Mean reciprocal rank

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:^[1]

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

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.

Example

For example, suppose we have the following three sample queries for a system that tries to translate English words to their plurals. In each case, the system makes three guesses, with the first one being the one it thinks is most likely correct:

Query	Results	Correct response	Rank	Reciprocal rank
cat	catten, cati, cats	cats	3	1/3
tori	torii, tori, toruses	tori	2	1/2
virus	viruses, virii, viri	viruses	1	1

Given those three samples, we could calculate the mean reciprocal rank as (1/3 + 1/2 + 1)/3 = 11/18 or about 0.61.

This basic definition does not specify what to do if none of the proposed results are correct, though reciprocal rank 0 could be used in this situation. It also does not specify what do to if there are multiple correct answers in the list. In this case, mean average precision is a potential alternative metric.

See also

• Information retrieval
• Question answering

References

1. E.M. Voorhees (1999). "Proceedings of the 8th Text Retrieval Conference". TREC-8 Question Answering Track Report. pp. 77–82.

External links

• D. R. Radev; H. Qi; H. Wu; W. Fan (2002). "Evaluating web-based question answering systems". Proceedings of LREC.