Trying to avoid doing a terrible job of explaning this...
As you know, one of the things about statistics (particularly with a system like Pitch F/X, that really can record *everything*) is that there's a sliding scale between sample size and accounting for all the variables. (I'd submit that the same holds true for watching somebody hit: you might see one terrible at-bat, but maybe it was just a bad matchup for the hitter, and so that's not enough to draw a judgment on.)
If you want, you can keep adding variables to see what the count is, what the number of baserunners are, the number of outs, etc. What you add in in terms of granularity you take away in terms of meaningfulness of the sample. It's a balance, and one where the judgment of the person looking at the statistics is really important. If you go too far, you end up with the absurdity of "So-and-So is 4 for 7 in the sixth inning of day games on the West Coast." That doesn't get you anywhere, and it shows a fundamental misunderstanding of how stats should be used.
On the other hand, let's suppose there's a distinct difference between how Pitcher X throws with runners on base versus the bases empty...now you're learning something, and you didn't have to watch every single one of his appearances to do it.
When you do take out all of the variables, then, yes, by the numbers lettng a strike go by on a 3-0 count will be a bad thing. (After all, *all else being equal* a 3-0 count is more advantageous than a 3-1 count.) Now, of course, almost everyone is going to take a strike on a 3-0 count. Still, that one "bad" outcome on a 3-0 pitch will be substantially less meaningful then (say) the outcome of the 3-1 or 3-2 pitch that gets hit into play.
To put it another way: taking a strike is technically bad, but much less bad than swinging at a 3-0 pitch that ends up as an out.
pup wrote:If swinging at a ball is bad, how does it account for something like O-Cab on Sunday (I think) swinging at a breaking ball that is up and out of the zone, because all he needed to do was hit a flyball to win the game?
Some stats do take into account situations like this. Are you familiar with WPA? In short, it's the change in the likelihood of a team winning the game based on the score, outs, and runners on base, without respect to the actual players in the game (cue pup and peek's

just bear with me). The point of WPA is to generally show how much of an effect a particular play had on the outcome of the game. Now, if a sacrifice fly improves the chance of a team winning the game (and it usually will, depending on how close the score is), then the player gets a positive WPA for the at-bat, even if it "looks bad" for his OBP. One of the ways you can graph a heat map is by WPA outcome. Voila: swinging at that pitch out of the zone scores as a positive result on the map, even though it resulted in an out, if the team gets a key run out of it.