1. e4.

If you know what that is, you might have just shouted something back at your computer. And no, the second baseman did not just make an error. Perhaps you’re an e5 sort of person (2. Nf3). Perhaps c5 is more your style (2. Nc3).

Maybe you have no idea what I’m talking about and are just wondering how long I’ll string you along until I reveal myself. I’m talking here about the game of chess, which is an obvious thing to talk about on a baseball website. I’m fascinated by the game despite being a truly awful player. There’s a certain logic to the game in that, theoretically at least, one could memorize a vast array of if-then statements branching out to all parts of the tree, researching the best move for each situation. But the number of possible universes that can be created in chess overwhelms even the best memories. Eventually, you start winging it. (For me, that’s around move no. 3.)

The thing is that an early mistake in the game can lead a player to be down a pawn (or a piece!), and as the game goes on, that sort of little advantage can be a big deal. If my opponent opens with 1. e4, should I play c5 and start a Sicilian game or perhaps play e5 and start a Spanish game? Which one is my opponent most versed in? Which one am I most versed in? There’s a bit of strategic thinking happening here. It’s entirely possible that my opponent is just as clueless as I am.

There are probably some chess aficionados in the audience who actually know what the Sinquefield Cup is or why it’s exciting that Lev Aronian won this year. Chess is a very cerebral game, and those who read Baseball Prospectus are generally pretty cerebral people, even (or especially) about their baseball. We will chase to the ends of the earth—or at least to the ends of the binary logistic regression—the most arcane details of the game. It’s easy to get caught up in the chess mindset with baseball and assume that everyone else is approaching the game like a chess match; that there’s careful consideration of each move and potential counter-move; that guys are thinking three plate appearances ahead; that the manager might see his sacrifice bunt more as a knight sacrifice. There are some chess players in MLB, but it won’t be any time soon that people in the game will see the letters “GM” and think of anyone other than “the guy who is running the team.”


A couple of weekends ago, I was on a flight from my now-home Atlanta to my ancestral homeland of Cleveland. Because flights are the only time I ever really get to read books (and because I don’t fly often), I was finally able to sit down with Travis Sawchik’s Big Data Baseball, which chronicles the ways in which the Pirates used advanced analytics to raise the Jolly Rodger over PNC Park over the past few years. If you haven’t yet, I command you to read it.

The book spends a lot of time discussing how the Pirates’ analytics department (led by BP alumnus Dan Fox) got manager Clint Hurdle to buy into what likely appeared to be some crazy ideas at first. (You want me to play how many infielders to the right of second base?) There was skepticism up and down the board, but the analytics department worked within that. Show a visualization of where an opposing hitter’s ground balls usually go, and the only logical response is “Yeah, I guess you’re right.”

As I descended into Cleveland, I found myself reflecting on how I might approach the same question. How would I convince someone who hasn’t taken a stats class and doesn’t know what a binary logistic regression is that my crazy-sounding idea is—at the very least—not crazy? In my head, I hit on the idea of a question: “What’s your game?” Everyone has a game that they play not just superficially, but with some devotion, even baseball players. (And the obvious answer, “baseball,” isn’t what I’m going for. Whether it’s Chutes and Ladders, blackjack, FIFA, or chess, everyone has a game.) And everyone who devotes themselves to a game has spent time trying to break the game itself. I guess that’s what I’m out to do. Baseball is my game, even though I will never play it at the major- (or minor- or independent- or park-) league level. I’ll also never be a professional blackjack or chess or Chutes and Ladders player, but I know that there are plenty of people out there who have studied how to beat these games before me. I’m just adding my own little piece of work to that pile.


When I say “beat the game,” I don’t mean finally getting to one of the apparent multitude of dragon-and-turtle-infested castles with questionable plumbing in which the actual princess is being hidden. Mathematicians who study games refer to the idea of “solving” a game. The idea is that there exists a certain type of game (chess is a good example, actually) where mathematically, there is at least one “correct” move at each point in the game that, no matter the counter-move, always contains a pathway for me to achieve at least a draw, if not a win. The trick is always following that path of “correct” moves as the game unfolds. Tic-tac-toe is, in this way, actually mathematically similar to (though much less complex) than chess. If my opponent opens by placing an X in the corner, I should place an O in the middle. My opponent’s best bet is to secure the corner opposite the original X, though I can assure a draw by simply grabbing one of the other corners. Assuming that neither of us makes a completely silly error, we will draw.

Baseball isn’t the sort of game that can be “solved” mathematically (there are certain conditions that need to be present for a game to be mathematically solved that completely rule out live sports), but you can still study it and play with the edges of it. Sometimes you play with more than the edges. Sometimes you figure out a new way to cheat the game. Fortunately, I’d argue that we happen to live in what I would call the Golden Era of Cheating at Games. There’s a certain demographic of people reading this around my age (I’m 35) who grew up in the era of the first commercially viable video games. I grew up first with an Atari 2600, then an 8-bit Nintendo, and eventually moved along to (from today’s perspective) hilariously bad PC games. I’m not much of a gamer any more, but I can appreciate how far games have come in the last 20 years. And in some sense, I’m extremely lucky that I grew up in the days when video games were really bad. I don’t know if anyone has ever really appreciated the cultural impact that bad video games had on baseball or America in general.

