F2score

The F2 score is a member of the F-beta family of metrics used to evaluate binary classifiers by combining precision and recall into a single number. Given a confusion matrix, precision P = TP/(TP+FP) and recall R = TP/(TP+FN), the F_beta score is defined as F_beta = (1 + beta^2) * (P * R) / (beta^2 * P + R).

When beta = 1, F_beta reduces to F1, the harmonic mean of precision and recall. For F2, beta^2 equals 4, so F2 = 5PR/(4P + R). This form places more emphasis on recall than precision, meaning the score increases more with improvements in the model’s ability to identify positive cases than with equivalent gains in precision.

F2 is commonly used in domains where missing positive instances is particularly costly. Examples include medical screening, where failing to detect a disease can have serious consequences, and other safety- or fraud-related tasks where false negatives carry heavier penalties than false positives. Like other F-beta scores, it is threshold-dependent and reflects the trade-off between precision and recall at a chosen decision threshold.

Limitations include sensitivity to class prevalence and the chosen threshold, and the fact that F2 condenses information into a single number that may obscure underlying errors. It should be interpreted alongside the confusion matrix, precision-recall curves, or alternative metrics (such as ROC AUC) to gain a fuller view of model performance.