# Area under the ROC curve

> The area under an ROC curve.

The area under an [ROC curve](https://wiki.g15e.com/pages/ROC%20curve.txt).

A number between 0.0 and 1.0 representing a [binary classification](https://wiki.g15e.com/pages/Binary%20classification.txt) model's ability to separate [positive classes](https://wiki.g15e.com/pages/Positive%20class%20(machine%20learning.txt)) from [negative classes](https://wiki.g15e.com/pages/Negative%20class%20(machine%20learning.txt)). The closer the AUC is to 1.0, the better the model's ability to separate classes from each other.[^1]

AUC ignores any value you set for [classification threshold](https://wiki.g15e.com/pages/Classification%20threshold.txt). Instead, AUC considers all possible classification thresholds.

![AUC](https://developers.google.com/static/machine-learning/crash-course/images/auc_abc.png)

## Formal definition

AUC is the <probability> that a classifier will be more confident that a randomly chosen positive example is actually positive than that a randomly chosen negative example is positive.[^1]

## Examples

A spam classifier with AUC of 1.0 always assigns a random spam email a higher probability of being spam than a random legitimate email. The actual classification of each email depends on the threshold that you choose.

## See also

- [ROC curve](https://wiki.g15e.com/pages/ROC%20curve.txt)

## Footnotes

[^1]: https://developers.google.com/machine-learning/glossary#auc-area-under-the-roc-curve