THE BOOK--Playing The Percentages In Baseball

I don’t know that I love it (as Tango says) when other people write about things that I’ve been meaning to write about or at least have been thinking about, but…

I have been thinking about and occasionally writing about this for a long time.  I have even put together some experiments along the same line that I had considered discussing with some MLB teams with which I have done some work.

One of the things that needs to be done with the pitch f/x data is to see to what extent pitchers as a whole and specific pitchers randomize their pitches.  And then to see how effective randomzing pitches is versus non-randomizing, or semi-randomizing (all pitchers to some extent randomize of efectively randomize their pitches).

Some people do not understand thatwhen a pitcher throws 50% FB in an 0-2 count or 90% in a a 3-0 count, is NOT the same thing as “randomizing” those selections.  In fact, it has nothing to do with it.  It is entirely possible that a pitcher could be throwing 50% fastballs in an 0-2 count, but that you could predict what pitch he is going to throw 70 or 80% of the time (although, obviously it will be more difficult to predict a pitch that is thrown 50% of the time than 90% of the time), based on certain “markers” (last pitch thrown, baserunners, outs, the particular batter, etc.).

I don’t think I have ever said this before in public, but I believe that I have an uncanny ability to predict pitches at all counts and I would love to quantify that.  I would also love to put myself up agasint a major league manager, coach, or player.  I believe that I could “beat them” in a pitch-calling contest.

I’d pay money to watch that!

Me too!

I’m a professional poker player who plays heads up (one-on-one) poker almost exclusively so I deal with a situation that has obvious parallels to the batter/pitcher matchup daily.

I would be very surprised if game theory had much value in pitch calling.  Game theory is about making yourself unexploitable against perfect opponents.  Batters are not perfect, they have exploitable tendencies.  You can’t exploit those tendencies unless you make yourself theoretically exploitable yourself.

Anecdotally, Curt Schilling seems like someone who obsesses over finding those exploitable tendencies and his results seem to far outpace his stuff/control the last few years.

"It would be a double-blind study, because neither the pitcher nor the hitter would need to know which system called the pitch.”

Sorry, but your terminology is a little bent here. The pitcher and the hitter are both subjects in the experiment you describe. “Double-blind” means that neither the subjects nor the experimenter know until after the study which recipients or doses are part of the control group. (This would naturally be hard to accomplish when comparing intentionally called pitches to randomly selected ones, since on each trial there must be an “experimenter” somewhere who knows whether he’s calling the pitch or not.) I like the idea, though.

Ah, sorry, didn’t spot that it was a blockquote. I guess I should take my complaint over to the Times.

JB, pitching is ALL about game theory.

Double blind studies are only necessary when the researcher can influence the results of the study.  In some cases, like this one, they can’t, and therefore it is not necessary.

Wow, I just read the article.  First, the author (not the NY Times) misuses the term “double blind”.  Then he suggests using a “randomized” test to figure out when to go for it on 4th down.  Huh?  How about we use a “randomized test” (whatever that even means) to determine when it is appropriate to walk a batter (an IBB) in a certain situation.  We can walk the batter a couple of hundred thousand times in, say 200 years of college baseball, and then not walk the batter in another couple of hundred years, and see what happens.  By the year 2467, we should have our results.

Experimental blinding exists precisely because unforeseen psychological factors can have powerful effects and placebo action has to be ruled out. In principle this is more so in a psychologically sensitive environment like a ball game, not less. If the catcher were not blinded in an experiment like this, the conviction with which he put down the planned/random signs could easily taint the experiment. (In real life catchers do put a ton of emphasis on not hesitating before giving the sign.)

The rule is, you blind as many participants as you can: as you guys probably know, the gold standard in medical research is in fact triple-blinding, whereby a separate, blinded analyst does the number-crunching on the results.

JB, I see your point.  So with Wily Mo Pena, let’s say he crushes fastballs and can’t hit the curve.  No one’s saying to throw each pitch half the time, randomly, so he has no chance to accurately guess what’s coming.  I think it’s more saying to throw 90% curves and 10% fastballs, or whatever the break-even point is for matching his skills with his expectations, and just randomize how those 90% and 10% are allotted over time.

As I said in my initial post, whether you throw a certain pitch 50% or 90%, you still MUST randomly mix them up (flipping a 10 sided coin if you will for the 90/10 pitches).  This is STILL game theory!  Not only that, but while it is true that in an 0-2 count, you can throw Willy Mo 90% curveballs or changeups and you might have to throw someone else (with good discipline and pitch recognition skills) 50/50, it is also true that in certain situations for certain pitchers, you would throw 90% fastballs (or whatever) to the good hitter (like a 3-0 count when you are winning 5-0 in the 9th inning - it is probably 100% there, or it should be).  Game theory involves knowing or estimating your opponent’s strategy, be it good or bad.  I suppose if your opponent were 100% oblivious to your strategy, then technically you would not need to “invoke” game theory, but one, that is NEVER the case in baseball, and two, that is just semantics - we can still say that were are “invoking” game theory and that game theory (which is simply the analysis and determination of optimal strategies in contests whereby one’s strategy or anticipation of that strategy at least partially dictates another’s strategy) tells us that we need not ever vary from one set strategy in any given situation.

Getting back to the Willy Mo example, if you threw 100% curveballs, you have to assume that eventually he would stop swinging at the bad ones and make good contact with the good ones.  Game theory, though (given Willy Mo’s weakness for the off-speed pitch, bad judgment, etc.), apparently tells us that 10% (or whatever it is - I doubt that it is that high) is enough to keep him “honest.”

