What does this equation mean?

Because retrieval and generation are separable, an end-to-end score is nearly uninformative about which one broke. Decompose it. Let $\mathcal{Z}_k(x)$ be the retrieved set and S(x) the set of spans that would suffice to answer x : $P(\text{correct}) = P\left(\mathcal{Z}_k(x) \cap S(x) \neq \emptyset\right) \cdot P\left(\text{grounded} \mid \mathcal{Z}_k(x) \cap S(x) \neq \emptyset\right)$. The first factor is a pure retrieval quantity: recall at k , measurable against relevance judgements with no generator involved, using the established information-retrieval apparatus that BEIR standardised [ 6 ] . The second is a pure generation quantity: given that sufficient evidence was present, did the model use it faithfully? Es and colleagues built RAGAS to score exactly this separation — retrieval effectiveness, the faithfulness with which the model uses retrieved passages, and generation quality — as a reference-free evaluation that does not require ground-truth answers, enabling faster iteration [ 17 ] .