AUROC — Area Under the ROC Curve

A binary classifier assigns a probability score to each sample. The ROC curve plots how the model's true positive rate (sensitivity) trades off against its false positive rate across every possible classification threshold.

Step 1 — each dot is a sample; its x-position is the model's predicted probability; drag the line to move the threshold:

TP — predicted positive, actually positive FP — predicted positive, actually negative FN — predicted negative, actually positive TN — predicted negative, actually negative

Threshold 0.50

Step 2 — at this threshold, the counts and rates that define one point on the ROC curve:

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True positives

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False negatives

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False positives

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True negatives

TPR = TP / (TP + FN) (y-axis)

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FPR = FP / (FP + TN) (x-axis)

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Step 3 — each threshold gives a (FPR, TPR) point. The ROC curve connects them all. The amber dot is your current threshold:

AUC

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AUC = 0.5 → random

The curve lies on the diagonal. The model's scores carry no signal above chance.

AUC = 1.0 → perfect

Curve hits the top-left corner. Every positive scores higher than every negative.

Threshold-independent

AUC evaluates the model across all cutoffs — useful when you haven't chosen a threshold yet.

Probabilistic interpretation

AUC = the probability that a random positive is ranked higher than a random negative.

Interactive AUROC curve learning resource with dark theme

AUROC — Area Under the ROC Curve