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Equation 5 · Part 9 · Measuring What a RAG System Retrieves, Not Just What It Answers

Starting index or lower bound: q=1

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

What this part means

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.

Its job in the formula

q=1 appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

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

Σ adds a collection of terms. Π multiplies them. The lower and upper labels tell you which terms belong to the collection.

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Sources cited in the surrounding passage

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