Based on the evidence, the phrase "based on" is getting challenged by the phrase "based off."
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.
"Based off" has been on the rise since around 1980. The numbers are still small, so people who prefer "based on" are in good shape. According to Google Books, the ratio of "based on" to "based off" is approximately ten thousand to one.
The threat may be distant, but "based off" is rising rapidly, which may be why Curzan's colleagues are noticing it in their students' writing and speech.
Honestly, we can make logical arguments for both phrases. "Based on" makes sense, because you're building something on the base or foundation. For example, you might say, "His argument was based on research by a noted scientist."
However, "based off" also has a foundation, but now you're using it as a jumping "off" point. In other words, you're launching off of it to the next point. For example, "Based off today's weather report, I don't think we should go to the beach."
We should point out that prepositions, which are notoriously idiomatic in English, don't actually have to be logical. Think about the phrase "as a result." Why not "in a result," "for a result," or "by a result?" The answer is because the idiom is "as a result."
This is often how prepositions work. They're fixed phrases, but those phrases can change over time. For now, Curzan thinks we should just let "based on" and "based off (of)" sit next to each other in variation.