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Equation 5 · Part 8 · Measuring What a RAG System Retrieves, Not Just What It Answers

Denominator: |Q|

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

What this part means

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

Its job in the formula

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

The passage around this formula

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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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the surrounding passage

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