Maybe the most important cultural legacy of the video game is the idea of one-player mode. Most games in the real world are multi-player. They pit two (or more) people against each other within some rule structure and have them go at it. While you are playing the game—assuming that your friends actually want to win—there is no space to stop the game and perhaps replay a move or a turn to see whether an alternate course of action would have worked out better for you. When I play chess on my phone, I have the “takeback” button to fall back on. In an actual chess game, I’d need a very understanding opponent to try to make that work.

When video games came along, though, there was no other person (in one-player mode, anyway). Suddenly, the opposing pitcher or the Russian army or the pathway to Willamette Valley or the indeterminate species of animal throwing hammers at your avatar was controlled by a computer. When I was growing up, it was a rather stupid computer. If I messed up on something, I could try again, either through the magic of the “save” button, or just thousands of repetitions. The computer didn’t care if I cheated, nor did it really change its strategy to compensate once I figured it out. And the fact that these games were all standardized meant that there was an army of other people who were out there trying to beat the same AI that I was. And then the internet linked us all together in ways that Nintendo Power magazine couldn’t, even if we all knew aleady the Bo Jackson play. There was suddenly a hive mind that was dedicated to beating Larry, and Larry didn’t care that I was cheating, and everyone was playing against the same Larry. And we all knew that one person who was just a little too into beating whatever the game was. But if you had questions, that’s who you went to.

There’s a certain moment in every video game in one-player mode where beating the computer in a straight-up game isn’t even a question. The fact that the early games were so limited made that point relatively easy to reach. But of course with a going rate of $30 to $40 for a new cartridge to challenge my mettle, sometimes I had to make do with the old ones. That meant creating my own challenge: going beyond the traditional rules of the actual game. Running little experiments. Maybe it was taking on a ridiculous handicap or maybe seeing just how big a score I could run up, but it meant a little bit of experimentation, the kind of experimentation that you couldn’t do in a live game. Games themselves became their own little laboratory, and the computer meekly complied. I’d argue that many of the people reading this article are products of that shift. We came of age in an era in which breaking a game became socially available and acceptable. It’s not surprising that some people took that same mindset and began trying to “break” other things. Some of us just happened to be baseball fans.

I’m left to wonder if the gap in the acceptance of sabermetrics is less about the gory mathematical details and more about that cultural gap. There are plenty of scouts who have no idea how the math works, but get the basic concepts and have faith that the numbers guys know what they’re doing. But, as I am fond of saying, the one thing baseball (and United States culture) will not tolerate is someone who appears to be trying too hard. Even if the math is right, why did you even try to do that in the first place? That’s not how respectable folk behave.


Seven. Plus or minus two.

I think the readership of Baseball Prospectus would love it if all players talked about the strategy of baseball like Trevor Bauer does, what with all his talk of effective velocity and the way that he picks apart all of the intricacies of pitch selection, attempting to use a player’s own neuropsychology against him. But Bauer is a bit of an outlier in talking like a chess master. There are a lot of catcher-pitcher conversations about pitch selection which, transcribed in their entirety, read: “So … fastball away?” “Cool with me.”

As I thought about how I would pitch some crazy sabermetric idea, I kept coming back to the number seven (plus or minus two). It’s generally believed that the average person can hold seven pieces of information in her/his brain at any one time. The classic example is that a person can remember seven randomly selected numbers at a time, which was great for remembering phone numbers back when phone numbers were seven digits long. Still, it’s not as simple as that. There’s a process known as “chunking” in which the person trying to remember those seven numbers can turn a few of them into a “chunk” with something holding them together. Suddenly, 8, 6, 7, 5, 3, 0, 9 becomes more than just seven random numbers. It becomes a chunk.

Still, in order to make something a chunk, you have to have something that glues the pieces of information together. That usually comes from years of experience in working on some issue. To put the shoe on the other foot, if you got a couple of pitching coaches together and got them started on the topic of pitch grips, they start with a base of knowledge that dwarfs mine. My eyes would glaze over faster than in a discussion of the finer points of the Scandinavian Defense in chess (1. e4 d5, 2. exd5 Qxd5). I have plenty of experience working with the numbers, and how quick I am to forget in my eagerness that not everyone knows what the hell a binary logistic regression is.

It’s not that pitchers or hitters or coaches are more or less gifted than the average bear in the smarts department. The idea that baseball players—or any other athletes—are all “big dumb jocks” is as foolish as the idea that all statheads are hopeless nerds living in mom’s basement. There are some who are incredibly smart, some who are incredibly dumb, and most are somewhere in the middle; it’s good to remember that none of them have a calculator out there with them. Few players dabble in the #GoryMath, but then I don’t really dabble in making my slider better. I’m no better or worse than any of them. I just spend my time doing different things.

