mean reciprocal rank (mrr)
**Mean Reciprocal Rank (MRR)** measures **position of first relevant result** — evaluating how quickly users find what they're looking for, with higher scores for relevant results appearing earlier in the ranked list.
**What Is MRR?**
- **Definition**: Average of reciprocal ranks of first relevant result.
- **Formula**: MRR = (1/|Q|) Σ (1/rank_i) where rank_i is position of first relevant result for query i.
- **Range**: 0 (no relevant results) to 1 (relevant result at position 1).
**How MRR Works**
**Reciprocal Rank**: 1/position of first relevant result.
- Position 1: RR = 1/1 = 1.0
- Position 2: RR = 1/2 = 0.5
- Position 3: RR = 1/3 = 0.33
- Position 10: RR = 1/10 = 0.1
**MRR**: Average reciprocal ranks across all queries.
**Why MRR?**
- **User-Centric**: Focuses on finding first relevant result quickly.
- **Simple**: Easy to understand and compute.
- **Practical**: Reflects real user behavior (stop at first good result).
- **Question Answering**: Ideal for QA where one answer suffices.
**When to Use MRR**
**Good For**: Question answering, navigational search, entity search (one correct answer).
**Not Ideal For**: Exploratory search, multiple relevant results, graded relevance.
**MRR vs. Other Metrics**
**vs. NDCG**: MRR only considers first relevant result, NDCG considers all.
**vs. Precision@K**: MRR position-aware, Precision@K counts relevant in top-K.
**vs. MAP**: MRR stops at first relevant, MAP considers all relevant results.
**Applications**: Question answering systems, entity search, navigational queries, chatbot response ranking.
**Tools**: Easy to implement, available in IR evaluation libraries.
MRR is **perfect for single-answer scenarios** — when users need one good result quickly, MRR accurately measures system effectiveness by focusing on the position of the first relevant result.