f1 score

F1 score collapses precision and recall into a single number using the harmonic mean rather than the ordinary average, and the choice of harmonic mean over arithmetic mean is not a minor technicality — it's the entire point. A model scoring 1.0 precision and 0.1 recall would average to 0.55 under a simple arithmetic mean, which looks like a reasonably competent model; the harmonic mean of the same two numbers comes out to 0.18, because harmonic means are dominated by whichever input is smallest, correctly flagging that a model which only ever makes one confident, correct prediction while missing 90% of the real positives is not a 55%-good model by any reasonable standard.

The harmonic mean's behavior is easiest to see by lining up a few models side by side rather than computing one score in isolation. A model with precision 0.9 and recall 0.9 scores an F1 of exactly 0.9 — when the two inputs are already balanced, the harmonic mean barely differs from a simple average; a model with precision 0.9 and recall 0.5 drops to an F1 of 0.64, pulled sharply toward the weaker number rather than splitting the difference at 0.7; and the earlier precision 1.0, recall 0.1 case collapses all the way to 0.18. The pattern is consistent: F1 punishes any model that's lopsided between the two metrics, no matter which one happens to be strong.

F1 treats precision and recall as equally important, which is frequently the wrong assumption, and the F-beta family exists specifically to fix that. F2 weights recall twice as heavily as precision, matching the cancer-screening priority described under recall, where missing a real case matters far more than one extra false alarm; F0.5 weights precision twice as heavily, matching the spam-filter priority described under classifier-precision, where deleting a real email is the costly mistake. Choosing plain F1 by default, without checking whether the underlying domain actually values precision and recall equally, is a common and easily avoided mistake — the beta parameter exists precisely so the metric can be tuned to match the real cost of each kind of error rather than assuming they're always the same.

F1 ignores true negatives entirely, which makes it the right metric for exactly the same situations where plain accuracy misleads. A dataset with 99% negative examples and 1% positive examples can produce a model with 99% accuracy by predicting "negative" every time, catching zero of the actual positive cases — F1 for that model collapses to 0 because recall is 0, correctly exposing the failure that accuracy alone hides. This is why F1 is standard in information retrieval, rare-event detection, and any classification task with a severely imbalanced class split, situations where a model that never guesses the minority class can otherwise look deceptively strong.

The reason F1 specifically uses the harmonic mean rather than any other way of combining two numbers is that it's the one averaging method that refuses to reward a model for being excellent at one thing while failing at the other — which is also exactly why it became the standard single-number leaderboard metric whenever a task genuinely requires a classifier to be good at both catching real positives and not crying wolf, rather than letting either half of the job compensate for failure at the other.