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.