where 𝑛 is the total number of active and decoy ligands and 𝛽 𝑖 is the false positive rate (FPR) for when the 𝑖th active is recovered in the ordered (by docking score) list. A greater pROC AUC value demonstrates enrichment and is attributed to the ability of a docking configuration to distinguish between actives and decoys. The pROC AUC expected for random selection is 0.434 (in contrast to 0.5 for the classical ROC AUC). Importantly, unlike the ROC AUC that enforces an upper bound of 1.0, the pROC AUC is formally unbounded. In practice, however, it is constrained by the relative frequency of recovering actives amongst decoys based on HTS.