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Equation 8 · Part 5 · What Actually Happens Between a Query and an Answer in RAG

=

RRF(d)=∑r∈R1k+r(d)\mathrm{RRF}(d) = \sum_{r \in R} \frac{1}{k + r(d)}
=

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

Reciprocal rank fusion avoids the currency problem by discarding scores altogether and combining rank positions instead. For a document d and a set of ranked result lists R , with r(d) the rank of d in a given list and a smoothing constant k : RRF(d)=∑r∈R1k+r(d)\mathrm{RRF}(d) = \sum_{r \in R} \frac{1}{k + r(d)}. Cormack, Clarke, and Buettcher introduced the method and reported that it consistently outperformed both the individual ranked lists and a Condorcet-style fusion baseline, with the specific virtue that it requires no score normalisation across systems with incompatible scoring functions [ 9 ] . That virtue is also its limitation: two documents ranked first in their respective lists count identically toward the fused score…

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.