Groovy Potential is the seventh track on the album Hitnrun Phase Two. Over two years earlier, however, the track was released through 3rdEyeTunes.com, Prince's own music store (the third track to be released on this website).
A 1:20 minutes preview of the track was streamed on 3rdEyeGirl YouTube account minutes before the track's release.
While specific recording dates are not known, it is assumed that basic tracking took place in early-to-mid 2012, at Paisley Park Studios in Chanhassen, Minnesota. Horn overdubs took place in late July 2012, also at Paisley Park Studios.
Michael B. Nelson has stated that the horns were recorded as a "10 horn arrangement", with muted brass and woodwinds recorded first, followed by a second pass using their standard set-up, "mostly playing off of each other but sometimes together".