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Reciprocal Rank Fusion

Reciprocal Rank Fusion (RRF) combines two or more ranked result lists into one. Reach for it when no single signal — BM25 over one field, BM25 over another, fuzzy match, vector distance — captures every relevant document, and each surfaces some that the others miss.

See Setup for the shared dataset used in all examples.

How it works​

For each branch, every matching document gets a rank (1, 2, 3, ...) under that branch's own scoring. RRF combines those ranks per document with:

rrf_score(d) = Σ over branches  1 / (k + rank_in_branch(d))

A document missing from a branch contributes nothing for that branch. Documents that rank high in any branch end up with a high combined score; documents that rank high in several branches dominate.

k controls how steeply top ranks outweigh lower ranks. The default in the original paper and in Elasticsearch is 60.

Template​

Copy the skeleton and replace each branch with your own ranking query:

WITH fused AS (
  -- Branch 1
  SELECT id, ROW_NUMBER() OVER (ORDER BY s DESC) AS rank FROM (
    SELECT id, BM25(movies_idx.tableoid) AS s FROM movies_idx
    WHERE title @@ ts_phrase('YOUR_QUERY')
    ORDER BY s DESC LIMIT 100
  ) t
  UNION ALL
  -- Branch 2
  SELECT id, ROW_NUMBER() OVER (ORDER BY s DESC) AS rank FROM (
    SELECT id, BM25(movies_idx.tableoid) AS s FROM movies_idx
    WHERE description @@ ts_phrase('YOUR_QUERY')
    ORDER BY s DESC LIMIT 100
  ) t
)
SELECT id, SUM(1.0 / (60 + rank)) AS rrf_score
FROM fused
GROUP BY id
ORDER BY rrf_score DESC
LIMIT 10;

Each branch:

  • selects (id, score) rows that match whatever predicate you want,
  • sorts by its own score, capped with a per-branch LIMIT (the window size — see Tuning),
  • assigns ranks with ROW_NUMBER().

The outer query sums 1 / (60 + rank) per id and returns the top fused results.

Worked example​

Same query word, two fields. "Alien" appears in the title of one film and only in the description of another:

Query
WITH fused AS (  SELECT id, ROW_NUMBER() OVER (ORDER BY s DESC) AS rank FROM (    SELECT id, BM25(movies_idx.tableoid) AS s FROM movies_idx    WHERE title @@ ts_phrase('alien') ORDER BY s DESC LIMIT 100  ) t  UNION ALL  SELECT id, ROW_NUMBER() OVER (ORDER BY s DESC) AS rank FROM (    SELECT id, BM25(movies_idx.tableoid) AS s FROM movies_idx    WHERE description @@ ts_phrase('alien') ORDER BY s DESC LIMIT 100  ) t)SELECT m.id, m.title, SUM(1.0 / (60 + rank))::DECIMAL(6,5) AS rrfFROM fused f JOIN movies m ON m.id = f.idGROUP BY m.id, m.titleORDER BY rrf DESC, m.idLIMIT 5;
Result
 id | title                         | rrf----+-------------------------------+---------  7 | Star Trek: The Motion Picture | 0.01639  8 | Alien                         | 0.01639

Each branch alone returns one document. Fused, both surface — and a document matching both fields would score about twice as high.

Tuning​

k — top-rank weight​

k = 60 is the published default and works well out of the box. Lower k widens the gap between top ranks; higher k flattens the curve so that the set of candidates matters more than the order within each branch.

k1/(k+1)1/(k+10)Top-vs-10 ratio
100.09090.05001.8×
600.01640.01431.15×
2000.004980.004761.05×

Window size — per-branch LIMIT​

Each branch's LIMIT N is the window: only the top N results per branch contribute. A document outside every branch's window scores 0.

  • Navigational ("I know what I want") queries: LIMIT 50–100.
  • Exploratory queries where the long tail matters: LIMIT 200+, at the cost of more rows flowing into the GROUP BY.

More branches​

Add another UNION ALL block per extra signal — the shape doesn't change:

WITH fused AS (
  -- branch 1: title BM25
  SELECT id, ROW_NUMBER() OVER (ORDER BY s DESC) AS rank FROM (...) t
  UNION ALL
  -- branch 2: description BM25
  SELECT id, ROW_NUMBER() OVER (ORDER BY s DESC) AS rank FROM (...) t
  UNION ALL
  -- branch 3: fuzzy, n-gram, or any other ranked source
  SELECT id, ROW_NUMBER() OVER (ORDER BY s DESC) AS rank FROM (...) t
)
SELECT id, SUM(1.0 / (60 + rank)) AS rrf_score
FROM fused GROUP BY id ORDER BY rrf_score DESC LIMIT 10;

When not to use RRF​

  • One signal dominates. If BM25 alone gives the right answer, fusing it with a weaker signal only dilutes the ranking.
  • You need calibrated scores. RRF discards the original scores in favor of ranks. If downstream code needs "this document is 92% relevant", rerank the fused candidates with a calibrated model instead.
  • Your branches' scores are already on the same scale. Then a weighted sum α·s₁ + β·s₂ is usually better — it doesn't throw away score magnitudes.

See also​