Introduction
The precision/recall trade-off depends on the threshold. To compare models (rather than thresholds), it helps to have a picture that shows all thresholds at once, and a single number that summarises it. The most widely used are the ROC curve and the area under it (AUC).
ROC stands for receiver operating characteristic — a name from radar engineers in World War II, who had to decide how sensitive to make radar receivers: too sensitive and every flock of birds triggered an alarm; not sensitive enough and enemy planes slipped through. Same trade-off, same tool.