"Based on" is standard English. You can use it in any context, both formal and informal. "Based off" and 'based off of" are only used by speakers of American English. They are informal AmE variants which have the same meaning.

Hi Sylvia, "based on" is a phrase stating/referring to a situation; [Macmillan dictionary: to use particular ideas or facts to make a decision, do a calculation, or develop a theory. Example: The plot of this story is based on the women of the 1800's. I will definitely vote this man based on his merits. However "based off" could have been used in a spoken language and is informal, refrain from using it. Have fun!

I don't think Americans always use "of". Based off (of) his body language, I don't think he got the job.

I suggest that you never use this in written articles. As mentioned by Su Ki, It Is only informal American English. I know it was someone else's article, but, quite honestly, the writing that is 'out there' on the net and even in 'famous' books like Life of Pi...makes my hair stand in end, it is so poor!

I know what "based on" means, but I have never heard someone say "based off of".