Inverse relation of precision and recall

Precision = TP/(TP + FP): of the records predicted positive, the fraction that are really positive (exactness). Recall = TP/(TP + FN): of all real positives, the fraction the classifier finds (completeness).

Inverse relationship

For a given classifier, improving one of them usually reduces the other, because both depend on the decision threshold.

• Lower the threshold (predict "positive" more readily): more real positives are found, so FN falls and recall rises. But more negatives are also wrongly accepted, so FP rises and precision falls.
• Raise the threshold (predict "positive" only when very sure): FP falls, so precision rises, but many positives are missed, so FN rises and recall falls.
• Extreme cases: predicting every record positive gives recall = 100% but low precision; predicting only one very certain record positive gives precision = 100% but very low recall.

Example: 100 real positives in 1000 records.

Because of this trade-off, the two are combined into the F-measure (harmonic mean), F₁ = 2·P·R/(P + R), and shown in a precision-recall curve. Each application chooses its own balance: cancer screening and fraud detection favour high recall, while spam filtering favours high precision (so that important mail is not wrongly blocked).