AUC (area under the ROC curve)
AUC (area under the ROC curve) is the area under the receiver operating characteristic curve. It is the probability that a credit or fraud score ranks a randomly chosen bad as riskier than a randomly chosen good. An AUC of 0.5 is chance, and 1.0 means every bad is ranked as riskier than every good.
Example
For illustration, imagine comparing 100 bad-good pairs from a credit score. If the score ranks the bad as riskier in 80 pairs, its AUC is 0.80. The corresponding Gini is 2 × 0.80 − 1, or 0.60.
How the ROC curve is drawn from score bands
As the cutoff moves through ordered score bands, count the share of all bads caught and the share of all goods caught. Plot those two shares for each cutoff to form the ROC curve.
The area under that curve brings the results across cutoffs into one measure. A larger area reflects stronger separation between bads and goods across the curve.
How AUC relates to Gini and KS
Gini converts directly from AUC: Gini = 2 × AUC − 1. For example, an AUC of 0.75 gives a Gini of 0.50.
AUC can help compare the ranking ability of scores assessed on the same bad-good cases. KS and AUC are related only under an assumption about score distributions, such as the binormal model, so converting between them is an approximation.
Questions we get asked
Does AUC tell me the right cutoff for a credit decision?
No. AUC summarizes the ROC curve across cutoffs, but it does not identify a cutoff for a credit policy. The shares of bads and goods caught at a particular cutoff are the relevant ROC point.
Does a high AUC mean a low bad rate?
No. AUC describes how a score ranks bads relative to goods. It does not state the share of applicants who are bad.
Why is converting KS to AUC only approximate?
A KS-to-AUC conversion is approximate because it assumes a shape for the score distributions. KS measures the gap at one score point, while AUC measures ranking across the full ROC curve, so equal AUC values can have different KS values.
Decisimo’s free Gini-to-AUC/KS converter relates those measures under the binormal model and includes a reference table.
