Precision and recall

Precision $=\frac{TP}{TP+FP}$: of everything flagged positive, how much really is? High precision means few false alarms.

Recall (sensitivity, true positive rate) $=\frac{TP}{TP+FN}$: of all real positives, how many did we find? High recall means few misses.

There is a trade-off controlled by the threshold: lowering it flags more items, raising recall and usually lowering precision. Which matters more depends on the cost of each error.

• Recall first: cancer screening, fraud detection, safety systems — missing a positive is very costly.
• Precision first: spam filtering, recommending content, legal discovery — false alarms are costly or annoying.