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The two retrievers fail in different directions, which is the entire justification for running both. Lexical retrieval, the BM25 family, scores documents by term overlap and fails on vocabulary mismatch: a query about “cannot log in” scores nothing against a document that says “authentication failure”. Dense retrieval, the family Karpukhin and colleagues established with a dual-encoder trained on question-passage pairs, embeds query and passage into a shared vector space and fails on precision, losing rare identifiers — part numbers, version strings, error codes — that carry little weight in a learned embedding but enormous discriminative value lexically; their dense retriever nonetheless reported nine to nineteen percentage points of absolute improvement in top-20 retrieval accuracy over a BM25 baseline on open-domain question answering, evidence that neither family dominates the other in general [ 2 ] . Fusing the two recovers most of each one’s strength. Reciprocal rank fusion, which Cormack and colleagues introduced and showed outperforming both individual rankers and a Condorcet-style combination, ignores raw scores entirely and combines rank positions across retrievers R with a smoothing constant k , $\mathrm{RRF}(d) = \sum_{r \in R} \frac{1}{k + r(d)}$. sidestepping the problem that a BM25 score and a cosine similarity are not directly comparable quantities [ 3 ] . A reranking stage — typically a cross-encoder scoring each retrieved candidate jointly with the query — can then sit downstream of the fused list and reorder it more precisely than either upstream retriever could alone.