THE BOOK--Playing The Percentages In Baseball

It is ridiculous that any player, let alone a great hitter like Piazza, would NEVER swing at a 3-0 pitch.  Obviously, how often you should swing at a 3-0 pitch depends on what kind of a hitter overall you are (the more power, the more often you should swing; as well, the better your “eye,” the more often you should swing).  Piazza being a power hitter (at least he WAS) should swing almost as much as anyone, although not having great pitch recognition skills and strike zone judgement should temper that somewhat).

What really should determine how often you swing at a 3-0 count is the game situation, particularly the runners and outs.  With 2 outs and a runner or runners on base, especially with a base open (or a base open and 1 out), there is no particular reason to take a 3-0 pitch, no matter who you are (power hitter or not).

Finally, game theory says that almost no one, especially a good and/or power hitter, should NEVER do the same thing (not swing in this case) 100% of the time.  That is a costly strategy.  It is like a poker player who never or always bluffs.  In fact, you cannot be a winning poker player if you always or never bluff at the pot.

Now, the reason why pitchers only throw Piazza a strike 60% of the time on a 3-0 count, even though he apparently never swings, is several-fold.  One, some of them are no doubt not aware of that (a mistake on their part and/or their catcher and coaches).  Two, pitchers can only throw around 70 to 75% strikes when they “have to.” Three, if they always threw a strike or at least tried to, presumably that would be a bad strategy for them, as Piazza would then start to swing more (and in fact, get closer to HIS optimal strategy).

I agree with your three points.  However, the questions is when does everyone realize this?  On a 3-0 count, you take 90% of the time.  So, even if you see Piazza take 100 out of 100 times, the average would have been ten.  Since pitchers only threw 60% strikes on him, it’s possible that the take-rate for that kind of ball-strike distribution would have been closer to 5%.  That is, on average, hitters swung 10% of the time on 3-0, given average ball-strike distribution.  With only 60% strikes being thrown to Piazza, pitchers might have been deathly afraid of him, and so, Piazza taking 100% of the time was acceptable.

If the pitcher alters that strategy (say pitchers follow the geniusus like Maddux or Moyer, who in my data, had the lowest ball-rate on 3-0 counts), Piazza may very well start to swing.  But, when will we know that?  All we are left with is inferences as to why Piazza swung at a pitch, and why the pitcher threw the pitch he did. It’s definitely something exciting to work on.

Carlos Delgado, as I’m sure others, keeps a PA-by-PA log of his atbats.  If only one of these guys who donate their logs to the sabermetric community.  It’d be an archeological finding that would be explored for years.  If Greg Maddux has such a diary, I’d be in heaven.  Or Iowa.

The answer to your question is what game theory is all about.  You first estimate whether the player you are playing against is going to use an optimal strategy or not.  If he is, then you use one yourself, and that is the end of that.  If you think that he is not (using an optimal strategy), which is often the case in baseball, then you adjust your strategty accordingly, making sure that you don’t go so far as to cause your opponent to start playing optimally.

No matter what your strategy, you have to make sure that you randomize your decisions.  So there is not really a, “At what point do I start doing X or Y?” You first guesstimate your opponents’ overall strategy, you then establish yours, and you randomize from there.  If you find out something different about your opponent, then you adjust the “mean” of your strategy, but it is always randomized.

One thing I forgot to mention is that there are some things that are dictated by a player’s “comfort” I suppose.  If Piazza is simply not comfortable ever swinging at a 3-0 pitch and if he does, he is not likely to have the requisite success, then he should not be forced to do so.  Of course, that is probably not the case.  He should be taught/told when to swing and how often versus the various pitchers.

Along with many other things, we could add several wins to a team by teaching them about game theory and how to use it to their advantage.  Some managers do it naturally and some do not.  For example, that is the essence of the surprise bunt or no bunt and some managers do it quite well.  Other managers are so horribly predictable when it comes to the sac bunt, that it is painful to watch.  IMO, there is nothing sadder than watching a manager call for a sac bunt when the defense is expecting it and breathing down the batter’s neck.  For those of you who don’t know what I am talking about, you MUST read “The Book.”

Hi Tom,

I’ve looked at 3-0 counts myself and I wrote up what I found at the Hardball Times:
http://www.hardballtimes.com/main/article/three-and-oh/

Here’s the list of batters who I found have never swung at a 3-0
Will Not Swing on 3-0
Name          Counts  Takes   BB   Swings 
Vizquel       187     185     57      0  
Eckstein      156     153     47      0  
Piazza        146     142     70      0  
Matthews      128     124     40      0  
Womack        120     118     35      0  
Hinske        120     117     41      0  
Vina          105     103     42      0   
(Sorry for the formatting, but don’t know any way
to improve it).
I actually have pitchers throwing almost 50% balls to Piazza on 3-0 (70 walks in 146 situations).

-John

MGL, I agree that tactical training on hitting approach could be a huge boon, and is probably the best place to be able to gain a bunch of wins.  I believe it’s the pot of gold yet to be unearthed.

John, that’s a great piece of research.  You will find that if you do the flip side (look at it from the pitcher’s perspective), you will see some fascinating results as well.  In the years I covered (unpublished), Maddux and Moyer were the frontrunners in terms of not throwing balls on 3-0 counts (low 20%).  I seem to remember Ryan Dempster being pretty lousy at it (high 40%).  I would say, with only doing the bare minimum research, is for most pitchers to emulate Maddux and Moyer’s approach to pitching.  Probably Schilling too.

Among the leaders that John published are a bunch of unscary hitters (Eckstein, Vizquel, Womack).  And they get a called ball 30% of the time.  In situations when a pitcher must throw a strike (3-0 count), and against hitters who won’t really make them pay for not being too careful, they still can only throw a strike 70% of the time.  Pretty sad.  (Of course, he can bump that up to 90% if he throws it down the middle, and takes a little off, but then even these three guys can hit it deep.)