At Bat

I have a theory about the baseball statistic "at-bat." An at-bat is any time a batter comes to the plate, sees some pitches off a pitcher, and either strikes out or puts some pitch in play, other than as a sacrifice bunt or a sacrifice fly. Notably, it excludes walks. But colloquially, we don't make this exclusion. Actually, we don't make a lot of the other exclusions either. Dustin Pedroia just drew a great walk off Mariano Rivera, and the NESN announcers said that he "had a great at-bat." Technically, no he didn't, because he didn't have an at-bat at all. He had a plate appearance. I have a theory about this divergence between the colloquial usage and the official definition: originally, all walks were considered intentional walks. This emerges from considering what feels to me like the organic evolution of the rules of baseball. The point, originally, was for the pitcher to throw something for the batter to hit, that the defense would then field and we'd see whether the batter reached base safely etc. But there were some difficulties: what if the batter hit the ball straight back? You couldn't expect a defense to cover a whole 360 degrees. So we get foul territory. What if the batter just kept refusing to hit what the pitcher was serving up, even though it was perfectly hittable? The game could go on forever if the batter could be infinitely selective, so we get the strikeout: If you see three hittable pitches that you don't demonstrate that you could hit, you're out. Conversely, though, it's unreasonable to expect a batter to swing at a pitch above his head, or behind his back, so we require pitchers to throw the ball to a certain area where the hitter's expecting it and can plausibly reach it. If the pitcher fails to do that enough times, the batter gets first base. Simple, right? And when you tell it that way, the base-on-balls feels very much like it's what happens when a pitcher passes on facing a given hitter. The point is to get a ball in play for the defense to handle, but the pitcher elected not to give the batter anything to hit. The batter didn't get a chance to do the thing batters are supposed to do, namely to hit the ball. In a sense, even though he stood in the batter's box and faced some pitching, the batter didn't get a chance to be truly "at bat."

This comes off very differently once batters start trying to draw walks, and pitchers start trying to get strikeouts. Now it feels like the base-on-balls represents, not a decision by the pitcher to pass on facing a certain hitter, but a victory for the batter over the pitcher in their confrontation. The batter came to the plate with the intention of reaching base, the pitcher had the intention of getting him out, and precisely one of them succeeded. It wasn't the pitcher. Maybe that was because the pitcher was trying to throw strikes, and failed; maybe it was because the pitcher was scared of the batter, and really did pitch around him; maybe it was a thirteen-pitch at-bat with half a dozen foul balls with two strikes, where the pitcher was throwing a decent percentage of pitches for strikes but eventually four balls just piled up. Any which way, it wasn't an avoided confrontation, it was a confrontation, and one side won it. That feels very much like a turn at bat, doesn't it?

Now, what isn't an at-bat is an intentional walk. So the way I'd revise the at-bat statistic would be to include unintentional walks only. Just add them in, to both the numerator and the denominator of the revised 'batting average' statistic. Perhaps also add in sacrifice flies to the denominator; I'm unsure about that one.* Sacrifice bunts should definitely be excluded and intentional walks should definitely be excluded, as they represent cases in which one side or the other genuinely wasn't trying to win the confrontation. I'm not sure what to do with hit-by-pitches. For the pitcher they feel very similar to walks: you let a batter reach first base, but without the dangers associated with a single on a ball in play of runners taking extra bases etc., because of control problems. For the batter, though, they feel quite different: if you draw a walk, it means you matched wits with the pitcher and came out ahead. If you get hit, well, he just plunked you. Certainly it is a skill; Chase Utley's been hit in nearly 3% of his plate appearances, while Jose Reyes gets drilled about 0.1% of the time, and not since 2010. And it clearly does represent a success in the whole not-getting-out thing. But, I dunno... ideologically, or something, it feels like we shouldn't be treating getting hit by a small hard object thrown very fast as a laudable accomplishment and something players should be developing a talent for.

So I think I'd redefine the at-bat as AB + BB - IBB + SF, where AB represents at-bats as currently defined. Batting average, then, would be (H + BB - IBB)/AB', where AB' is the new formulation of at-bats. This is, I think, a good measure of the proportion of the time that a hitter prevails when he enters a confrontation with the pitcher genuinely trying to reach base and the pitcher genuinely trying to prevent him from doing so. This is basically just on-base percentage minus the intentional walks and the hit-by-pitches, reflecting the fact that I do think on-base percentage, i.e., let's pay attention to walks, is basically superior to batting average as currently defined, i.e. let's not, but also the fact that IBBs and HBPs do feel different from the hitter's perspective, like they weren't really given a chance to compete with the pitcher. Now, we should also care about on-base percentage as such; for instance, a large part of Barry Bonds' skill was intimidating the opposing pitchers so much that they rightly chose to give him first base outright rather than even attempt to face him (even once when it meant forcing in a run!). Perhaps we might also want to expand the on-base percentage calculus, penalizing batters for sacrifice bunts, double plays grounded into, and being caught stealing, to reflect an overall "how good are you at not burning through your team's limited supply of outs?" metric. Including sacrifice bunts would mean that we'd be penalizing players for things that are deliberate strategy, but if AVG' became closer to what OBP is now, it would presumably regain much of its discarded importance, and OBP could become less of an "up is always better" thing and more of just a descriptor. High AVG' would always be desireable; a high OBP' - AVG' gap would be nice, but not particularly essential, and not necessarily all that much under a player's own control.

Also, I'd definitely like to see statistics such as "Walks per 9 innings pitched" for pitchers redefined to include hit batsmen. I know that cuts in precisely the opposite direction from how I want to treat HBP's for batters, but as I said, I do think it feels very different for pitchers than it does for hitters.


*On the one hand, a sacrifice fly is not deliberate in the way a sacrifice bunt is, i.e. you'd prefer to have hit that fly ball a bit harder or on a slightly different angle and have had a hit or a home run instead. On the other hand, it is definitely true that players will try to maximize their chances of getting at least a sacrifice fly, i.e. some kind of fly ball to the outfield, at the expense of overall on-base percentage in certain situations. On the third hand, this can also happen in situations where a ground-out will score a key run, and we don't give hitters credit for sacrifices when they get RBI ground-outs. It's a whole bloody mess, and I'm inclined to say that the batter did a thing which, from their point of view, ideally would've resulted in their reaching base, even if they might've been uncommonly satisfied with a particular outcome that did not include their reaching base, so let's count it as an at-bat. I think you see dugouts treating players who've just had an RBI ground-out very similarly to players who've just had an RBI sac-fly.