BM25 Ranking: How Search Engines Score Documents

Query Terms

BM25 Parameters

Term-frequency saturation k₁ 1.50

Length normalization b 0.75

Top Result

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Corpus size N

Avg doc length

How it works

BM25 (Okapi BM25) is the probabilistic ranking function behind most classical search engines and the "baseline" every neural ranker is measured against. For query Q with terms t and document D:

score(D,Q) = Σ_t IDF(t) · f(t,D)·(k1+1)
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                    f(t,D) + k1·(1 − b + b·|D|/avgdl)

IDF(t) = ln( 1 + (N − n(t) + 0.5) / (n(t) + 0.5) )

f(t,D) — raw term frequency of t inside D.
IDF(t) — rarer terms across the N-document corpus score higher; n(t) is how many documents contain t.
k1 — controls term-frequency saturation: at k1=0 a term only matters if present at all (binary); high k1 lets repeated occurrences keep adding score almost linearly.
b — controls length normalization: at b=0 document length is ignored; at b=1 long documents are penalized in full proportion to how much longer than average they are, so they cannot win purely by repeating words.

Click the term chips to build a query, then drag k1 and b — the corpus of 18 synthetic documents re-ranks itself live: bar height and glow track the BM25 score, and the tallest bar is the engine's #1 hit for that query.

Higher BM25 score → taller, brighter bar Score ≈ 0 for this query

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