There is probably no known answer to this question, but it would be interesting to know, so it’s worth asking just in case.
What percentage of pitches are fouled off?
This is of interest because it permits assessing the advantage of pre-1903 batters (when fouls were not strikes.)
I don’t mean any disrespect to the OP, but this phrase actually made me laugh out loud.
Baseball is probably the most well-studied sport there is; every single pitch and its outcome are recorded, analyzed, sliced, diced, and analyzed some more. I am quite certain that the answer to the question not only known, but known to a precision of several decimal points, and could be broken down per year, per team, per age and handedness of batter, day vs night games, righties vs. lefties on the mound, or pretty much any other way you want to slice it.