While it is true that based on is still the universally preferred version of the expression, especially in formal writing, based off (of) seems to gain more and more popularity. So much so, that Merriam-Webster has a whole article about it that provides some answers.
While it's more common to say that something is "based on" something
else—as in "The movie is based on a book"—people increasingly say
"based off" or "based off of": "The movie is based off (of) a book."
"Based off" isn't wrong, but it's relatively new, and is likely to
sound wrong to some people.
The expression based off of is indeed new, and its use has been increasing in both American and British English, but the Americans seem to adopt it with less restraint:
M-W records the use of the expression in recorded speech since 1979 and it appeared in edited text soon after:
We don’t know why “based off” (often extended to “based off of”) is
moving into territory “based on” has occupied since the mid-18th
century, but we do know that its use is relatively new. Preliminary
research shows it popping up in recorded speech as far back as 1979:
[Coach Jack] Pardee admitted that some of the substituting so far has been based "on guesswork, calculated guesswork," because no one on his staff was certain how the youngsters would hold up under pressure. "How can you tell how a Neal Olkewicz will play?" he asked. "You have a good idea, based off what he did in practice from the start of camp, but until they play, you can't definitely say."
— Paul Attner, The Washington Post, 16 Oct. 1979
A large group of lenders were persuaded to accept price risk, political risk, completion risk and operating risks, since there were no guarantees from the sponsors and the sale price was based off the world market prices.
— Mining Magazine, November 1981
But Grammarphobia seems to have dug deeper and found an even earlier date:
While “based off” may have become more popular recently, it’s not
unseen in older writing. It’s been used occasionally since the early
1930s, mostly in trade journals. The earliest example we’ve been able to confirm appeared in a May 1931 issue of National Petroleum News:
“To consumers: … discounts are based off tank wagon price, and affect purchases of 1,000 gallons or more per month” (this notation appeared several times in column listings).
Here it is again in 1952:
“Based off 1951 figures, the proposed constitutional amendment would cut Federal revenues by $16,000,000,000 a year” (from the Bulletin of the Metal Trades Department of the American Federation of Labor).
The M-W article compares the progress of the use of base off (of) with that of another similar phrase and records its proximity in meaning:
But if the use strikes you as very new that would make good sense: it’s seen a remarkable increase in popularity in the 21st century. Interestingly, the synonymously used phrase “going off (of)” has followed a similar use trajectory. The phrase going off (of) evokes the image of moving away from information or an idea that serves as a useful point of departure. It’s likely that “based off (of)” evokes the same image for people who use it.
As you may have noticed already, the sources quoted by M-W are American, and it is interesting to see that go off (of), just like base off (of), has also been more used by the Americans and is becoming more common as we speak. So I couldn't resist comparing the evolution of the preposition off of on both sides of the Atlantic, and again we find the same result. In 2002, CAGEL describes off of, in passing, as specific to American English:
Off licenses an of phrase only in AmE (%He fell off of the wall).
Anne Curzan, a linguist and a professor of English at the University of Michigan, wrote an article about this issue in the Chronicle of Higher Education in October 2013, but unfortunately, I couldn't find a usable link to it, so I will have to use sources that quote her. Grammarphobia says:
The author of the article, Anne Curzan, wrote: “I have mentioned the construction to a few colleagues, and it’s clear at least some of them are circling it in student writing.” The use is also found outside routine classroom writing. Curzan passed along this example from the academic journal Exceptional Children (March 2012):
“For our study, the parameters used in the simulation were based off of values derived from a large empirical data set.”
As Curzan wrote in her article:
“With ‘based on’ one could argue that because things are physically built on bases, it makes more sense to say ‘based on.’ I agree: That is perfectly logical. But language isn’t always logical, and once ‘based on’ becomes as much or more metaphorical than literal, it doesn’t seem surprising to me that the preposition might shift—especially given that one can metaphorically ‘build off’ things.”
The expresion is more used by students and their linguist professors witness its force and find themselves as before an accomplished fact about which they cannot really do much :
This is an issue English Professor Anne Curzan has been hearing about from her colleagues. They say "based on" is correct, but their students tend to use "based off" or "based off of." Curzan says this is a losing battle. (Podchaser)
Grammarphobia indicates the increase in use is seen also in British English, and gives another explanation of what people might have in mind when they use it:
And we’ve found other recent examples of “based off” in academic journals, both American and British. By the way, “based off of” is just a puffed up version of “based off.” Our suspicion is that people who use “based off of” may have the phrase “on the basis of” in mind.
Grammarphobia have done their homework really thoroughly, as they quote very recent discussions among linguists about this issue, which also attribute this expression to youth:
Discussions of “based off” have come up periodically on the Linguist List, the online discussion group of the American Dialect Society, but only in the last 10 years. Writing on the list in 2006, Seán Fitzpatrick commented: “My daughters were discussing a forthcoming movie, and the 21-year-old said you had to give the auteur credit for originality, since the movie was ‘not based off a book, not based off another movie, and not based off a TV show.’ ”
Another contributor, the linguist Arnold Zwicky wrote, “it’s now very widespread.” And it’s become even more widespread since 2006. Writing on the list in 2014, the slang lexicographer Jonathan Lighter reported a sighting of “based off” with another meaning: “as a result of; by reason of; from.”
For the time being, base off (of) is defined as an American informal phrase synonymous of the still more common base on:
(US, informal) To base on (Wikipedia, WordSense)
while dictionaries like Cambridge, Macmillan and Collins have no entry for it, redirecting either to based on or to off(-)base. Surprisingly, American Heritage Dictionary doesn't record it either.
An MA (English) [not from the young generation!] says on Quora:
Some people say “based off of” where I would say “based on.” It seems
incorrect to me to say “based off of,” but I cannot offer a rule of
grammar that is violated by “based off of,” so perhaps it is a new
phrase entering the language.
while another British user (not in his twenties either) claims to be unfamiliar with based off:
I’m unfamiliar with the term, “based off”. Perhaps it’s used in US English. In British English, we typically say, “based on” - as in “Sherlock is a crime drama television series based on Sir Arthur Conan Doyle's Sherlock Holmes detective stories.”
On the same page, another British user called Charles Gray, advocates very vividly against the use of based off, though he acknowledges its "englishness" (a very interesting read which I decided not to quote, as this post has become unacceptably long.
CONCLUSION: Based off (of) is still controversial and its use seems to point to the generation gap. While older professors frown at it, the phrase seems to gain field and its "wave" will not be stopped by language correctness nostalgics. In academic writing, it may be safer to use based on (universally understood and accepted), it still feels too soon to impose base off (of). However, when those students become professors themselves, if they haven't already, we can be pretty sure that base off (of) will make its way into more formal writing as well.