According to this article
http://www.html5rocks.com/en/mobile/high-dpi/
The magic number seems to be 150.
Dividing the physical ppi by the ideal ppi of 150, gives the device pixel ratio.
E.g. a device with 445ppi would have a dpr of 3 ->> 445 / 150
The simple calculation seems to hold up okay for many items on this list,
http://en.wikipedia.org/wiki/List_of_displays_by_pixel_density