We used to say “based on” when something (an idea, a film, a TV show) arose as the result of the existence of something else, or was built on a foundation of something else. A movie is “based on” a book, for example. We still should say “based on.”
Not sure where “based off of” comes from, but let’s put it out of its misery posthaste (that means right away). “Based off” doesn’t even make sense, because developments can only be based “on” something. Things only rest on other things, not off them. If it were based off, it would go flying from its foundation.
Perhaps the TV term “spinoff” is partly responsible for this. But a spinoff is still “based on” the original series.
Off with “based off of”…at least based on everything’ I’ve read.