# Mean Reciprocal Rank (MRR) Measure

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A Mean Reciprocal Rank (MRR) Measure is a ranking performance measure based on the average of the reciprocal ranks for list results.

**Context:**- It can be represented as [math] \text{MRR} = \frac{1}{|Q|} \sum_{i=1}^{|Q|} \frac{1}{\text{rank}_i}. \! [/math].

**Counter-Example(s):****See:**Harmonic Mean, Multiplicative Inverse, Information Retrieval Task, Discounted Cumulative Gain, Mean Average Precision

## References

### 2016

- (Wikipedia, 2016) ⇒ https://en.wikipedia.org/wiki/mean_reciprocal_rank Retrieved:2016-5-18.
- 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. The mean reciprocal rank is the average of the reciprocal ranks of results for a sample of queries Q: : [math] \text{MRR} = \frac{1}{|Q|} \sum_{i=1}^{|Q|} \frac{1}{\text{rank}_i}. \! [/math] where [math] \text{rank}_i [/math] 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.

- The

### 2009

- "Encyclopedia of Database Systems - MMR."
- QUOTE: The Reciprocal Rank (RR) information retrieval measure calculates the reciprocal of the rank at which the first relevant document was retrieved. RR is 1 if a relevant document was retrieved at rank 1, if not it is 0.5 if a relevant document was retrieved at rank 2 and so on. When averaged across queries, the measure is called the Mean Reciprocal Rank (MRR).