Equation 19 · Part 2 · Measuring What a RAG System Retrieves, Not Just What It Answers

Symbol R

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}}

R

What this part means

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.

Its job in the formula

R is one of the signed contributions combined to compute the quantity on the left.

Full expressionSymbol RArticle meaning

Where the article explains it

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.

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…

Read this part in the article →

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.

Open the illustrated variables: a letter stands for a value guide →

See this notation across published equations →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.