0032 fbeta substitutes tp predicted and support algebraically

0032 — FScore substitutes tp/predicted/support algebraically, not via precision and recall

Status: accepted · Date: 2026-08-14

Context

The textbook F-beta formula is (1 + beta^2) * P * R / (beta^2 * P + R) for precision P and recall R. The obvious implementation computes P and R first — each already available as Precision.Score / Recall.Score — and substitutes. scikit-learn's fbeta_score does not do this: it derives F-beta from the raw tp/predicted/support counts directly. Substituting P = tp/predicted and R = tp/support into the textbook formula and cancelling tp leaves score = (1 + beta^2) * tp / (predicted + beta^2 * support) — algebraically the same value when predicted and support are both nonzero, but not the same computation.

Going through P and R first applies Prf.Divide's zero-division policy up to three times for one F-beta value: once for P, once for R, and once more for the combined denominator, which can itself look like zero even when the uncombined one is not. (The inline version of this claim read "twice — once for each of them, and once more for a denominator", counting two where it then listed three; this sweep re-counted against Prf.FScore and corrected it to three, the same kind of correction docs/decisions/0018 records for its 4079→4088 figure.) It also fails to reproduce scikit-learn whenever tp is zero but predicted or support is not: the textbook route replaces an undefined P or R with the zero-division policy's value (0, 1 or NaN) before combining, while scikit-learn — and the direct-substitution formula — still returns a well-defined 0 from the combined fraction, since the numerator (1 + beta^2) * 0 is exactly 0 and the denominator is not.

Decision

Prf.FScore computes (1 + beta^2) * tp / (predicted + beta^2 * support) directly from the three raw counts, routed through the single Prf.Divide call the substituted formula needs — never through Precision/Recall's own already-divided values.

Consequences

• Prf.FScore's comment carries a pointer here instead of restating the derivation and the divergence it prevents.
• Verified by PrfOracleTests.Matches_sklearn_precision_recall_fscore_support, whose corpus fbeta field spans multiple beta values including the tp == 0 edge this derivation exists for, compared at MetricsCorpus.Tolerance (1e-9).