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Equation 11 · Part 4 · Retrieval Is an Evidence System, Not a Memory

Symbol k

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

What this part means

the smoothing constant.

Its job in the formula

k occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

Where the article explains it

The simplest fusion, reciprocal rank fusion, ignores scores entirely and combines rank positions across retrievers R with a smoothing constant k : RRF(d)=∑r∈R1k+r(d)\mathrm{RRF}(d) = \sum_{r \in R} \frac{1}{k + r(d)}.

The passage around this formula

Hybrid wins because the failures are close to independent. The simplest fusion, reciprocal rank fusion, ignores scores entirely and combines rank positions across retrievers R with a smoothing constant k : RRF(d)=∑r∈R1k+r(d)\mathrm{RRF}(d) = \sum_{r \in R} \frac{1}{k + r(d)}. Cormack and colleagues introduced it and showed it consistently beat both the individual systems and Condorcet fusion [ 7 ] . Its virtue is that it needs no score normalisation, which matters because a BM25 score and a cosine similarity are not commensurable quantities. Its…

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A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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