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Chapter 5.2 - Reciprocal Rank Fusion

[!info] Combining scores from sparse and dense retrievers.

When you run a Hybrid Search, FAISS gives you a list of results based on meaning, and BM25 gives you a list based on keywords. How do you combine them? You cannot just add their scores together because they are on completely different mathematical scales! We use Reciprocal Rank Fusion (RRF). It completely ignores the raw scores and instead looks only at the Rank (position in the list).

The RRF Formula​


def reciprocal_rank_fusion(faiss_results, bm25_results, k=60):
    fused_scores = {}
    
    # Process FAISS Ranks
    for rank, doc_id in enumerate(faiss_results):
        fused_scores[doc_id] = fused_scores.get(doc_id, 0) + 1 / (k + rank + 1)
        
    # Process BM25 Ranks
    for rank, doc_id in enumerate(bm25_results):
        fused_scores[doc_id] = fused_scores.get(doc_id, 0) + 1 / (k + rank + 1)
        
    # Sort by highest fused score
    return sorted(fused_scores.items(), key=lambda x: x[1], reverse=True)

[!tip] The K Constant The constant k=60 is a mathematically proven optimal value that prevents the #1 result of one list from completely dominating the final fused list.