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Computing Retrieval Metrics From Raw Results

You are given the top-5 retrieved chunk IDs for four evaluation queries, each with one gold chunk:

Query Gold chunk Top-5 results (ranked, best first)
Q1 G1 A, G1, B, C, D
Q2 G2 G2, E, F, B, A
Q3 G3 A, B, C, D, E
Q4 G4 F, A, B, G4, C
  1. Compute recall@5, MRR, and NDCG@5 (binary relevance) by hand.
  2. Your re-ranker is then changed so that Q1's gold chunk moves from rank 2 to rank 1, and everything else is unchanged. Recompute MRR and explain, in words a non-technical stakeholder would understand, why recall@5 does not change but MRR does.
  3. A colleague proposes reporting only recall@20 (retrieve a much larger candidate set, don't re-rank) as the system's one retrieval metric going forward. What is missing from that plan?

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