# Scoring a classifier with ROC AUC

I'm confused about how scikit-learn's roc_auc_score is working.

As I understand it, an ROC AUC score for a classifier is obtained as follows:

1. Sample from the parameter space
2. Fit the model
3. Make predictions with the model to get $$Y_{predicted}$$
4. Calculate $$P(F_P)$$ and $$P(T_P)$$ via $$Y_{true}$$ and $$Y_{predicted}$$

The above steps are performed repeatedly until you have enough $$(P(F_P), P(T_P))$$ points to get a good estimate of the area under the curve.

The sklearn.metrics.roc_auc_score method takes $$Y_{true}$$ and $$Y_{predicted}$$ and gives the area under the curve based only on these. How is this possible? It seems you'd need multiple sets of $$Y_{true}$$ and $$Y_{predicted}$$ coming from different forms of the model (i.e. trained with different parameters) in order to get multiple $$(P(F_P), P(T_P))$$ points to estimate the area under the curve.

I'm clearly not understanding something here. What is it?