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Probability forecasts for binary outcomes, often referred to as probabilisticclassifiers or confidence scores, are ubiquitous in science and society, andmethods for evaluating and comparing them are in great demand. We propose andstudy a triptych of diagnostic graphics that focus on distinct andcomplementary aspects of forecast performance: The reliability diagramaddresses calibration, the receiver operating characteristic (ROC) curvediagnoses discrimination ability, and the Murphy diagram visualizes overallpredictive performance and value. A Murphy curve shows a forecast's meanelementary scores, including the widely used misclassification rate, and thearea under a Murphy curve equals the mean Brier score. For a calibratedforecast, the reliability curve lies on the diagonal, and for competingcalibrated forecasts, the ROC and Murphy curves share the same number ofcrossing points. We invoke the recently developed CORP (Consistent, Optimallybinned, Reproducible, and Pool-Adjacent-Violators (PAV) algorithm based)approach to craft reliability diagrams and decompose a mean score intomiscalibration (MCB), discrimination (DSC), and uncertainty (UNC) components.Plots of the DSC measure of discrimination ability versus the calibrationmetric MCB visualize classifier performance across multiple competitors. Theproposed tools are illustrated in empirical examples from astrophysics,economics, and social science.

Evaluating Probabilistic Classifiers: The Triptych