based on or based off
Before reading this blog you should go back to the blog profit from, profit off, profit off of which follows a similar path.
Particles are the little words that we used to class as prepositions. Goodness knows what they are called now. When they are used in conjunction with verbs, they fuse with the verb to create a compound verb with a new meaning. They are slippery little things. We turn the lights off but in some South-East Asian Englishes they turn the lights up.
There are many instances where different language communities have made different choices about what is the appropriate particle to use with a particular verb. We may think it is logical to base a new thing on an old thing, the old thing providing support for the new. We may not only thing it is logical but we think it is proper because base on is a collocation we inherited from British English which we all know is the one true English. So when the Americans say base off we flinch and look disapproving. (Quite a lot of Australians are using base off as well).
But the most severe look of disdain is saved for base off of which we all know is wrong. Language conventions being as ad hoc as they are, it is no surprise to find that this formulation used to be ok in British English (a long time ago) and is still ok in American English. As the conventions stand in Australian English at the moment, off of is beyond the pale.