Two questions
Precision and recall answer different questions about the same predictions.
- Precision asks of everything I flagged as positive, how much was right. It divides true positives by true positives plus false positives.
- Recall asks of everything that was truly positive, how much did I catch. It divides true positives by true positives plus false negatives.
The tension
The two usually trade off. Lowering the decision threshold flags more cases, which catches more true positives and raises recall, but also pulls in more false positives and drops precision. Raising the threshold does the reverse.
Choosing which matters
- Favor recall when missing a positive is expensive, like disease screening or fraud alerts.
- Favor precision when a false alarm is expensive, like flagging email as spam or banning accounts.
Neither is universally better. The right balance comes from the cost of each error type in your setting.
Key idea
Precision measures how trustworthy positive predictions are while recall measures how many true positives are caught, and the decision threshold trades one against the other.