For a binary classifier, classification precision is , the fraction of predicted positives that are correct, while classification recall is , the fraction of actual positives recovered. If a search returns ten items, six relevant, from a collection containing fifteen relevant items, precision is and recall is . Raising a decision threshold often trades recall for precision, traced by a precision-recall curve, but precision need not improve at every threshold. Zero denominators require an explicit reporting convention. Both measures depend on which class is called positive; precision also depends strongly on prevalence.
A plot of classification precision against classification recall as a threshold changes. An uninformative ranking has expected precision equal to the positive prevalence. Comparisons should retain the same evaluation population or explicitly account for changed prevalence.
The fraction of genuinely positive cases recovered by a classifier. The denominator counts all reference-positive cases, , rather than positive predictions. In a diagnostic setting this is diagnostic sensitivity.
The fraction of predicted positives that are genuinely positive. It depends on prevalence as well as the true positive rate and false positive rate.
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Precision and recall are two important metrics used to evaluate the performance of classification models, particularly in settings where the classes are imbalanced or when the cost of false positives and false negatives differs significantly. ### Precision - **Definition**: Precision is the ratio of true positive predictions to the total number of positive predictions made by the model. It answers the question: "Of all the instances that were predicted as positive, how many were actually positive?