Reciprocal Rank Fusion (RRF)

Used in Qdrant.

$RRF(d)={\sum }_{r\in R}\frac{1}{k+r(d)}$

• $R$ is the set of rankers
• $r(d)$ is the rank of document $d$
• $k$ is a constant (typically 60)

Why is this better than doing a linear combination?

It’s motivated in the quadrant This is more sophisticated than just averaging scores, because it’s rank-based rather than score-based, which handles the different score distributions between dense and sparse searches better.

Resources

• https://medium.com/@devalshah1619/mathematical-intuition-behind-reciprocal-rank-fusion-rrf-explained-in-2-mins-002df0cc5e2a