Reciprocal Rank Fusion (RRF)

Reciprocal Rank Fusion (RRF) is a lightweight algorithm for merging two or more ranked result lists into a single combined ranking. It is the standard glue in a hybrid search pipeline, where it fuses the output of a keyword retriever and a vector retriever. RRF's defining feature is that it ignores the raw relevance scores entirely and looks only at each document's rank in each list.

How the formula works

For every document, RRF sums 1 divided by (k + rank) across all the lists it appears in, where rank is its position in that list and k is a small constant (commonly 60) that softens the influence of top positions. A document that ranks near the top in several lists accumulates a high fused score; a document buried in every list scores low. Items appearing in multiple lists are naturally rewarded, while a single strong appearance still contributes.

Why rank instead of score

Different retrievers produce scores on incompatible scales: BM25 values are not comparable to cosine similarity values, and naively adding them lets one system dominate. By collapsing everything to rank position, RRF sidesteps score normalisation and works without tuning, which is why it is the practical default for combining sparse and dense retrieval.

For a self-hosted retrieval stack, RRF needs no training and almost no compute, making it an easy, transparent way to get the best of both retrievers before an optional reranking pass refines the top results for your RAG pipeline.