Yesterday's precision and recall were single slices at a specific threshold (usually 0.5). But classification models don't output 0 or 1 — they output probability scores, and where you cut that score completely changes precision and recall. Today we cover ROC curves and PR curves that sweep the threshold from 0 to 1 to draw full performance, and AUC that summarizes curves into a single number. The core question is "where do we set the threshold?" and the answer comes from business trade-offs.
A classifier outputs a score like P(Positive) = 0.73. Set threshold t: if score ≥ t, classify as Positive.