A batter's surest wish, in any batting moment, is to know what pitch is coming. It helps greatly to know the standard logic for when pitchers throw what. In the bigs, for the most part, batters do know this—it's just that the damn pitchers and catchers know some stuff too, etc.
Statistically and logically, certain ball/strike counts predict fastballs, and certain counts are more likely to bring curves (changeups, sliders, what-have-you). The keys here are predict and likely, because you never really know, do you, until a pitch is thrown. A really bad pitcher (or catcher) may not know when to throw what, so all bets are off. A really good battery breaks the logic in winning ways, keeping batters off-balance and guessing wrong.
Regardless of who knows what, in most at-bats at all playing levels a hitter faces a pitcher who has a fastball and something else, and there's a logical basis for guessing pitches:
Batter ahead in the count: 1-0, 2-0, 2-1, 3-0 & 3-1.
These are hitter's counts. Look fastball. The fewer strikes on the batter, the more he's looking for a pitch only in his sweetest little zone.
Batter behind in the count: 0-1, 0-2 & 1-2.
Look breaking ball or off-speed. Watch the pitcher for patterns: what is he doing to your teammates when he's ahead in the count? Look to hit anything in the zone (that is, the umpire's zone — you gotta know that, too).
Neutral counts: 0-0, 1-1 & 2-2.
On these counts, any pitch may come. You can watch a pitcher for patterns — most obviously, the first-pitch fastball — but at nothing-nothing, one-and-one or two-and-two, it's up in the air. Expect everything. At no count, the hitter should have a very small and strict zone; at two-and-two, he's protecting the whole thing.
With runners in scoring position, neutral counts go fastball.
It's another advantage to the hitter in these situations, and good rbi men know this. They don't feel pressure with men on, they let the pitcher feel it. He's likely to go with his best in these situations. Very likely. And for most pitchers, that's his fastball. Seeing this logic makes a good hitter more comfortable and quickens his bat.