If a skill were repeatable a player would be able to do it every time. That's why I say that throwing a baseball and swinging a bat are repeatable skills - not with the same accuracy, but the skills to throw and swing are repeatable. Statistics have proven that some players are better at striking the ball squarely than other players which surprises me given that they're trying to strike a moving sphere with a cylinder but their ability to strike it squarely repeatedly isn't a skill anyone has. More frequently, yes. Repeatedly, no.
As to BA & BAPIP, I know from personal experience (I know, but still....) that when I stepped into the batters box I'd always look at the defensive alignment. I found that on those times when all I could see was fielders I wasn't very successful at getting a hit but when all I could see was grass I was very successful. Call it mental, call it what you want, but it's the way it was.