Precision

Precision, or positive predictive value, is TP / (TP + FP): conditional on the model saying "positive", the probability that it is right. It is undefined when the model makes no positive predictions, a case scikit-learn handles with its zero_division parameter. False negatives do not enter the formula at all, so a model that flags only its single most certain case can score 100% precision while missing nearly everything; precision is meaningless without recall or a fixed operating point beside it. In ranking and retrieval it is usually reported at a cut-off, precision@k, and averaged over recall levels as average precision (AP); object detection reports mean AP over classes, with COCO additionally averaging over intersection-over-union thresholds from 0.5 to 0.95.

Unlike recall, precision depends directly on prevalence. By Bayes' rule, PPV = (sensitivity × prevalence) / (sensitivity × prevalence + (1 − specificity) × (1 − prevalence)). A detector with 99% sensitivity and 99% specificity applied where only 0.1% of events are malicious has a precision of about 9%: roughly ten false alarms for every true one. This base-rate effect is the arithmetic behind alert fatigue in security operations and false-positive screening results in medicine, and it means precision measured on a balanced or enriched test set overstates what will be seen in production unless it is reweighted to the real class mix.

Precision is controlled through the decision threshold. Raising the threshold typically raises precision, but not strictly monotonically (it can dip when a few high-scoring negatives remain), whereas recall can only stay the same or fall. The precision-recall curve traces this trade-off; under heavy class imbalance it is more informative than the ROC curve, because the false positive rate stays deceptively small when negatives vastly outnumber positives (Davis & Goadrich, 2006; Saito & Rehmsmeier, 2015). Operational requirements are therefore often phrased as "maximum recall subject to precision of at least X".

The word collides with other meanings. In metrology (ISO 5725) precision means the closeness of repeated measurements to each other, a property of variance rather than of correctness; in numerics it refers to floating-point formats such as FP16 or BF16 used for model weights. In retrieval-augmented generation, "context precision" measures how much of the retrieved material is relevant, a retrieval metric distinct from the precision of the final answer.