There is no such study, it is based on Dr. Deming's experience.
"I should estimate that in my experience most troubles and most possibilities for improvement add up to the proportions something like this: 94% belongs to the system (responsibility of management), 6% special."
Page 315 of Out of the Crisis
Getting hung up on the figure 94% is a mistake. His point was that you improve performance going forward by improving the system not blaming people. His two books provide background and the thought process involved behind why we are failing to manage better. Changing the people, while leaving the system in place, most often doesn't help.
Variation does confuse people sometimes. The same mistake as say yelling at someone any time results are really bad. Most likely results will get better. Not because yelling helps but essentially regression to the mean. So you can move people out after really bad results and things get better. Of course, most of the time they would have gotten better if you left the people there (and did nothing or yelled).
Even when the person did totally mess up, why did the system allow that? Why did the system put that person in a place where they were not qualified? Answering and fixing these types of questions would help improve the system. Yes, occasionally the answer might be Joel was hired sensibly, managed and coached sensibly but he just became a complete jerk and won't respond to coaching and this is only his fault. But normally that won't be the case, the even when the person seems nearly totally to blame (and that isn't even a very common situation - normally there are obvious weaknesses in the system that put them in the place to fail and will likely put anyone else in the same place in the future).