---
title: Hybrid Search
---

ParadeDB's full text and similarity search APIs can be combined in the same query to execute [hybrid search](/documentation/concepts/search#hybrid-search).

<Note>
  This guide uses the `mock_items` table, which was created in the quickstart. It assumes that the entire
  [quickstart](/documentation/getting-started/quickstart) tutorial has been completed, including the vector search section.
</Note>

## Reciprocal Rank Fusion

Reciprocal rank fusion is a popular hybrid search algorithm that:

1. Calculates a BM25 and similarity score for the top `n` documents.
2. Ranks documents by their BM25 and similarity scores separately. The highest-ranked document for each score receives an `r` of `1`.
3. Calculates a reciprocal rank for each score as `1/(k + r)`, where `k` is a constant. `k` is usually set to `60`.
4. Calculates each document's reciprocal rank fusion score as the sum of the BM25 and similarity reciprocal rank scores.

The following code block implements reciprocal rank fusion over the `mock_items` table. BM25 scores are calculated against the query `description:keyboard` and similarity scores are
calculated against the vector `[1,2,3]`.

```sql
WITH bm25_ranked AS (
    SELECT id, RANK() OVER (ORDER BY score DESC) AS rank
    FROM (
      SELECT id, pdb.score(id) AS score
      FROM mock_items
      WHERE description @@@ 'keyboard'
      ORDER BY pdb.score(id) DESC
      LIMIT 20
    ) AS bm25_score
),
semantic_search AS (
    SELECT id, RANK() OVER (ORDER BY embedding <=> '[1,2,3]') AS rank
    FROM mock_items
    ORDER BY embedding <=> '[1,2,3]'
    LIMIT 20
)
SELECT
    COALESCE(semantic_search.id, bm25_ranked.id) AS id,
    COALESCE(1.0 / (60 + semantic_search.rank), 0.0) +
    COALESCE(1.0 / (60 + bm25_ranked.rank), 0.0) AS score,
    mock_items.description,
    mock_items.embedding
FROM semantic_search
FULL OUTER JOIN bm25_ranked ON semantic_search.id = bm25_ranked.id
JOIN mock_items ON mock_items.id = COALESCE(semantic_search.id, bm25_ranked.id)
ORDER BY score DESC, description
LIMIT 5;
```

<Accordion title="Expected Response">
```csv
 id |         score          |       description        | embedding
----+------------------------+--------------------------+-----------
  1 | 0.03062178588125292193 | Ergonomic metal keyboard | [3,4,5]
  2 | 0.02990695613646433318 | Plastic Keyboard         | [4,5,6]
 19 | 0.01639344262295081967 | Artistic ceramic vase    | [1,2,3]
 29 | 0.01639344262295081967 | Designer wall paintings  | [1,2,3]
 39 | 0.01639344262295081967 | Handcrafted wooden frame | [1,2,3]
(5 rows)
```
</Accordion>

Here, we see that the top five results either contain `keyboard` in the `description` field or have an `embedding` of `[1,2,3]`.
