Batters vs. Pitchers - Familiarity Advantage

[simdynasty]

I was wondering if anyone has data or knows of a study that has looked at who gets the advantage over time, the batter or the pitcher? In other words, if a batter and pitcher face each other 30 times in a career, was the batter more or less likely to have success in the 1st appearance vs. the 30th appearance?

Thanks for any help you can provide.

Tyson