I notice that Americans under the age of 30 are now saying “based off of” instead of “based on.” I Googled to see if that was a trend and found this handy graph by Ann Curzan:
In published books, “based on” still outnumbers “based off of” by a ratio of 100,000:1, but “based off” has risen (from zero instances) since ca. 1980. Of course, books do not provide a representative sample of all communication, since young adults publish relatively few of them, and young authors tend to be copy-edited by older people. In speech and emails, “based off of” is clearly becoming more common.
I personally prefer “based on” because one preposition is neater than two in a row, and the metaphor makes more sense if something is on rather than “off of” a base. I concede, however, that language evolves and there is nothing sacrosanct about which prepositions follow each verb. (And if I’m going to complain, the use of “around” to indicate a topic seems worse.)