F1 classification score:
formula and worked example

Why a single balanced score exists

Precision and recall pull in opposite directions. A classifier that flags only the cases it is most sure about will have high precision and poor recall; one that flags everything will have perfect recall and poor precision. Comparing models on one of these alone invites cheating by moving the threshold.

The F1 score ties the two together. It is high only when both are high, which makes it a common headline metric for tasks with rare positives, such as spam filtering, defect detection or entity extraction, where overall accuracy is dominated by the easy negatives.

It is not the only way to combine them, and it quietly assumes precision and recall matter equally. When they do not, a weighted variant is more honest.

A short history explains the choice of mean. In information retrieval the early question was how to rate a search system that returns a list: precision rewards a clean list and recall rewards a complete one. The harmonic mean was adopted because it behaves sensibly at the extremes, giving no credit to a system that returns the whole database just to reach perfect recall.

Formula and inputs

• Precision: of everything the model flagged, the share that was correct, true positives divided by (true positives + false positives).
• Recall: of everything that was really positive, the share the model found, true positives divided by (true positives + false negatives).

The expression is the harmonic mean of the two. In terms of raw counts it simplifies to 2 x TP divided by (2 x TP + FP + FN), which is a handy cross-check if you have the confusion matrix and not the ratios.

Be careful about which class counts as positive. In a binary problem F1 is normally computed for the minority or target class, and the score for the other class will be different. Say which one you report, or the figure cannot be reproduced.

Worked example: precision 0.8, recall 0.6

A document classifier flags items as relevant. Of the items it flags, 80% are relevant, and it finds 60% of all relevant items.

1. 1Multiply precision and recall: 0.8 x 0.6 = 0.48.
2. 2Double it: 2 x 0.48 = 0.96.
3. 3Add the two inputs: 0.8 + 0.6 = 1.4.
4. 4Divide: 0.96 / 1.4 = 0.685714, about 0.686.

What 0.686 tells you

A score of 0.686 sits between the two inputs and closer to recall, the weaker one. It tells you the model is moderately balanced but would benefit most from finding more of the real positives. An F1 of 1 would mean perfect precision and recall, and 0 means one of them is zero.

There is no universal good value. What passes for strong depends on how hard the task is, how noisy the labels are and what a human annotator would score on the same data. A more useful habit is to compare against a simple baseline and against the previous version of the model on the same test set.

Look also at the pair behind the score. An F1 of 0.686 might come from 0.8 and 0.6, or from 0.69 and 0.68; the first model flags carefully and misses a lot, while the second is evenly balanced, and they behave very differently in use.

If the score will be reported to non-specialists, pair it with one sentence of consequence: out of every 100 items that matter, this model finds about 60, and about 20 of every 100 items it flags are noise. That is more persuasive than any decimal.

Raising precision while recall stays put

Lifting precision from 0.8 to 0.88 moves F1 from 0.6857 to 0.7135, a gain of about 0.028 for a precision rise of 0.08. The score responds less than one-for-one because recall is the bottleneck. Moving recall from 0.6 to 0.66 instead would give an F1 of about 0.723, a bigger improvement, showing that the weaker side is where effort pays more.

Where F1 misleads

• Treating it as a measure of overall quality. It ignores true negatives, so a model can score well on F1 while performing poorly on the negative class.
• Averaging F1 across classes without saying how. Macro averaging treats rare and common classes equally, while micro averaging weights by frequency, and they can give very different answers.
• Using it when the costs of false positives and false negatives are clearly unequal. A weighted F-beta score or a cost-based metric fits better.
• Comparing scores obtained on different datasets or class mixes as though they were on one scale.
• Reporting a single score without the threshold it was computed at.

Choosing and tuning with F1

Suppose two spam filters both reach 0.69 F1. Filter A has precision 0.95 and recall 0.54; filter B has precision 0.55 and recall 0.93. For an inbox, where deleting a real message is painful, A may be preferred. For a moderation queue where missed abuse is costly, B may be better. The same F1 hides opposite behaviours, which is why teams often tune the threshold on a validation set and then report the full precision-recall pair.