How can I find out what version of Debian a particular version of Ubuntu is based on?

Ubuntu releases aren’t based on Debian releases. During the development of an Ubuntu release, packages are imported from Debian unstable, until the Debian import freeze (in the past, LTS releases imported from testing, and this is what the linked wiki page still suggests; however looking at my packages shows that 18.04 is importing packages from unstable). This means that a given Ubuntu release will have non-Ubuntu-maintained packages in whatever version was in Debian at the time of the import freeze (barring explicit sync requests); but that doesn’t match what the next release of Debian will contain.

So trying to tie a release of Ubuntu to a release of Debian would just end up being misleading.

You can look at the contents of /etc/debian_version to see the Debian codename of the version (under construction) from which packages were pulled; you can also match Debian import freeze dates from the release schedules (for example, Artful’s, Bionic’s, Cosmic’s, or Disco’s). You’ll see from this that the same Debian release feeds multiple Ubuntu releases (e.g. Stretch, which ended up being Debian 9, fed Xenial, Yakkety, Zesty and Artful; Buster, which will end up being Debian 10, fed Bionic and Cosmic, and is feeding Disco), with quite different package versions each time.

Ubuntu normally imports packages from Debian unstable until the "Debian import freeze". For earlier LTS releases they chose to import from Debian testing instead but nowadays all releases (both LTS and non-LTS) import from unstable. You can find the date of the "Debian import freeze" by looking at the "release schedule" pages. For example according to https://wiki.ubuntu.com/ArtfulAardvark/ReleaseSchedule the Debian import freeze happened on the 24th August 2017.

However for many core packages Ubuntu makes their own descisions and often ends up with newer versions because they have less concerns about supporting esoteric architectures and configurations. For example at the time of Artful's Debian import freeze Debian sid had Linux kernel 4.12 but Ubuntu Artful shipped with 4.13.