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Mean Reciprocal Rank (MRR)

Description

MRR considers the rank of the first relevant document retrieved. It emphasizes the importance of retrieving relevant documents early in the ranking.

Info

A higher MRR indicates that relevant documents are retrieved at higher ranks (closer to the top).

Formula

\[ \mathrm{MRR} = \frac{1}{\lvert Q\rvert} \sum_{i=1}^{\lvert Q\rvert} \frac{1}{\mathrm{rank}_i} \]
  • \(\lvert Q\rvert\) is the number of queries
  • \(\mathrm{rank}_i\) is the rank of the first relevant document for query \(i\)

Example

If the first relevant document for a query is retrieved at rank 3, the reciprocal rank is \(1/3\). MRR averages these reciprocal ranks across multiple queries.