# Mean Reciprocal Rank (MRR)

$$\newcommand{\Correctrank}{\mathrm{rank}}$$

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.

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