Merging incompatible scores
A RAG system often runs several retrievers, such as a keyword search and a vector search. Their scores live on different scales, so you cannot simply add them. Reciprocal rank fusion, or RRF, sidesteps this by combining the lists using only the rank position of each item, never the raw scores.
The formula
For each document, RRF sums a contribution from every list it appears in. Each contribution is one divided by a constant k plus the document's rank in that list:
- A document ranked first gets a large contribution.
- A document ranked low gets a small one.
- The constant k, often around sixty, softens the gap between top ranks.
Documents that appear high in several lists accumulate the most, so cross system agreement is rewarded.
Why ranks not scores
Ranks are comparable across any retriever because they only need an ordering. This makes RRF a robust, tuning light way to fuse heterogeneous systems.
Why it matters
RRF is the default fusion method for hybrid search because it is simple, needs no score calibration, and reliably lifts items that multiple retrievers agree on.
Key idea
Reciprocal rank fusion merges ranked lists using only positions, summing one over k plus rank, so it fuses retrievers with incompatible scores and rewards cross system agreement.