\(\newcommand{\Correctrank}{\mathrm{rank}}\)

Mean Reciprocal Rank is a measure to evaluate systems that return a ranked list of answers to queries.

For a single query, the reciprocal rank is \(\frac 1 \Correctrank\) where \(\Correctrank\) is the position of the highest-ranked answer (\(1, 2, 3, \ldots, N\) for \(N\) answers returned in a query). If no correct answer was returned in the query, then the reciprocal rank is 0.

For multiple queries \(Q\), the Mean Reciprocal Rank is the mean of the \(Q\) reciprocal ranks.

\[\mathrm{MRR} = \frac 1 Q \sum_{i=1}^{Q} \frac 1 {\Correctrank_i}\]