$$\mathrm{avgdl}$$

Equation 13 · AI Agents & Systems

From BM25 to Agentic Retrieval: A History of Retrieval-Augmented Generation

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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 advance over a raw term-frequency-times-IDF score: a term’s contribution grows quickly at first and then flattens, so a document that happens to repeat a query word fifty times does not dominate one that uses it three times in the right place. Decades later, this same function remains the default first-stage ranking method built into widely used open-source search engines, which is a strong…

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