Game theory is used for virtually every pitch in baseball given the batter’s weaknesses, the situations, the pitcher’s strengths and weaknesses, etc.  But is is still game theory.  In fact, I would venture that you will not find any one pitch thrown by any one pitcher to any one batter in the same situation 100% of the time, atlhough you can probably find many examples of that in the short term (1,2, 5 or even 10 pitches).

Anyway, it is a great topic, although I think this was a weak article with weak examples given by someone who, it appears to me, is weak in this area, or perhaps just in baseball.

I guess that is what you get from an economist who teaches law?

Except for one-pitch pitchers like Mo.  Just an amazing pitcher.

In his case, and all pitchers, it’s not just a matter of speed of pitch, and class of pitch, but also location and release.

Once the optimal frequency has been determined for all the different combination of pitch parameters and contextual parameters (identity of batter, count, runners on base, leverage), then it’s a matter of selecting a random number.

Yes, to #12.  Exactly.  Even Mo mixes up his pitches as we can see from the pitch f/x article on him.  And pitchers with only 1 or 2 pitches will mix up location and perhaps velocity.  Obviously depending on your repetoire and the effectiveness and control of each of your pitches, sometimes it is better to throw a predictable good pitch (like Mo) than randomly throw one of several lesser pitches.  That is one of the things that makes for a great pitcher.  If he can throw several effective pitches with good control he can randonly mix them up in many or most counts.  That should be devastating.  My guess is that one reason why a good pitcher (pitcher with good stuff) may not be successful or not successful at times is that they throw one (more more) pitches too often or too infrequently (e.g. Sabathia in the post-season, Felix Hernandez early in the season) and/or while they throw with the appropriate frequencies, they do not randomize them (and the batter has an idea what is coming based on certain factors).

Teams do NOT look into this as much as they should (or at all).  That is one reason why the pitch f/x data is a gold mine.  It enables teams to do this.

Let me draw a parallel to poker.

All the cards have been dealt, I have a hand that can only win by bluffing and my opponent has bet.  Folding has an expected value of 0.  I am only going to bluff when I think bluffing has an expected value greater than 0.

If this is the first hand I’ve ever played with someone and my judgement is that bluffing has a negative expectation, I will never bluff.  A game theory guy might say I should bluff 15% or whatever to prevent myself from being exploitable.  I think that’s just throwing money away.

That’s not to say that I will never bluff in that spot.  If my opponent is observant he’ll see that I’m not bluffing him and adjust, in which case bluffing will become profitable.  Obviously the trick is staying ahead of the game.

There are some factors that effectively randomize my bluffing.  There is a lot more information beyond the cards and the betting that factors into my decision of whether or not bluffing is correct.  Information like my perception of my opponent’s emotional state, my perception of his perception of mine (you can endlessly level this), the speed with which my opponent bets etc.  This is all information that my opponent will process differently than me (or not process at all).  So when I process all the information and 15% of the time it adds up to me thinking bluffing is correct, my bluffing will be effectively random to my opponent but I will make more than I would had it been truly random.

That last point is very important to the baseball discussion.  In a game, the pitcher/catcher have access to a lot more information than just the batter’s name and the game state.  They also have a vast amount of experience processing and analyzing that information even if they don’t do it consciously.  This is the kind of thing Blink was written about.

The first couple of pages to the Game Theory chapter (by MGL) in The Book can be found here:

http://www.insidethebook.com/c12.shtml

J.B. I think we are all on the same page here.  We’re talking past each other a little and getting into a “war of semantics.” For example, “game theory” doesn’t “dictate” any particular strategy any more than astronomy dictates a method for studying the universe.  “Game theory” is merely the science of “math in the context of a game or contest” which can be used to optimize strategy in that game or contest.

To say that “game theory might suggest that bluffing is correct 15% of the time” doesn’t mean anything.  If you are implying that using game theory to optimize one’s strategy suggests bluffing 15% of the time, then by definition, that can’t be true if it is better to never bluff, as in your example. If it is correct to never bluff, then game theory would dictate never bluffing if what you mean by “game theory” is using math to determine your optimal strategy. 

The 15% of the time optimal bluffing frequency might be the answer to the optimization question given another set of circumstances.  “Game theory” (math) merely allows us to determine optimal short and long-term strategies given a particular set of circumstances, and sometimes given a particular utility (for example, are we trying to optimize winning in THIS particular poker session or in subsequenbt sessions as well?).

In any case, it is clear that in most (maybe all - I am not sure) cases, if there is only one matchup (as in you are only going to face one batter or throw one pitch or this is the last hand or bet in poker you are ever going to make/play), then generally there is only one correct play to be made and it is not necessary to employ a random selection process (with given percentages).  But that is usually not the case in baseball and in other contests as well.  And that also does not mean that we are not invoking “game theory” to come up with the correct strategy.  If a pitcher is facing Wily Mo with an 0-2 count once and only once in his career then it is probably correct for him to throw an off-speed pitch out of the zone.  If Wily knew that, which he shouldn’t, then he would simply not swing at that pitch.  I think we can all agree that if you are going to face Wily several time over a game, season, or career, that you cannot do that every time and in fact you will have to randomly vary your pitches (but still probably throw that off-speed pitch 80% of the time).  We can also agree that it is the same case (that you cannot throw the off-speed pitch 100% of the time) for all pitchers team or league-wide.

The interesting thing is that, let’s say that you are in fact only going to face Wily Mo one time and that’s it - never again.  Let’s also say that he knows that and that he has some degree of intelligence (or help from the bench).  Knowing that you think you have to throw an opp-speed pitch out of the zone, wouldn’t he simply not swing (or crush the ball if you accidentally leave it in the middle of the zone)?  In that case, even if it were your only matchup with Wily, you STILL might have to mix up your pitches, especially if Wily were smart and knew that this was your only appearance against him!