National treasure David Laurila speaks with Don Mattingly on hitting. It’s a great interview. Here’s a bit on batters having a two-strike approach:
Laurila: You mentioned Derek Jeter. Can you elaborate on his thoughts?
Mattingly: “Derek talks about how we need to have some type of two-strike approach. There are times when you really need to put a ball in play. That’s when you need to at least have that in your bag. When you talk about two different swings… two-strike approach is more of a thought-process than it is a change in the swing. You might shorten it a little bit, but it’s more of a thought-process that helps you to put the ball in play.
“What’s really happened over the years is [a philosophy of] ‘Never get away from your best swing; always keep going for it.’ That’s probably good for certain circumstances, but there are other ones like, ‘Man, we’ve got second and third, and they’re playing the infield back, and all I need is a groundball to the right side to get a run, and to get a guy to third with a chance for another run.’ Instead, you get a strikeout and a pop up, and you’re out of the inning.
“Derek is definitely a believer in putting the ball in play, being able to move runners, being able to add on a run. But you don’t totally go away from some of the things that the numbers tell you will score you more runs. You listen to both sides. There are times for everything [and] never one absolute way to do it. You need to add some common sense to the whole thing.”
FanGraphs.com
The whole interview is worth the read, espeically the parts about how Mattingly developed as a hitter.

