Interpreting Hybrid Retrieval Metrics: RRF Scoring, BM25 vs. Dense Vector Diagnostics

Hybrid search architectures combine exact keyword lexical matching (Apache Lucene BM25) with semantic vector search (cosine similarity over dense embeddings) using Reciprocal Rank Fusion (RRF).

This diagnostic guide details how to interpret RRF ranking scores, identify when BM25 outperforms vector embeddings (exact code symbols, error codes), and troubleshoot semantic drift.

1. Reciprocal Rank Fusion (RRF) Formula

ext{RRF\_Score}(d) = \sum_{m \in \{ ext{BM25}, ext{Vector}\}} rac{1}{k + r_m(d)} \quad (k pprox 60)

where $r_m(d)$ is the 1-indexed rank of document $d$ within search model $m$ .