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Reciprocal Rank Fusion merges ranked lists without comparable scores

RRF combines ranked result lists from multiple sources using only rank positions, avoiding the problem of incomparable scoring systems.

๐ŸŒฑ Seedling Mar 26, 2026 ยท 1 min read
information-retrieval search algorithms

Reciprocal Rank Fusion (RRF) is an algorithm for merging ranked result lists from multiple independent sources. Its key insight: ignore raw scores entirely and use only rank positions. This sidesteps the problem that different systems use different scoring parameters, making their raw scores incomparable.

The Formula 

RRF_score(document) = ฮฃ  1 / (k + rank_in_list)
                      for each list containing the document

where k is a constant (standard value: 60) that controls how much weight top-ranked results get relative to lower-ranked ones.

Example

Document X appears at rank 2 in List A and rank 5 in List B:

RRF(X) = 1/(60+2) + 1/(60+5) = 0.01613 + 0.01538 = 0.03151

Document Y appears at rank 1 in List A but is absent from List B:

RRF(Y) = 1/(60+1) = 0.01639

Even though Y ranked higher in List A, X’s presence in both lists gives it a higher fused score. This is a desirable property: documents confirmed by multiple independent sources are likely more relevant. Consensus across sources is a strong relevance signal.

Why It Works

  • No score normalization needed โ€” only ordinal rankings matter
  • Rewards cross-source agreement โ€” appearing in multiple lists boosts a document
  • Simple to implement โ€” no machine learning, no parameter tuning beyond k
  • Robust โ€” works even when different lists use entirely different retrieval methods (e.g., combining keyword search with semantic vector search)
  • [[Federated search]] โ€” the primary use case where RRF merges results from independent indexes