Equation 19 · Part 4 · Measuring What a RAG System Retrieves, Not Just What It Answers

subscript

P(\text{correct}) \;=\; \underbrace{P(R)\,P(\text{correct} \mid R)}_{\text{grounded in retrieved evidence}} \;+\; \underbrace{P(\lnot R)\,P(\text{correct} \mid \lnot R)}_{\text{correct without sufficient retrieved evidence}}

subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

Full expressionsubscriptArticle meaning

The passage around this formula

The measurement structure explains the divergence directly. Let R be the event that the retriever’s top- k results contain sufficient evidence to answer the query, and let “correct” mean the generated answer is judged faithful and relevant. Total correctness decomposes as $P(\text{correct}) \;=\; \underbrace{P(R)\,P(\text{correct} \mid R)}_{\text{grounded in retrieved evidence}} \;+\; \underbrace{P(\lnot R)\,P(\text{correct} \mid \lnot R)}_{\text{correct without sufficient retrieved evidence}}$ . An end-to-end accuracy score measures the left-hand side only. The two terms on the right are exactly what generation metrics and retrieval metrics separately illuminate, and the second term is the one an aggregate score cannot see at all. P( $\text{correct}$ $\mid$ $\lnot$ R) is the probability the model answers correctly despite the retriever having failed — because the underlying language model already…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the article section

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