how many pitcher vs. batter at bats are significant?

[Triumph36]

I was thinking more about this today - I can see it now in our sabermetric future:

"Coach, why am I out of the lineup?"
"You're 0 for 24 against this guy."
"But my stats haven't even regressed to the mean yet!"

24 at-bats is not long enough for we, the observers of statistics, to make a judgement. However, it's plenty of time for batters and managers to make a decision, and this is where statistical analyses break down - we are not dealing with randomized events; a deck of cards, the location of an electron - we are dealing with people. Batters are aware of who they can't hit, and pitchers are aware of guys who can't hit them. Saying these things don't have any effect means one of two things - it's unquantifiable, so it's unimportant, or all that stuff cancels out in the end so it doesn't show up in the statistics. I have a hard time believing either position.