Lift

Lift measures how much better a model's ranking is than random selection, at a given depth of the ranked list.

\[\text{Lift at top } k\% = \frac{\text{positive rate in the top } k\% \text{ of predictions}}{\text{overall positive rate}}\]

Example: 2% of customers respond overall, and the top 10% by model score respond at 8%. Lift at 10% = 8 / 2 = 4×.

Building it

1. Score every instance and sort by predicted value, highest first.

2. Split into buckets (usually deciles).

3. For each bucket (or cumulatively), divide the actual rate by the baseline rate.

Regression: same idea with a numeric target. Rank by predicted value, then compare the mean actual value in each bucket to the overall mean. Image

Related charts

Chart	x-axis	y-axis	Random baseline
Lift chart	% of population targeted (ranked)	Lift (rate ÷ baseline rate)	Flat line at 1
Cumulative gains (= cumulative response curve)	% of population targeted (ranked)	% of all positives captured	Diagonal

The gains chart and the cumulative response curve are the same chart under two names. The lift curve is the gains curve divided by the diagonal.

When to use

• Targeting budget: you'll contact only the top k%. Lift at k answers "how much better than random at that depth?"

• Imbalanced data with a small positive class.

• Comparing models at a specific depth, where AUC instead averages over every threshold.

Caveat: lift depends on the base rate. The maximum possible lift is 1 / base rate, so a 4× lift on a 2% base rate isn't comparable to one on a 30% base rate.