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Published equation contexts

MRR=1∣Q∣∑q=1∣Q∣1rankq\mathrm{MRR} = \frac{1}{|Q|}\sum_{q=1}^{|Q|} \frac{1}{\mathrm{rank}_q}

Why this formula appears here

Recall at k is the simplest of the four: the fraction of relevant documents that appear anywhere in the top k results. It answers one question only — did the evidence make it into the candidate set at all — and says nothing about where within that set it landed. Mean reciprocal rank answers the positional question for the single best hit: MRR=1∣Q∣∑q=1∣Q∣1rankq\mathrm{MRR} = \frac{1}{|Q|}\sum_{q=1}^{|Q|} \frac{1}{\mathrm{rank}_q}. averaged over a query set Q , where rankq\mathrm{rank}_q is the position of the first relevant result for query q . Mean reciprocal rank was formalised as the primary scoring metric for the TREC-8 Question Answering track, the first large-scale evaluation of domain-independent question answering systems, where it assigned a value of 1/r to a…

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qq

Symbol q

q occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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q=1q=1

Starting index or lower bound: q=1

This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.

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∣Q∣|Q|

Ending index or upper bound: |Q|

This label says where the repeated addition, multiplication, or accumulation stops. It sets the last term or end of the range.

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rankq\mathrm{rank}_q

Denominator: rank_q

The complete quantity below the fraction bar; it must be nonzero for this division.

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How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.

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Published contexts (1)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

MRR=1∣Q∣∑q=1∣Q∣1rankq\mathrm{MRR} = \frac{1}{|Q|}\sum_{q=1}^{|Q|} \frac{1}{\mathrm{rank}_q}

Equation 5 · AI Agents & Systems

Measuring What a RAG System Retrieves, Not Just What It Answers

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

Recall at k is the simplest of the four: the fraction of relevant documents that appear anywhere in the top k results. It answers one question only — did the evidence make it into the candidate set at all — and says nothing about where within that set it landed. Mean reciprocal rank answers the positional question for the single best hit: MRR=1∣Q∣∑q=1∣Q∣1rankq\mathrm{MRR} = \frac{1}{|Q|}\sum_{q=1}^{|Q|} \frac{1}{\mathrm{rank}_q}. averaged over a query set Q , where rankq\mathrm{rank}_q is the position of the first relevant result for query q . Mean reciprocal rank was formalised as the primary scoring metric for the TREC-8 Question Answering track, the first large-scale evaluation of domain-independent question answering systems, where it assigned a value of 1/r to a…

Meanings in this article

  • QQ: the averaged over a query set.
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