Precision measures what share of a model’s positive predictions are correct. Recall measures what share of the real positive cases the model actually found. They answer different questions and usually trade off against each other: catching more real cases means accepting more false alarms. Choosing the right balance is a business decision, not a technical one.
Key takeaways
- Precision = TP ÷ (TP + FP): of what you flagged, how much was right?
- Recall = TP ÷ (TP + FN): of what existed, how much did you find?
- Raising one usually lowers the other, controlled by the decision threshold.
- Precision matters when false alarms are costly; recall matters when misses are costly.
- Both come from the confusion matrix and both ignore true negatives.
Precision and recall explained in simple terms
Fishing with a net. Precision asks: of everything in my net, how much is actually fish rather than weeds and boots? Recall asks: of all the fish in the lake, how many did I catch? A tiny, selective net has high precision and low recall. A huge net dragging the bottom has high recall and poor precision.
The formulas
| Metric | Formula | Plain English |
|---|---|---|
| Precision | TP ÷ (TP + FP) | Trustworthiness of positive predictions |
| Recall (sensitivity) | TP ÷ (TP + FN) | Coverage of the real positives |
| Specificity | TN ÷ (TN + FP) | Coverage of the real negatives |
A worked example
A model screens 1,000 CVs for a role; 100 candidates are genuinely qualified. It flags 120 CVs, of which 80 are genuinely qualified.
- TP = 80, FP = 40, FN = 20
- Precision = 80 ÷ 120 = 67%: two thirds of shortlisted candidates are worth interviewing.
- Recall = 80 ÷ 100 = 80%: four fifths of qualified candidates were found.
Twenty qualified candidates were missed, and recruiters will waste time on forty unsuitable ones. Whether to tune for fewer wasted interviews or fewer missed candidates depends on which is more costly to this organisation.
The trade-off in action
Lowering the decision threshold flags more cases:
| Threshold | Flagged | TP | FP | FN | Precision | Recall |
|---|---|---|---|---|---|---|
| 0.8 | 60 | 55 | 5 | 45 | 92% | 55% |
| 0.5 | 120 | 80 | 40 | 20 | 67% | 80% |
| 0.3 | 250 | 95 | 155 | 5 | 38% | 95% |
Same model, three very different behaviours. The model’s ranking ability has not changed; only where you draw the line has.
Which matters more?
| Situation | Prioritise | Reason |
|---|---|---|
| Cancer screening | Recall | Missing a case is far worse than a follow-up test |
| Spam filtering | Precision | A lost business email is worse than a spam message getting through |
| Fraud detection | Depends | Balance blocked customers against losses |
| Legal document discovery | Recall | Missing relevant evidence is unacceptable |
| Product recommendations | Precision | Irrelevant suggestions erode trust |
| Safety alerts | Recall | Missed hazards are the dangerous failure |
A useful framing: ask which error you would rather explain to a customer, a regulator or a court.
Beyond a single threshold
A single precision and recall pair describes one operating point. To judge the model itself:
- Precision-recall curve: plots the trade-off across all thresholds.
- PR-AUC: the area under that curve, the preferred summary when positives are rare.
- ROC-AUC: measures ranking ability, but can look flattering with severe imbalance.
- F1 score: a single number balancing the two at one threshold.
Multi-class averaging
With several classes, precision and recall are computed per class and then averaged:
| Method | How it averages | When to use |
|---|---|---|
| Macro | Unweighted mean across classes | Rare classes matter equally |
| Weighted | Weighted by class frequency | Reflects overall performance |
| Micro | Pools all TP, FP and FN | Equivalent to accuracy in single-label tasks |
Report macro averages when minority classes matter, which is usually the case in business problems.
Practical guidance
- Always report both, plus the counts behind them.
- State the threshold used; a metric without one is incomplete.
- Choose the operating point from error costs, not from the default 0.5.
- Check precision and recall separately for key subgroups to detect bias.
- Re-check after deployment, since class balance drifts.
Limitations
- Neither accounts for true negatives.
- Both depend on the chosen threshold.
- Precision is unstable when very few items are flagged.
- They say nothing about how confident or calibrated predictions are.