Equation 19 · Part 3 · Measuring What a RAG System Retrieves, Not Just What It Answers

=

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}}

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

Full expression=Article 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

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the article section

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