What Is BM25?

🧩 The three quantities, and what the two parameters do to them

A BM25 score is a sum with one addend per query term, and each addend multiplies two factors together. The first is an inverse document frequency weight, which rises as fewer documents in the collection contain the term: a term present in almost every document contributes almost nothing, and a rare one carries most of the score. The second is a saturating function of how often the term occurs in this document, divided by a correction for the document's length. A query term the document does not contain adds zero, and a document is never penalised for containing something the query did not ask about.

Saturation is the property that separates BM25 from counting occurrences, and it is the part most often described wrongly. The frequency factor has the shape of a quantity divided by itself plus a constant: it climbs steeply over the first few occurrences and then flattens, approaching a ceiling however many more arrive. A document mentioning a term forty times scores above one mentioning it four times, but only slightly, and never ten times as high. The parameter written k1 sets how fast that flattening happens — a low value collapses towards a presence-or-absence test after the first occurrence, a high value keeps the response closer to a straight count.

Length normalisation is the second parameter and it settles a different question: whether a long document is relevant or merely large. The correction divides by the document's length relative to the average length across the collection, scaled by a parameter written b. At b = 0 length is ignored entirely and long documents accumulate score simply by containing more words; at b = 1 the correction applies in full, and a document twice the average length has to repeat a term proportionally more often to match what a shorter neighbour scores. Implementations commonly ship k1 near 1.2 and b near 0.75. Both are tuning values rather than constants of the method, and the pair that suits a collection is found by measuring on it.

Two things follow from that list, and both surprise readers who expect a score to be a property of a document. A BM25 score depends on the collection, because two of the quantities it reads are collection statistics rather than document ones — so the same document and the same query return a different number once unrelated documents are indexed, and a threshold tuned on one corpus means nothing on another. And the scores are not calibrated: they are unbounded above and dependable only for ordering within one query's results, never for comparison between queries.

🗃️ How the Registry classifies a keyword ranking task

Ranking a documentation corpus against a keyword query is filed as information retrieval in this registry's classification, and the reason is structural rather than editorial: a ranking function reorders a set that already existed and adds no member to it. Every document that could appear in the result was in the collection before the query was written, which is the property this class is defined by.

The Registry's canonical brief for this entry is filed as: Rank a documentation corpus against a keyword query using term frequency and document length normalisation. Submitted for assessment it is classified as Information retrieval, and its wording is hashed once — to 8c3f7013a116e7c0…, the first sixteen of sixty-four hexadecimal characters — with the wording itself never stored. The hash is what the derivation reads. That class's own page is /tasks/retrieval.

Classification is one of three inputs. The other two are the configuration submitted with the task, and the permanent chart derived from that configuration — fixed by the model name, the training cutoff and the temperature alone, and never reading the task at all. The same ascendant, ruling planet and harmony therefore appear on every assessment a given configuration receives, whatever it was asked to do. The derivation is published in full at /method.

❓ Questions about bm25

What is BM25?

BM25 is a ranking function that scores a document against a keyword query from three quantities: how often each query term occurs in the document, how many documents in the collection contain that term, and the length of the document relative to the collection average. It is the default lexical ranking in several widely used search engines.

What does the name Okapi BM25 mean?

BM stands for best matching and 25 identifies the variant, one of a numbered series of weighting functions developed in the same line of work. Okapi was the retrieval system in which the function was first implemented, and the name stayed attached to it.

What do the parameters k1 and b control?

k1 controls how quickly the contribution of a term saturates as it occurs more often in one document. b controls how strongly a document longer than the collection average is discounted: at zero the length is ignored, at one the correction is applied in full.

Why does the same document score differently after new documents are indexed?

Because two of the quantities in the formula belong to the collection rather than to the document: how many documents contain each query term, and the average document length. Indexing more documents changes both, so scores drift even when neither the document nor the query has changed.

Is BM25 obsolete now that vector retrieval exists?

The two rank on different evidence. BM25 matches terms that are literally present, which is what an identifier, a code or a rare name requires; vector retrieval matches positions in an embedding space, which is what a paraphrase requires. Systems that need both commonly run both and fuse the results rather than replacing one with the other.