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!

Be careful with the median for performance metrics! Robustness to a small number of outliers is a good thing in most cases, but if you use the median a method may look good that in fact gives you a bad result in, say, 30 or 40% of the cases, and that's mostly not appropriate. I have used one-sided upper 10% trimmed means in such cases (probably not implemented in standard packages either) to express that I'm happy if I can have a good fit in 90% of the cases even if up to 10% predictions (or whatever performance you are measuring) are bad, but I don't want to tolerate more than that. It depends on the specific situation though.
Other than that, in principle your idea makes some sense, and the fact that it isn't implemented anywhere (or at least not where you looked) could be explained by the fact that many people don't think very much about the specific performance metric and are happy with what is available by default, which is often motivated by certain mathematical considerations that may be rather irrelevant for the application in hand. Many fairly simple but nonstandard things that can be useful in a certain situation are not implemented in standard packages. It's always good to question ones own ideas, but the bare fact that it isn't implemented doesn't mean there's something fundamentally wrong with it.
By the way here's something we've written some time ago: Some thoughts about the design of loss functions
