Tonight’s Tigers game has been postponed until Thursday on account of rain in D.C., so I thought I’d take this opportunity to consider one of Rod Allen’s favorite topics of conversation: swinging on a 3-0 pitch. This is a topic of interest for me because it exists at the intersection of two things I think are really important in baseball: plate discipline and strategy.

Let’s set the stage for a moment. Generally speaking in baseball, when a hitter gets himself into a 3 balls, 0 strikes count, the manager gives him a “red light” indicating that he is instructed not to swing at the next pitch because the pitcher has recently had trouble finding the zone and the batter should accept a free pass if the pitcher is offering it. If you take a strike on 3-0, you still have two pitches to choose from while the pitcher still has no margin for error. It’s a good percentage play. A quality major league player will recognize the value in accepting a free pass and will take the pitch.

But 3-0 pitches are very often fastballs right down the middle because pitchers are trying not to walk you and that pitch is presumably the easiest to throw for a guaranteed strike. That makes sense, except that it makes no sense at all. If the pitcher had the ability to control his pitches that well, he shouldn’t have gotten behind 3-0 in the first place and even if he grooves one on 3-0, he’s going to go back to nibbling at the strike zone on the next pitch. Either the pitcher shouldn’t have gotten into a 3-0 count or he shouldn’t care about issuing a four pitch walk if he is just going to issue a five pitch walk twenty five seconds later.

It’s a pretty standard paradigm. If you get behind a hitter 3-0, you usually groove a fastball. If a hitter is ahead 3-0, he usually takes. Except when he doesn’t.

Rod Allen, the Tigers TV color man, has made a lot of this during the first few weeks of the season because he thinks really good hitters should attack the 3-0 pitch more often because it’s usually such a good pitch. His logic makes sense. If you know a straight fastball is coming, you can probably do significant damage that might be better than a walk. There is a risk in swinging, in that you might make an out, but if you get exactly what you are expecting, it could be beneficial to swing. Rod tells us Cabrera and Fielder have the green light 3-0, but don’t like to swing too often when they get it. Which makes sense given the risk while also knowing if they get ahead 3-0, they’re probably getting walked soon anyway.

But maybe we have this wrong. I’m a huge proponent of plate discipline and taking the base on balls, but maybe hitters should be more aggressive on 3-0 pitches. After all, so many of them are batting practice fastballs waiting to get crushed. Is there an inefficiency here that hitters can exploit?

Let’s start with some basic data. Tigers hitters have been in 65 3-0 counts so far this season and 39 have ended in walks. Of those 65 plate appearances, 28 ended after the fourth pitch. 25 of those were walks. What this indicates is that Tigers hitters have put the ball in play just three times in a 3-0 count. I don’t have access to the data, but I think we can probably assume the Tigers haven’t swung an missed at a 3-0 pitch this year, but there may be a foul ball in there somewhere and we have to ignore those away.

In those 3 plate appearances in which the Tigers went for it 3-0, here are the numbers. Obviously, they are gaudy: .667 batting average, 1.667 slugging percentage (.964 OBP when you leave the walks in). A three run homerun by Cabrera, a single by Peralta, and an out by Prince.

Notice the pitch sequence during the HR at bat to Cabrera (I mean, what do you expect here?):

But let’s take this a little further and go back to the 65 3-0 counts in general. If they walked 25 times on 4 pitches and put the ball in play on 3 others, then there are 37 at bats that got to 3-0 and then went at least 5 pitches. So 37 times, the Tigers took a 3-0 pitch for a strike. What happened after they did that?

After the Tigers got to 3-0 and took the fourth pitch for a strike, they went on to hit .391/.595/.609. Not bad at all. It’s not better than when they swing on 3-0, but obviously a sample size of 3 in the first analysis isn’t that predictive. What I think is interesting is the on base percentage. If you get to a 3-0 count, your odds of getting on base at any time during the at bat are .769. If you take the next pitch for a strike, it drops to .595. In other words, if you take a 3-0 strike, you’re sacrificing a ~17% change of getting on base to avoid the risk that you’ll make an out. That’s an interesting trade off to make given that you have a .667 batting average swinging 3-0 so far this year. (If you take out the intentional walks, which you obvious aren’t swinging at, the point holds)

So this means we should think about swinging on 3-0 more often because taking a 3-0 strike, which should be easy to hit, reduces your chance of getting on base pretty substantially, right?

Well, not exactly. This could be a small sample illusion. Last year, the Tigers hit .250 swinging on 3-0 and .192 in at bats that started 3-0. In 2011, it was .250, .232. What’s going on there?

I’m not really sure. The Tigers put 3-0 pitches in play just 4 times in 2012 and 8 in 2011, so it’s not like the sample size is much different than this season. The number of ABs that got that far is much bigger in the two complete seasons however. But the on base pattern does hold in larger samples. It’s around .700 when you get to 3-0, but it drops down substantially when you take a strike.

Essentially, if you get into a 3-0 count, taking a strike substantially changes your odds of getting on base. If you see a strike on 3-0, maybe you should swing. If you’re looking for exactly what you get. There is a chance to out fox your opponent. Pitchers expect you to take, so they groove it. If you swing, there is an above average change you will get a base hit because you know it’s a fastball, but there is also a good chance it will give pitchers pause when throwing you 3-0 pitches in the future because they don’t want to throw a meatball if you’re swinging. Which means in the future, they won’t do that so much and you’ll get more walks 3-0 and won’t have to continue the at bat into counts in which you have worse odds.

It’s kind of fun to think about. There is an optimal rate at which you should swing 3-0 and I don’t think we’re there. You can’t swing too much or you’ll end up on base less overall, but swinging too little also huts you because your odds of reaching base 3-1 are much worse than 3-0 and you’ve also sacrificed a chance at a 3-0 hit.

So next time Rod talks about Cabrera or Fielder swinging 3-0, think about it a little more carefully. There is probably good reason to swing 3-0 at a higher rate. Of course, no one wants to make an out on a 3-0 pitch, so hitters probably won’t be doing this any time soon.