Lift

Study guides: Exam ATPA, Exam MAS-II

Lift is a model performance metric used to evaluate how much better a predictive model performs relative to a random baseline when targeting a fraction of the population. It is commonly used in insurance for fraud detection, marketing, and pricing model validation.

$\text{Lift at decile } d$

$= \frac{\text{Response rate in top-}d\text{ decile}}{\text{Overall response rate}}$

$\text{Cumulative Lift}$

$= \frac{\text{Responses captured in top fraction}}{\text{Expected responses if random}}$

Lift chart (gains chart) construction:

Score all observations using the model
Rank observations from highest to lowest predicted probability
Divide into deciles (10% groups)
For each decile, compute the actual response rate
Plot cumulative lift vs. fraction of population targeted

A lift of 2 at the top decile means the model identifies twice as many positives in that decile as random selection would
In P&C ratemaking, "lift chart" usually means something else: the Quantile Plot, which sorts a holdout set by predicted loss cost into equal-exposure buckets and compares actual with predicted in each. Two rating models are compared with a Double Lift Chart, which sorts on the ratio of the two models' predictions — not by overlaying two lift curves
Lift is closely related to the AUROC and Gini Index — all measure ranking/discriminatory ability
At 100% of the population: cumulative lift = 1 for any model (all positives are eventually captured)

Calculating Lift for the Top Decile A fraud detection model is applied to 1,000 claims. 100 claims are actual fraud (10% base rate). In the top decile (100 highest-scored claims), 35 are fraudulent. What is the lift?

Answer Response rate in top decile: $35/100 = 35\%$ . Overall response rate: $100/1{,}000 = 10\%$ . $\text{Lift} = \frac{35\%}{10\%} = 3.5$ The model is 3.5 times better than random at identifying fraud in the top-scored decile.