How the ROC curve maps classification thresholds
A binary classifier typically outputs a probability or score, not a hard decision. The ROC curve plots how the true positive rate and false positive rate change as you vary the decision threshold from 0 to 1. At threshold 0, every example is predicted positive: TPR is 100%, FPR is 100%. At threshold 1, every example is negative: both rates are 0%. The curve between them traces the performance frontier available to the model across all threshold choices. A classifier that separates the classes cleanly pushes the curve toward the top-left corner; one that gives random scores produces a diagonal line.
AUC as a single summary metric
The area under the ROC curve (AUC) compresses the entire threshold frontier into one number between 0 and 1. AUC of 0.5 means the model is random. AUC of 1.0 means the model achieves perfect separation at some threshold. The metric is threshold-agnostic and useful when you do not yet know which operating point your application demands. Unlike accuracy, AUC is immune to class imbalance: a model trained on data that is 99% negative cannot game AUC by predicting all negatives. This property makes ROC/AUC the standard tool for initial model evaluation and comparison.