Physical meaning: Pick a random positive and a random negative sample. AUC is the probability the model scores the positive higher. AUC = 0.5 is random guessing; 1.0 is perfect ranking.
It only cares about ranking - not thresholds, not absolute score values. It is invariant to monotonic transforms.
Implication: high AUC does not mean calibrated probabilities. For CTR prediction, where scores drive bidding and money, you must check calibration on top of AUC (e.g., bucket predicted mean vs. actual CTR).
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