The beauty of the infield shift is that the entire strategy can be proven and implemented using two steps. 1) Here’s a graph of where Smith hits most of his ground balls. 2) Go stand there. It fits on an index card. As sabermetricians, we often pride ourselves on our ability to make ever-more-complex equations that more accurately model reality. Or what we think reality is. I have no doubt that hiding somewhere in those equations is real insight on how to run a baseball team more efficiently. As a group we spend much less time on distilling all of that down so that it fits on the proverbial index card. The second piece is as important as the first.


I have a chess app on my phone that I’ll occasionally play, but it has a little button that I’ve come to have a love/hate relationship with. The button is a little light bulb (I think it’s supposed to represent “give me an idea”) that suggests a potential move that I might make. Seeing that I’m not much of a player, I find myself hitting that button a lot. Worse than that, I find myself saying, “yeah, sure, I’ll make that move.” Do that enough times, and suddenly I realize that I didn’t actually play that game. It was the computer playing itself with me as the intermediary. Even if I win, it’s something of an empty victory. I didn’t come up with those ideas.

I have to imagine that there’s a certain resistance along the same lines for the second baseman who finds himself in short right field making what has suddenly become a routine ground-ball play. Sure, he made the play and the batter is out and that’s a good thing for his team, but he might be asking himself, “Why am I even out here?” Even if he understands it intellectually, there’s probably a bad taste in his mouth. If he had made an amazing play because he had worked on his fielding drills more in the offseason or done some agility work to improve his range, the extra play would have felt good. Even though we should probably credit the coaches or trainers that he worked with some, it’s pretty obvious where the on-the-field credit goes. If he makes an easy play that is easy because some computer told him to stand there, is he merely a pawn in the game to be moved around?


I know that I wish everyone in baseball thought like a chess master, that everything is logical and pieces might be sacrificed for the greater good. The reality is that crazy strategies need more than just mathematical proofs. You’re going to have to get past some pretty strong cultural barriers that you may not have even noticed that were there. I’ve named three above. There are probably more lurking out there.

If there’s something to be said for Sawchik’s book (and there are a lot of somethings to be said for it!) it’s that the doubt felt up and down the Pirates organization as they tried some of these ideas was a main character throughout and the book was more about the process that the Pirates went through in getting these ideas onto the field. If you haven’t yet read his book, and you want to know where the real “next great frontier” is in sabermetrics, read (or re-read) it and pay attention to that character. That’s the real equation that has to be solved in this whole mess.

Thank you for reading

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though I can assure a draw by simply grabbing one of the other corners. Assuming that neither of us makes a completely silly error, we will draw.

Amusingly, grabbing one of the other corners is just such a silly error. The game you describe goes, for example: X a1, O b2, X c3, O a3. Now X plays c1, blocking O's potential line and setting up threats at b1 and c2; O can't block both.
Whoops... I got my strategies mixed up. This is why my 6-year-old always beats me. Best strategy is to take one of the four "middle" squares.
Yep (in fact given symmetry that's the only other strategy). The fact that I knew this without really thinking about it probably means I spent far too much of my childhood playing this silly game.
The only winning move is not to play.
Check out the King of Kong: A Fistful of Quarters.

And I'll be enjoying that Tommy Tutone ear worm for the rest of the day. Thanks. Something wrong with 36-24-36, other than not enough digits?
That's why APBA and Strat are such great games ...
Robbed!! No "Gory mathematical details"!
When I was a kid and we played sandlot ball, we would put a player 'where the hitter usually hits the ball'. I never thought about it. And we were happy if that person made the play. But as I got older, the history & symmetry of traditional defensive placement seemed logical and created 'fairness of opportunity'. Using an asymmetrical defense is of course more efficient but changes our idea of 'fairness'. What I find interesting about this is that it's changing batter habits. In combination with contemporary pitcher usage, hitting the ball where they ain't is becoming increasingly more common. I expect this trend to continue & pull hitters(or that habit) to lose market position. I don't know if that breaks the game, but it sure changes it.
I love the analogy to sandlot ball. If a team has just five fielders, where do you play them? Now what if you have six? So using the same logic you used to place fewer fielders, where do you place them if you have nine? Love looking at it that way... Breaking the game.
The chess analogy actually works surprisingly well if you look not at chess itself, but rather at its variant Kriegspiel, in which you only see your own pieces on the board and have to infer where the opponent's are -- see e.g. for a description. The addition of the problem of imperfect information (since your inference about the opponent's pieces is always incomplete) makes the decision-making process very similar to what a manager goes through.
I was a dead pull hitter in high school and our rival team would often move their right fielder all the way to left center when I was up. What was amazing was that our coach once convinced the umpire that this was illegal and the ump forced the opposing team to move at least one fielder to the right of dead-center.

I also have a question for the BP team. I had a very creative (and cerebral) coach as a teenager. He would use shifts not just to position his defense more efficiently but to deliberately try and get a hitter to altar his swing. For example: the huge 3 hitter on the opposing team would come up and our coach would make a big show of shifting our defense to the opposite field really dramatically. He then would have our pitcher dump loopy, high-school curveballs into the strikezone. More often than not, the amped up power hitter trying desperately to pull to the open field would dribble one to short for an easy out. The question is, are you aware of any coaches who do or may be doing this? Would be really interesting if we could find an example and if it has an effect.