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The weighted harmonic mean of precision and recall, beta being what recall is worth relative to precision.

public static double Score(ConfusionMatrix cm, double beta, Averaging average = Averaging.Binary, int posLabel = 1, ZeroDivision zeroDivision = ZeroDivision.Zero)
public static double Score(ReadOnlySpan<int> yTrue, ReadOnlySpan<int> yPred, double beta, Averaging average = Averaging.Binary, int posLabel = 1, ZeroDivision zeroDivision = ZeroDivision.Zero, ReadOnlySpan<int> labels = default, ReadOnlySpan<double> sampleWeight = default)

Parameters — cm is a matrix already counted, or pass yTrue and yPred. beta is the weight of recall relative to precision and must be finite and non-negative. average reduces the per-class scores, posLabel is the class reported under Averaging.Binary, zeroDivision decides an undefined score, labels fixes the label set and its order, and sampleWeight weights the samples.

Returns — double in [0, 1], larger meaning better.

Exceptions — ArgumentOutOfRangeException when beta is negative or NaN — positive infinity scores the recall, as fbeta_score does (#1466) — and when beta is finite but its square overflows, past √double.MaxValue ≈ 1.3407807929942596e154, where fbeta_score's beta ** 2 raises OverflowError (#1540); ArgumentNullException when cm is null; ArgumentException when Averaging.Binary meets more than two classes, or two without posLabel — an absent positive class takes the zeroDivision value instead, and labels is not read on a binary target — or sampleWeight holds a non-finite value or is zero throughout; UndefinedMetricException when the metric is undefined and zeroDivision is ZeroDivision.Throw.

Example — the same filter scored twice: once as if a missed spam cost twice a false alarm, once the other way round.

using Lodestar.Metrics;

int[] yTrue = [1, 1, 1, 1, 0, 0, 0, 0];
int[] yPred = [1, 1, 0, 0, 1, 0, 0, 0];

double recallHeavy = FBeta.Score(yTrue, yPred, 2.0);        // => 0.5263…
double precisionHeavy = FBeta.Score(yTrue, yPred, 0.5);     // => 0.625

Remarks — beta has a reading that makes it easy to choose: it is how many times more you care about recall than about precision. beta = 2 is the standard "a miss is worse than a false alarm" setting — screening for a disease, catching fraud — and beta = 0.5 the standard opposite, where a false alarm is the expensive one, as in a filter that deletes mail. beta = 1 is exactly F1, and F1.Score is the same call with the argument spelled into the name.

The two numbers above are the whole idea in one line: the recall-heavy score is below F1 because this filter's recall is its weak side, and the precision-heavy score is above it.

Two traps. beta = 0 is legal and collapses the metric to plain precision, which is a surprising amount of nothing to get from a call that looks like it is measuring both; if that is what you want, say Precision.Score so the reader knows. And scikit-learn accepts beta = inf — the limit that collapses to recall — where this refuses it with ArgumentOutOfRangeException; use Recall.Score.

Applies to — net10.0, netstandard2.0.

See also — FBeta.PerClass, F1.Score, Precision.Score, Recall.Score, the Python equivalence table.