📏 F1-score

F1-score#

The harmonic mean of precision and recall.

Important

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What it is#

The F1-score combines precision and recall into one number by taking their harmonic mean:

\[F_1 = 2\cdot\frac{P \cdot R}{P + R} = \frac{2\,TP}{2\,TP + FP + FN}.\]

It ranges from 0 to 1, and is high only when both precision and recall are high.

Why harmonic#

Using the harmonic mean makes F1 penalize lopsided models — a classifier with 0.95 precision but 0.20 recall scores a low F1, unlike accuracy or a plain average. This makes F1 far more informative than accuracy on imbalanced data, and it deliberately ignores true negatives.

Its variants#

For multiclass problems, F1 is aggregated with micro, macro or weighted averaging; the general Fβ score tilts the balance toward recall (β > 1) or precision (β < 1) when the two errors carry different costs.

Theme: Classification & Averaging Metrics · All terminology

Hint

Mind map — connected ideas

Harmonic Mean · Precision (a.k.a. Positive Predictive Value, PPV) · Average Precision (AP) · Accuracy · Macro Averaging · Micro Averaging

Hint

More in Classification & Averaging Metrics

Accuracy · AUC (Area Under the Curve) · Average Precision (AP) · Binary Classification · Classification Probability · Discriminatory Power · Gini Coefficient · Harmonic Mean · Log Loss (also called Logarithmic Loss or Cross-Entropy Loss) · Macro AUC · Macro AUROC (Macro-Averaged AUROC) · Macro Averaging · Macro F1 · Macro Precision