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…field came to call BM25 — “Best Match 25,” after its position in a numbered sequence of variants the group had tried. Written in its now-standard form, a document D scores against a query Q as $\mathrm{score}(D, Q) = \sum_{q_i \in Q} \mathrm{IDF}(q_i) \cdot \frac{f(q_i, D) \cdot (k_1 + 1)}{f(q_i, D) + k_1 \cdot \left(1 - b + b \cdot \dfrac{|D|}{\mathrm{avgdl}}\right)}$. where f($q_i$, D) is the frequency of query term $q_i$ in D , |D| is the document’s length, $\mathrm{avgdl}$ is the average document length in the collection, and $k_1$ and b are tuned constants controlling term-frequency saturation and length normalization respectively. The saturation term is the substantive…

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