Gini coefficient

The Gini coefficient originated in economics as a measure of income inequality (Gini, 1912)^{[1]Jump to source 1 in the sources list}, building on the Lorenz curve (Lorenz, 1905)^{[2]Jump to source 2 in the sources list}. In credit modeling, an analogous geometric construction is used: the Cumulative Accuracy Profile (CAP, also called the credit-scoring power curve) plots the cumulative fraction of defaults captured against the cumulative fraction of the population ranked by model score from worst to best. The credit-modeling “Gini” — also called the Accuracy Ratio (AR), and mathematically equivalent to Somers’ D for binary outcomes^{[5]Jump to source 5 in the sources list[6]Jump to source 6 in the sources list} — measures the area between the CAP curve and the diagonal expected from a random model. The two Ginis share geometric intuition but are not numerically interchangeable across the income-inequality and binary-classifier domains.

In a binary classification setting, the Gini coefficient is mathematically equivalent to 2 × AUC − 1^{[3]Jump to source 3 in the sources list}, where AUC is the area under the ROC curve. The probabilistic interpretation: AUC equals the probability that a randomly chosen positive (default) case is scored higher than a randomly chosen negative case — equivalent to the Wilcoxon / Mann-Whitney U statistic^{[4]Jump to source 4 in the sources list}. Some practitioners prefer Gini because it stretches the meaningful range — credit models rarely score below an AUC of 0.50, so the [0, 1] Gini scale is more interpretable than the [0.5, 1.0] AUC scale. The Basel Committee on Banking Supervision adopted the Accuracy Ratio / Gini as a standard discriminatory-power measure for internal-ratings-based model validation^{[7]Jump to source 7 in the sources list}.

AUC ↔ Gini conversion

Like AUC, the Gini coefficient captures only the ranking quality of a model — its ability to score positives higher than negatives. It does not measure calibration, the accuracy of the predicted probabilities themselves. A model can score a high Gini while systematically over- or under-predicting default rates within score bands, which is why monitoring practices typically pair Gini with a calibration measure such as Brier score or expected calibration error^{[9]Jump to source 9 in the sources list[10]Jump to source 10 in the sources list}. Mathematically the binary-classifier Gini can be negative (a model that ranks worse than random), but credit-scoring models in practice live in [0, 1].