# Dividing the MAE by the average of the values

I would like to parse the MAE (Mean Absolute Error) to a percentage value. I know there is the MAPE (Mean Absolute Percentage Error), however it has some drawbacks as going to infinity if one of my values is zero. I had the idea of dividing the MAE by the average of my values, but I could not find any reference on that.

The formula I intended to use is the following, having $$y$$ as the real value and $$\bar y$$ as the prediction:

$$\frac{MAE}{AVG(y)} = \frac{\frac{\lvert y_1 -\bar y_1\rvert + \lvert y_2 -\bar y_2\rvert}{n}}{\frac{\lvert y_1 + y_2\rvert}{n}} = \frac{\lvert y_1 -\bar y_1\rvert + \lvert y_2 -\bar y_2\rvert}{\lvert y_1 + y_2\rvert} = \sum{\frac{\lvert y -\bar y\rvert}{\sum{\lvert y\rvert}}}$$

Using this, the percentage Error could only get to infinity if all y values are 0 which will never happen in my dataset. Please note that I cannot have negative Values for $$y$$ and $$\bar y$$ in my dataset, so the difference will always be the true difference.

In the end I want to say for example: "the average error in my prediction is 10%"

Does anyone have any sources that this was done before? Is there some serious drawbacks to it or do I overlook anything?