Relevance and BM25medium3-5 years

Two documents both mention `kafka`: one five times, one fifty times. Under BM25's default `k1 = 1.2`, would the fifty-mention document score roughly ten times higher on that term? Walk through why or why not.

No — BM25's term-frequency component saturates, so it does not scale linearly with raw mention count the way naive tf × idf would. In the formula f(t,D)·(k1+1) / (f(t,D) + k1·(length factor)), both the numerator and part of the denominator grow with f(t,D), so the ratio approaches a ceiling rather than climbing without bound. Going from five to fifty mentions moves the score noticeably less than tenfold — the lesson's own framing is that "the fiftieth mention adds almost nothing" once term frequency is already large relative to k1. This is deliberately why keyword-stuffing a document with a term stopped being an effective way to win rankings.

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