ROC Curve & AUC
The ROC curve shows what your model would do at EVERY threshold, not just one: plot catch-rate against false-alarm-rate as the cut-off slides, and the area under it (AUC) becomes the probability that a random positive outscores a random negative. Threshold-free and comparable across base rates — which is also exactly what it hides.
01.The Problem: You Have Scores, Not Decisions
Your fraud model doesn't say "fraud" or "not fraud".
It gives every transaction a score: 0.92, 0.31, 0.77…
Somebody still has to pick a threshold — the cut-off that turns scores into decisions.
And here is the awkward part: which model is "better" can depend on a threshold nobody has chosen yet.
Model A wins if you set the bar high. Model B wins if you set it low.
So how do you compare models before the business picks a cut-off?
Evaluate every possible threshold at once and draw the result.
That drawing is the ROC curve.
Its single-number summary is AUC — the area under that curve.
Together they answer one clean question:
How good is this model's ranking, regardless of any decision?
From Scores to Curve to Single Number 📈
From Scores to Curve to Single Number 📈
The ROC is the locus of (FPR, TPR) over all thresholds; AUC collapses it to the probability that a random positive outranks a random negative.
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