Recall

Recall (also called sensitivity) answers: "of everything that was actually positive, how much did the model actually catch?" — the right metric when a false negative is the costly, dangerous error.

Formula

Worked Example

Using the same confusion matrix (\(TP=15, FN=5\)):

Of the 20 actual fraud cases, the model caught 15 — 75% of all real fraud, missing the remaining 5.

from sklearn.metrics import recall_score

y_true = [1]*20 + [0]*80
y_pred = [1]*15 + [0]*5 + [1]*10 + [0]*70

print(recall_score(y_true, y_pred))   # 0.75

When Recall Is the Metric That Matters Most

High recall matters most when a false negative is dangerous or costly: missing an actual cancer diagnosis, letting real fraud through undetected, failing to flag a genuinely defective product before shipping. In all these cases, missing a true positive has severe consequences — worth tolerating more false alarms to catch nearly every real case.

Recall Can Be Trivially Maximized — A Genuine Trap

# Predicting "positive" for EVERYTHING achieves perfect recall...
y_pred_naive = [1] * 100
print(recall_score(y_true, y_pred_naive))   # 1.0 -- perfect, but useless

from sklearn.metrics import precision_score
print(precision_score(y_true, y_pred_naive))   # 0.2 -- terrible precision reveals the problem

This is exactly why recall is almost never reported alone — a model that predicts "positive" for everything achieves perfect recall while being practically worthless, which is only revealed by also checking precision.

Practical Use Cases

• Medical screening — missing a real disease case (false negative) is typically far worse than a false alarm requiring further, harmless testing
• Security and fraud detection — missing genuine fraud is usually costlier than investigating a false alarm

Common Mistakes

• Reporting recall alone without precision, hiding a model that simply over-predicts the positive class to inflate this one number.
• Confusing recall with precision — recall only considers actual positives, ignoring how many predicted positives were wrong.

Interview Relevance

Q: "Why would a cancer-screening model prioritize recall over precision?" A false negative (missing an actual cancer case) can be life-threatening, while a false positive typically only leads to additional, safer follow-up testing — the asymmetric cost of the two error types makes recall the priority, even at some expense to precision.

Practice Question

Given \(TP=90, FN=10\), compute recall by hand. Now suppose \(FN=90, TP=10\) instead — recompute and interpret the dramatic difference.

Related ML Notes

• Precision
• F1-Score
• ROC-AUC