What is reciprocal rank fusion (RRF)?

Reciprocal Rank Fusion (RRF) is a method of combining (fusing) the results of multiple search engines or ranking models to improve the quality of the final list of results.

The idea is to merge document ranks from different sources using a formula that considers the reciprocal rank of each document in each list:

Formula for evaluating document d:

[ \text{score}(d) = \sum_{i=1}^n \frac{1}{k + r_i(d)} ]

where:

• (n) — the number of lists,
• (r_i(d)) — the rank of document d in the i-th list (if the document is not present, the rank can be considered infinite or very large),
• (k) — a small constant shift (usually 60) to reduce the influence of high ranks.

RRF works well in information retrieval tasks and systems with multiple relevance sources, including RAG (Retrieval-Augmented Generation) and LLM, where it is necessary to combine results from different models or indexes to enhance answer quality.