Finally, this brings us back to the area under ROC curve. The AUROC visualizes the relationship between the true positive rate, the false positive rate, and the probability threshold of your model. As you lower the probability threshold from left to right, your model makes a greater number of positive predictions increasing the true positive rate and the false positive rate.

What would the AUROC look like for a perfect model? A perfect model would have a 100% true positive rate at all times, a 0% false positive rate at all times, and 100% confidence in every prediction.

If the model is always 100% confident in every prediction, it doesn't matter where you set the probability threshold. The true positive rate and the false positive rate will never change. The AUROC of a perfect model would look like this red line. See how the area under the perfect ROC curve is greater? That's why it's called the area under the ROC curve, AUROC. The area under the ROC curve of a perfect model is a score of 1.0 for the true positive rate multiplied by 1.0 for the false positive rate, which is equal to 1.0 or 100%, kind of like an R squared of 1. The better your model, the closer its AUROC will be to 1. The AUROC of a completely random model would be 0.5, meaning that you'd be just as well off flipping a coin.