Which metric remains informative across varying thresholds for binary classification?

• A. Precision
• B. ROC-AUC
• C. Recall
• D. Accuracy

Answer: (B)

When evaluating binary classifiers, you often explore how the model would act if you changed the decision threshold. The metric that stays informative across all those potential thresholds is ROC-AUC. The ROC curve shows how the true positive rate (sensitivity) and the false positive rate (1 − specificity) trade off as you sweep the threshold from very low to very high. The AUC—the area under that curve—summarizes how well the model can separate positives from negatives across the entire range of thresholds. Because it integrates performance over all possible cutoffs, it doesn’t rely on choosing a particular threshold, making it robust to where you decide to classify as positive.

In contrast, precision and recall depend on where you set the threshold: tighten the threshold to classify more confidently as positive increases precision but lowers recall, and relax it does the opposite. Accuracy also depends on the chosen cutoff and can be misleading if the class distribution is imbalanced, since it can look good simply by predicting the majority class.

A helpful intuition is that AUC reflects the model’s ability to rank positive instances higher than negative ones: a higher AUC means a better overall ranking, regardless of the exact threshold you end up using.