← Back to article

Equation 23 · Measuring What a RAG System Retrieves, Not Just What It Answers

What does this equation mean?

P(correct∣¬R)P(\text{correct} \mid \lnot R)

Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

Read it piece by piece

PP

Symbol P

inflated by memorisation rather than by any generalisable capability, and every end-to-end score computed against that reference set overstates what the retrieval component is doing.

Understand this part →

RR

Symbol R

R is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Understand this part →

How to interpret it

Read this expression with the definitions, units, and assumptions supplied by the article.

What the article says around this equation

The mechanism is not exotic. A benchmark released as a public dataset, a paper, or a web page is exactly the kind of content large-scale pretraining crawls are built to ingest. A survey of benchmark data contamination in large language models lays out the resulting problem directly: leading models trained on web-scale corpora can inadvertently incorporate benchmark data into their training sets, which inflates measured performance in ways that do not reflect genuine capability, and the survey catalogues detection methods and alternative assessment strategies developed specifically to counter it [ 12 ] . For RAG evaluation the consequence is sharper than for a plain language-model benchmark,…
Read the full surrounding passage
The mechanism is not exotic. A benchmark released as a public dataset, a paper, or a web page is exactly the kind of content large-scale pretraining crawls are built to ingest. A survey of benchmark data contamination in large language models lays out the resulting problem directly: leading models trained on web-scale corpora can inadvertently incorporate benchmark data into their training sets, which inflates measured performance in ways that do not reflect genuine capability, and the survey catalogues detection methods and alternative assessment strategies developed specifically to counter it [ 12 ] . For RAG evaluation the consequence is sharper than for a plain language-model benchmark, because contamination corrupts exactly the term this article has been isolating: a contaminated model can produce a correct, fluent answer with the retriever disabled entirely, which means P(correct\text{correct} ∣\mid ¬\lnot R) is inflated by memorisation rather than by any generalisable capability, and every end-to-end score computed against that reference set overstates what the retrieval component is doing.

Read the equation in its article →

Sources cited in the surrounding passage

These citations give research context. Read each source to check which claims it supports.

Return to Measuring What a RAG System Retrieves, Not Just What It Answers

See this formula across 2 published contexts →

Browse the mathematical compendium →