Precision vs recall vs F1 vs AUC

Precision = TP/(TP+FP): "of what I predicted positive, how many are right". Recall = TP/(TP+FN): "of all positives, how many did I find". F1 = harmonic mean of precision/recall; balances when classes are roughly balanced. ROC-AUC = area under TPR vs FPR curve: threshold-invariant, works well at balanced classes. PR-AUC = area under precision vs recall curve: MUCH better at imbalanced classes. Decision rule: pick metric by the cost asymmetry. Search for cancer: high recall, accept low precision. Spam filter with user friction cost: high precision, accept missing some spam. Ranker / retrieval: NDCG@k with graded relevance. Senior nuance: F1 is a single-threshold summary; pick continuous metrics when you sweep thresholds. For imbalanced data, PR-AUC is the right answer. Production: track calibration (Brier, ECE) for probabilistic predictions.