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Reciprocal Rank Fusion

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Reciprocal Rank Fusion

A score-based result merging algorithm that combines ranked lists from multiple retrieval systems without requiring calibrated scores.

Formula

For each document d across k ranked lists:

RRF(d) = Σ 1 / (rank(d, list_i) + c)

Where c is a constant (typically 60) that dampens the impact of high-ranked documents.

Why RRF

  • Score-agnostic: BM25 and dense vectors use incomparable scales; RRF only uses rank positions
  • Simple: No learned weights, no calibration
  • Robust: Consistently beats more complex fusion approaches in practice

Limitations

  • Treats all systems equally — no way to weight one retrieval path more than another

  • Loses fine-grained score signal; two items at rank 1 contribute identically even if scores differ greatly

  • Does not account for query-type variance (some queries may benefit more from lexical vs. semantic)

  • Criticized in RRF is Not Enough for losing signal in hybrid search contexts

  • Can rank below sparse-only or dense-only retrieval on some queries; in Qdrant’s hybrid-routing work RRF was the best route for only ~3% of ~230,000 labelled queries — see Andrei Cristea - Qdrant Vector Search and Hybrid Routing

Weighting, and why the constant matters

The constant is not decoration. Because it dominates the denominator at low ranks, it also sets the scale of the output, which is why raw RRF scores come out as small, hard-to-read numbers that barely separate. Weights fix both problems at once.

In MongoDB’s $rankFusion, where k = 60 is a fixed built-in, a weight of 30 on each of two pipelines rescales the summed score into a comfortable ~0.0–1.0 range: each pipeline contributes at most ~0.5, and a document ranked first in both lists lands at ~1.0.

Equal weights also produce structural ties: a document at rank 1 in list A and a document at rank 1 in list B score identically, since rank is all RRF sees. Assigning different weights per pipeline is the way to break them — and doubles as the knob for expressing that one retrieval path should count for more than another, which plain unweighted RRF cannot do.

Worked end-to-end with numbers in Reciprocal Rank Fusion and Relative Score Fusion.

Weighted RRF and Choosing k (Qdrant)

Qdrant parameterizes both knobs directly on the query: k since v1.16.0, and per-prefetch weights (Weighted RRF) since v1.17.0. Qdrant’s formula for a document at position pos in one prefetch is 1/((pos+1)/weight + k − 1), reducing to 1/(pos+k) at equal weights — the same shape as above, but zero-based, so Qdrant’s default k=2 is not directly comparable to the original RRF paper’s k=60 (one-based); porting that paper’s convention requires k=61.

How to Tune Hybrid Search in Qdrant measured how much k matters across five datasets: at k=2, rank 1 carries 5.50× the weight of rank 10; at k=61, only 1.15×. Datasets with about one relevant document per query did best at low k (2 or 5); datasets with tens or hundreds of relevant documents per query did best at high k (20 or 61) — on WANDS, k=2 vs. k=61 picked a different top result for 42% of queries. Weight pairs are only valid for the k they were tuned at, and a prefetch’s own standalone score doesn’t say which way to weight it — e.g. weighting the weaker solo retriever higher can still win, because weights act on positions within each list, not on absolute score quality. A weight of 0.0 keeps a prefetch’s documents in the result, scored at 0.0, rather than excluding them. Tied scores are more common at low k; the fix is to request more results, sort client-side by descending score then ascending ID, and keep the first N.

Explainability

Because the contribution of each list is just w × 1/(k + rank), RRF is unusually easy to explain. Engines can expose the per-pipeline rank, weight, and resulting term — including a marker for lists the document did not appear in — making a fused score fully reconstructible. See Search Results Explainability.

RRF is also implementable directly in SQL — see Search using PostgreSQL for a PostgreSQL hybrid query fusing FTS and pgvector results.

RRF is the default fusion method in Hybrid Search pipelines combining:

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