As the title reads what is the difference? Plotting the ROC w.r.t probability scores gives the stair cased version.
But in my opinion I find that using binary decision is better because the ROC curve is just a summary of the different confusion matrices w.r.t different thresholds. And the confusion matrix shows the binary decisions.
Is their an advantage or certain situation where plotting the ROC curve with the prob.scores is better than the binary decisions?