Numerator: 1

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 : $\mathrm{RRF}(d) = \sum_{r \in R} \frac{1}{k + r(d)}$. 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 cost is that it discards score magnitude. Bruch and colleagues analysed fusion functions directly and found convex combination of normalised scores outperformed reciprocal rank fusion both in-domain…

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