ROC score for binary classification problem, where the predictions are either 0 or 1

For problems with binary classification, roc auc curve or roc auc score is often used to rate a model. But does the ROC ACC make sense in the context of a binary classification model that outputs only 0 or 1 for each observation (so no probability between [0,1] but only 0, 1)

• What is ROC ACC CURE and ROC ACC? Or is it AUC? – gunes Nov 10 '19 at 18:27
• @gunes sry, roc auc score – Felix Ha Nov 10 '19 at 18:35

If the classifier, at its final step, doesn't produce a probability, and only makes $$0,1$$ predictions; ROC doesn't make sense because in order to draw a meaningful curve you need to sweep a threshold value. If all the values are either $$0$$ or $$1$$, sweeping the threshold makes no changes doesn't change the assigned classes, and has the same TPR, FPR for all the intermediary thresholds.