Precision vs recall vs F1, finally clear
Two questions, two metrics, one tradeoff. Plus the class-imbalance trap that makes accuracy meaningless. Free one-page PDF.
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Every argument about classifier quality is secretly one of two questions. Precision: when the model raised an alarm, was it right? Recall: of all the real cases, how many did it catch? Get these two straight and the rest of the metric zoo falls into place.
The four outcomes
| predicted positive | predicted negative | |
|---|---|---|
| actually positive | TP · true positive | FN · missed one |
| actually negative | FP · false alarm | TN · true negative |
Precision
TP / (TP + FP): of my alarms, how many were real?
Optimize precision when false alarms are the expensive error. A spam filter with low precision sends real mail to the junk folder. Fraud review queues drown analysts when precision drops.
Recall
TP / (TP + FN): of the real ones, how many did I catch?
Optimize recall when a miss is the expensive error. Cancer screening, safety inspections, search: the false negative is what hurts.
F1
2PR / (P + R): the harmonic mean. It punishes imbalance between the two, so you cannot buy a good F1 by maxing one and ignoring the other. Use it when you need a single number and classes are skewed.
The threshold dial
Every classifier outputs a score; the threshold turns it into a yes/no.
- Raise it: precision up, recall down. Fewer, surer alarms.
- Lower it: recall up, precision down. Catch more, cry wolf more.
You rarely get both. The threshold decides which one you buy with the other.
The trap: 99% accurate, 100% useless
On data with 1% fraud, a model that always predicts "legit" scores 99% accuracy and catches zero fraud. Accuracy is blind to imbalance because the giant true-negative cell dominates it.
The fix: report precision and recall (or F1), never accuracy alone. And make "what is the class balance?" your first question about any classifier.
Frequently asked questions
- What is the difference between precision and recall?
- Precision asks: of everything I flagged positive, how much was actually positive? Recall asks: of everything that was actually positive, how much did I catch? Precision punishes false alarms, recall punishes misses.
- When should I use F1 instead of accuracy?
- Whenever classes are imbalanced, which is most real problems: fraud, churn, defects, disease. Accuracy rewards predicting the majority class; F1 combines precision and recall so a model that catches nothing cannot score well.
- What is a good F1 score?
- There is no universal threshold: it depends on the class balance and the cost of each error type. Compare against a baseline (random, or always-positive) and against the business cost of FP vs FN rather than chasing an absolute number.
- How does the decision threshold trade precision against recall?
- Raising the threshold makes the model pickier: fewer alarms, higher precision, lower recall. Lowering it catches more true cases but cries wolf more. Plot the precision-recall curve and pick the point that matches your error costs.
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