Reciprocal Rank Fusion

Reciprocal Rank Fusion (RRF) is a simple yet effective technique for combining ranked lists from multiple retrieval systems into a single unified ranking. For each document, RRF computes a score by summing 1/(k + rank) across all retrieval systems, where k is a constant (typically 60) and rank is the document's position in each list.

The formula Score(doc) = sum of 1/(k + rank_i(doc)) for each retrieval system i elegantly handles the fusion problem without requiring score normalization. Since it operates on ranks rather than raw scores, it works even when different retrieval systems produce scores on incompatible scales (e.g., BM25 scores vs. cosine similarities).

RRF is the most commonly used fusion method in hybrid RAG systems that combine BM25 and dense retrieval results. Its popularity stems from its simplicity (no learned parameters), robustness (works across diverse retrieval methods), and consistent effectiveness (competitive with more complex learned fusion approaches). Alternative fusion methods include learned weighted combination and cross-attention-based merging, but RRF remains the go-to starting point for hybrid search.