F1 score

F1 is the harmonic mean of precision P and recall R: F1 = 2PR / (P + R), which in confusion-matrix terms is 2TP / (2TP + FP + FN). True negatives do not appear at all, which is why F1 suits retrieval and rare-class detection and why it says nothing about how well the negative class is handled. The general form Fβ = (1 + β²)PR / (β²P + R) weights recall β times as much as precision; F2 is common where misses are expensive and F0.5 where false alarms are. The measure descends from van Rijsbergen's effectiveness measure E in information retrieval (1979), of which F is the complement.

The harmonic mean is dominated by the smaller operand: P = 1.0 and R = 0.1 give F1 ≈ 0.18, whereas the arithmetic mean would be 0.55. For multiclass and multilabel problems the per-class scores must be aggregated, and the choice changes the number: macro-F1 averages per-class F1 equally (so rare classes count as much as common ones), micro-F1 pools TP, FP and FN across classes (and for single-label multiclass equals accuracy), weighted-F1 weights by class support. Even "macro-F1" has two definitions in the literature (the mean of per-class F1 versus the F1 of mean precision and mean recall), and they can differ noticeably (Opitz & Burst, 2019). When a class has no predicted and no true positives F1 is undefined; scikit-learn exposes this through its zero_division parameter.

F1 is threshold-dependent and not maximised at 0.5. Lipton, Elkan and Narayanaswamy (2014) showed that for calibrated probabilities the F1-optimal threshold equals half the achievable maximum F1, so a model capable of F1 = 0.6 should be thresholded near 0.3; the threshold is tuned on the validation set, never the test set. F1 is also non-decomposable: averaging per-fold or per-batch F1 is not the same as computing F1 on pooled counts (Forman & Scholz, 2010), and it cannot be optimised directly by per-example losses, so training typically uses cross-entropy with thresholding afterwards.

Critics note that F1 changes if the positive class is relabelled, depends on prevalence, and fixes an arbitrary equal weighting of the two error types; Hand and Christen (2018) argued it is ill-suited to comparing record-linkage methods, and the Matthews correlation coefficient is often recommended when both classes matter. Task-specific variants abound: entity-level F1 in named-entity recognition counts a prediction correct only with exact span and type, while SQuAD-style F1 measures token overlap between predicted and reference answers.