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The term frequency component is where BM25 gets clever. Rather than counting raw occurrences, it applies saturation — the score grows quickly at first but flattens out as frequency increases. A term appearing 5 times contributes much more than a term appearing once, but a term appearing 50 times contributes barely more than one appearing 20 times. This is controlled by the parameter k₁ (typically set between 1.2 and 2.0). Set it low and the saturation kicks in fast; set it high and raw frequency matters more. This single design choice is what makes BM25 resistant to keyword stuffing — repeating a word a hundred times in a document won’t game the score.
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