Equation 1 · Measuring What a RAG System Retrieves, Not Just What It Answers
What does this equation mean?
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
Symbol k
k is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
How to interpret it
Read this expression with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
A retrieval metric is computed from three things only: a query, a ranked list of documents or passages returned for it, and a set of relevance judgements — a labelled mapping from each query to the documents that count as relevant, usually built by human assessors ahead of time. None of the three requires a generator. This is the methodological point worth holding onto before any of the specific metrics: recall at k , precision at k , mean reciprocal rank and normalised discounted cumulative gain are all properties of a ranking function evaluated against ground truth, and they can be computed the moment the retriever returns its list, with no language model ever invoked.
Sources cited in the article section
- [3] The TREC-8 Question Answering Track Report ↗
- [2] BEIR: A Heterogeneous Benchmark for Zero-shot Evaluation of Information Retrieval Models ↗
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