What is relative score fusion?

Relative score fusion combines results from multiple RAG retrievers by normalizing each retriever's scores relative to its own candidate list, then combining the normalized values. It is useful when BM25 and vector search produce scores on different scales.

How does it work?

1. Run two retrieval methods, such as BM25 and dense vector search.
2. Keep each result's original retrieval score and stable chunk ID.
3. Normalize scores separately within each retriever. A common approach is min–max normalization:

normalized = (score - minimum) / (maximum - minimum).

1. Merge candidates by chunk ID. When a chunk is absent from one list, follow a defined missing-result policy, often assigning that branch zero contribution.
2. Combine the normalized scores with chosen weights, then sort the merged results.
3. Optionally rerank the best candidates before sending them to the LLM.

Simple numerical example

Suppose the query asks about payment error PAY-409. Two chunks have these example scores:

• Chunk A: BM25 = 12, vector = 0.70
• Chunk B: BM25 = 6, vector = 0.90

Assume the BM25 score range of the retrieved set is 2–12 and the vector score range is 0.50–0.90.

After min–max normalization:

• Chunk A: BM25 = 1.00, vector = 0.50
• Chunk B: BM25 = 0.40, vector = 1.00

With equal 50% weights:

• A: 0.5 × 1.00 + 0.5 × 0.50 = 0.75
• B: 0.5 × 0.40 + 0.5 × 1.00 = 0.70

So A ranks above B under this illustrative fusion rule. In production, the normalization range should come from each retriever's complete candidate score list, not merely these two displayed chunks.

How is this different from RRF?

• Relative score fusion uses normalized *score magnitudes*. The distance between scores affects the final ranking.
• Reciprocal Rank Fusion (RRF) uses *rank positions* rather than raw similarity values. It avoids the need to normalize different score scales.

Relative score fusion can preserve useful score differences, but it is sensitive to normalization choices and outlier scores.

Important cautions

• If all scores in one list are identical, min–max normalization divides by zero. Define a safe fallback.
• A single extreme score can compress the remaining normalized values.
• Weights must be validated on representative queries rather than chosen arbitrarily.
• Candidate-list sizes, missing records, and retriever score distributions can change results.
• Enforce document permissions before exposing or combining retrieved text; evaluate Recall@K, nDCG@K, and grounded answer quality.

Interview takeaway

Relative score fusion normalizes each retriever's scores within its own result set and combines them using weights. Unlike RRF, it retains relative score differences, but requires careful normalization, missing-result handling, and evaluation.