That's a good thread you bumped, thunder.
To summarize and translate that thread into batting average terms, you might put it like this:
You have to separate the expectation for the whole season from the expectation for one at bat. There are way more factors than this, but let's say McHenry has a 35% chance of getting a hit every time he comes to the plate. Each AB is it's own, separate event. The simulated average he compiles throughout the season is nothing more than the culmination of all the 35% chance-of-hit ABs he had throughout the season. Even if he's batted .175 in his first 200 AB, though that was an unlikely and unlucky average, it has no bearing on AB# 201 - he still has a 35% chance of getting a hit. The expectation wouldn't be that he'll hit .525 in his next 200 AB to even it out, it's still that he'll hit .350 over the next 200 AB.