Precision (information retrieval, $\mathrm{TP}/(\mathrm{TP}+\mathrm{FP})$)

Precision measures the relevant fraction of an information retrieval system's returned documents. For relevant-document set $R$ and nonempty returned-document set $S$, it is $|R\cap S|/|S|$. The denominator concerns what was returned, whereas recall concerns all relevant documents.^[ref]

If $R=\{2,4,6\}$ and $S=\{1,2,3,4,5\}$, two of five returned documents are relevant, giving $2/5=0.4$. Adding irrelevant document seven reduces precision to $2/6$ while leaving recall at $2/3$. This exposes the cost of adding unhelpful results. Returning nothing makes this ratio undefined; a reported score must state any convention used for that case.