Reciprocal Rank Fusion

RRF is a highly effective, unsupervised method used in hybrid search architectures to merge results from different retrieval algorithms without requiring complex score normalization. Different search paradigms—such as dense vector embeddings (which capture semantic meaning) and BM25 sparse retrieval (which captures exact keyword matches)—produce relevance scores on entirely different mathematical scales. Directly comparing or combining these raw scores is fundamentally flawed. RRF solves this by ignoring the raw scores entirely and focusing solely on the rank position of a document within each respective list. It assigns a new score to each document by calculating the sum of the reciprocal of its ranks across all lists, applying a smoothing constant (k) to prevent heavily weighting the absolute top positions. The formula is `RRF_score = 1 / (k + rank_1) + 1 / (k + rank_2) + ...`. By fusing results this way, RRF consistently produces a final ranked list that is better than any individual retrieval method on its own. It ensures that documents highly ranked by both keyword and semantic searches bubble to the top, providing the downstream LLM with the most comprehensively relevant context possible.