Is there any way to install MPV without having to compile it from source?
Debian offers the mpv package since Jessie, and it's available on testing/unstable, so it should be included in universe repositories, as Ubuntu imports unstable repositories for non-LTS releases, and testing for LTS. Just make sure you have the universe repository enabled, your package lists updated, and run sudo apt-get install mpv.
This ppa seems to work (I just tried it): https://launchpad.net/~mc3man/+archive/mpv-tests/
There is also a bug https://bugs.launchpad.net/ubuntu/+bug/1208633 and I hope they sync it for Trusty, it really looks promising.