In this Wired story that is about exploding old sports myths, the answer is ... "very."
Caption, on Wired: When a hitter has a 3-0 count, the umpire becomes much less likely to call a fourth ball, expanding the strike zone considerably. Conversely, when a hitter is facing a 0-2 count, his strike zone will shrink.
The graphics illustrate that difference.
That said, this also is another reason for games taking longer than they need to. Umps, either walk the batter or punch him out!
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