceptual)

  1. Sort customers by predicted uplift (descending).
  2. Divide into groups (deciles or percentiles).
  3. Plot the Qini curve: cumulative incremental response (treatment group minus control group) vs. population proportion.
    • X-axis: fraction of population targeted.
    • Y-axis: incremental gain due to treatment.
  4. Compute Qini coefficient = normalized area between model’s Qini curve and the diagonal (random baseline).

4. Formula (Simplified)

If $G_{\text{model}}(x)$ is the cumulative gain from the model and
$G_{\text{random}}(x)$ is the gain from random targeting, then:

$\text{Qini Coefficient} = \frac{\int_0^1 \big( G_{\text{model}}(x) – G_{\text{random}}(x) \big) dx}{\int_0^1 \big( G_{\text{perfect}}(x) – G_{\text{random}}(x) \big) dx}$

  • Range: 0 to 1 (higher = better).
  • 0.5+ is decent; close to 1 = excellent separation.

5. Example (Marketing Campaign)

  • Suppose you target top 20% customers ranked by uplift score.
  • A random selection yields +100 purchases.
  • Your model targeting yields +300 purchases.
  • The Qini curve for your model is above random, and the coefficient quantifies this improvement.

6. Relation to Other Metrics

Summary

  • Qini coefficient evaluates uplift model ranking performance.
  • Measures how well the model identifies individuals who are truly influenced by treatment.
  • Computed as normalized area under the Qini curve (incremental gain vs population).