Mean reciprocal rank

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The mean reciprocal rank is a statistic measure for evaluating any process that produces a list of possible responses to a sample of queries, ordered by probability of correctness. The reciprocal rank of a query response is the multiplicative inverse of the rank of the first correct answer: 1 for first place, 1⁄2 for second place, 1⁄3 for third place and so on. The mean reciprocal rank is the average of the reciprocal ranks of results for a sample of queries Q:^[1][2]

${\displaystyle {\text{MRR}}={\frac {1}{|Q|}}\sum _{i=1}^{|Q|}{\frac {1}{{\text{rank}}_{i}}}.\!}$

where ${\displaystyle {\text{rank}}_{i}}$ refers to the rank position of the first relevant document for the i-th query.

The reciprocal value of the mean reciprocal rank corresponds to the harmonic mean of the ranks.