f1 score
**F1 score** is the **harmonic mean of precision and recall** — balancing quality and coverage in a single metric, widely used when both precision and recall matter equally.
**What Is F1 Score?**
- **Definition**: Harmonic mean of precision and recall.
- **Formula**: F1 = 2 × (Precision × Recall) / (Precision + Recall).
- **Range**: 0 (worst) to 1 (perfect).
**Why Harmonic Mean?**
- **Penalizes Imbalance**: Low precision or recall significantly reduces F1.
- **Balanced**: Requires both precision and recall to be high.
- **Example**: P=1.0, R=0.1 → F1=0.18 (not 0.55 like arithmetic mean).
**F1 vs. Arithmetic Mean**
**Arithmetic Mean**: (P + R) / 2 = (1.0 + 0.1) / 2 = 0.55.
**Harmonic Mean (F1)**: 2PR/(P+R) = 2×1.0×0.1/(1.0+0.1) = 0.18.
**Harmonic mean penalizes imbalance more**.
**When to Use F1**
**Good For**: Binary classification, information retrieval, when precision and recall equally important.
**Not Ideal For**: When precision and recall have different importance (use F-beta instead).
**F-Beta Score**: Generalization allowing different precision/recall weights.
- **F2**: Weights recall 2× more than precision.
- **F0.5**: Weights precision 2× more than recall.
**F1@K**: F1 score computed on top-K results.
**Limitations**
- **Binary**: Doesn't handle graded relevance.
- **Equal Weighting**: Assumes precision and recall equally important.
- **Ignores True Negatives**: Only considers positives.
**Applications**: Classification evaluation, information retrieval, search evaluation, any precision-recall trade-off.
**Tools**: scikit-learn, standard in ML libraries.
F1 score is **the standard for balanced evaluation** — by harmonically combining precision and recall, F1 provides a single metric that requires both quality and coverage to be high.