Is Median Absolute Percentage Error useless? I'm working on a project focused on pricing houses.
Looking online I see a lot of works and companies providing the performances of their model using the median instead of the mean (see for example Zillow).
And to me this makes total sense, since its a statistic less influenced by outliers (in my scenario big and particular houses).
Also since I would like to have a greater interpretability of the performance of my model I used the Absolute Percentage Error, instead of the squared error.
In the end what I ended up using is the Median Absolute Percentage Error, and with my surprise I discovered that is not a common metrics, it doesn't have a wikipedia page, few sites provide an explanation of what it is, sklearn doesn't even have it as a metrics inside the sklearn.metrics._regression.py module.
And my question is: why?
Fixing it was a no brainer, really 2 line of code and I created my own version of it and I can easily run my model with this new metric, but I was wondering if maybe I'm missing something, like if its completely useless or maybe there are other metrics that works better.
If anyone could give me some insights that would be great!

The potential issue with absolute percentage error is that it is not symmetric with respect to over and underestimating. If you overestimate by a factor of 2 you will get an error of 100%, if you underestimate by a factor of 2 you will get an error of only 50%.
If you model is so good that most estimates are very close to the true value this effect becomes relatively small but if some estimates are way off this will impact your model choices. A model that occasionally make severe underestimates but no overestimates will look better than a model that occasionally makes severe overestimates.
Whether this happens in your case and if it does whether it is a problem depends on your specific situation but it is something to be aware off when looking at absolute percentage errors.
