Precision asks how many of your positive predictions were correct. Recall asks how many of the real positives you actually caught. Both put true positives on top; only the denominator changes.

Precision divides true positives by every case you flagged, so false positives hurt it. Recall divides true positives by every case that was truly positive, so misses hurt it. Neither metric counts true negatives, which is why both survive when negatives vastly outnumber positives.

// flagged 100 items, 80 were right; 200 real positives exist
const precision = 80 / 100; // 0.80
const recall = 80 / 200;    // 0.40

Reading them together stops a common trap. A model that flags one obvious case scores perfect precision and almost no recall. A model that flags everything scores perfect recall and terrible precision. Neither number means much alone, so quote both, plus how many predictions produced them.

A confusion matrix lays out predictions against actual labels, giving four counts for a binary classifier. Rows usually hold the true labels and columns hold the predictions, but check the axis order before reading someone else's matrix, because libraries differ.

• True positives: cases that were positive and you called them positive.
• True negatives: cases that were negative and you called them negative.
• False positives: negatives you flagged anyway, the false alarms.
• False negatives: positives you let through, the misses.

The raw counts matter more than any single score. They show which error dominates, and they show how lopsided the classes are. A model can look strong while its false negative cell holds most of the positives. Every headline metric is built from these four numbers, so start here when a result looks odd. A quick sanity check: the four cells must sum to your evaluation set size.

F1 is the harmonic mean of precision and recall, computed as two times their product divided by their sum. A plain average would let strong precision cover for weak recall. The harmonic mean will not; it sits close to the smaller of the two numbers.

Precision 1.0 with recall 0.1 gives an F1 near 0.18, not 0.55. That gap is exactly what stops a model from scoring well by flagging one safe case.

F1 helps when you need one number to rank models or pick a cutoff, and the positive class is rare. It refuses to reward a model that games one side.

The cost is what it assumes. It weights precision and recall equally, which rarely matches real error costs, and it ignores true negatives entirely. When one side matters more, use F-beta, which lets you weight recall up or down.

Push for precision when acting on a wrong flag causes direct damage. A spam filter that buries a real invoice loses the user money. Auto-removing content or auto-blocking an account has the same shape: the false alarm is visible, immediate and hard to undo.

Recall wins when a miss is the expensive outcome and a false alarm is cheap to check. Disease screening is the classic case; a flagged patient gets a second test, but a missed tumor keeps growing. Security alerting and safety recalls follow the same logic.

The test that decides it is simple. Ask what happens after a positive prediction. If a human or a cheap second stage reviews every flag, push recall and accept noise. If the prediction acts on its own, protect precision, because nobody catches the mistake.

Sensitivity is recall under another name: of all the real positives, the share your model catches. Specificity is its mirror on the other class: of all the real negatives, the share you correctly leave alone. Medical and diagnostic work usually uses these two names.

A receiver operating characteristic (ROC) curve is built from exactly this pair. The vertical axis is sensitivity. The horizontal axis is one minus specificity, also called the false positive rate. Each point on the curve is one decision cutoff.

Knowing the pair keeps you honest. Raising sensitivity almost always lowers specificity, since catching more positives means flagging more negatives too. Quoting one alone hides that cost, which is how a screening test with 99% sensitivity can still drown a clinic in false alarms.

The receiver operating characteristic (ROC) curve traces one classifier across every possible decision cutoff. Each point pairs the true positive rate with the false positive rate at that cutoff. Sliding from a strict cutoff to a loose one walks you along the curve.

Read it by corner. The bottom left is flagging nothing, the top right is flagging everything, and both are useless. The diagonal line is guessing at random. A curve that bulges up and to the left is separating the classes well.

The practical use is choosing where to operate. Find the largest false positive rate your team can absorb, read up to the curve, and take the cutoff there. One caution: with very rare positives the curve can look great while most of your flags are still wrong.