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Equation 5 · Part 2 · Measuring What a RAG System Retrieves, Not Just What It Answers

Symbol q

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

What this part means

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

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

…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…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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