  Binary decisions are very common in artificial intelligence. Applying a
threshold on the continuous score gives the human decider the power to control
the operating point to separate the two classes. The classifier,s
discriminating power is measured along the continuous range of the score by the
Area Under the ROC curve (AUC_ROC) in most application fields. Only finances
uses the poor single point metric maximum Kolmogorov-Smirnov (KS) distance.
This paper proposes the Area Under the KS curve (AUC_KS) for performance
assessment and proves AUC_ROC = 0.5 + AUC_KS, as a simpler way to calculate the
AUC_ROC. That is even more important for ROC averaging in ensembles of
classifiers or n fold cross-validation. The proof is geometrically inspired on
rotating all KS curve to make it lie on the top of the ROC chance diagonal. On
the practical side, the independent variable on the abscissa on the KS curve
simplifies the calculation of the AUC_ROC. On the theoretical side, this
research gives insights on probabilistic interpretations of classifiers
assessment and integrates the existing body of knowledge of the information
theoretical ROC approach with the proposed statistical approach based on the
thoroughly known KS distribution.
