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Washington Nationals PDB: Non-Physical Aspects Affecting Pitching, Part Two

Part Two of the pre-season Pitching Daily Brief examines another "non-physical" factor that influences pitching performance and evaluation: game theory.

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Jonathan Ernst

Whaddya say! Whaddya say!

Before beginning this article, I pay tribute Stan Musial, also known as "the Man." I also wanted to highlight two of the best articles that I have read on Musial for readers less familiar with him. A member of the National Baseball Hall of Fame, Musial was a career .331/.417/.559 hitter. By all accounts, however, he was an even greater person.

The ineffable Joe Posnanski wrote this "Where are they now?" feature for Sports Illustrated in 2010, and recently offered this retrospective at Sports on Earth after Musial's passing.


This is the second part of my pre-season look at pitching and pitching evaluation in Major League Baseball. A pitcher's performance is affected by many things, but nearly all factors are related to either his non-physical (see my first piece, along with this one) or physical performance (think actions related to throwing the baseball).

To conclude my look at non-physical aspects affecting pitching, I am excited to review current thought and research on game theory and its application to the pitcher/batter matchup.

B. Game Theory, Pitching, and Hitting

Game theory is the study of strategic decision making. It is used to understand how choices are (or should be) made in different areas of our world, including anti-trust law, fashion supply chain management, literature, and national defense. Considering the breadth and depth of information available to many over the internet, it is no real surprise that people starting applying the concept to baseball.

What does game theory have to tell us about the pitcher/batter matchup?

i). Basic Game Theory, with Examples

Assume that I am pitching, and that you are hitting. You know my best pitch, pathetically, is an 80 MPH fastball that couldn't break Moe Szyslak ("[big sigh]...Sears catalog" kills me every time). In fact, it's practically my only pitch; maybe every thirty or so pitches, I'll throw a curve ball in the dirt. Game theory is what you apply when you ask yourself what you think is coming (the fastball, of course).

310toJoba states that game theory

basically asserts that a player in a zero-sum game will select options that minimize their maximum losses. To be overly thorough and clarify even further, a zero-sum game is a situation where the "players" can only benefit at the expense of each other because the possible payoffs from any set of actions is exactly the same....Not surprisingly the interactions between batters and pitchers are zero-sum games. Either the pitcher "wins" and the batter makes an out, or the batter "wins" and gets on base.

He highlights studies that claim that pitchers probably throw too many fastballs on balance, and buttresses this point using the value of fastballs thrown by top-tier pitchers (I'll cover valuation stats in a later post).

Back to my example above. I'm probably getting shelled every time I take the mound, because everyone knows a BP fastball is on the menu. After you conclude the fastball is coming, the next application of game theory to understand is what I (the pitcher) will do about my current pitch usage pattern.

Let's even out the scenario and move forward to your second at-bat. Now assume I somehow have a great fastball, and so-so curve. I use the heater 90% of the time and the curve 10%, less drastic than above, but still weighted heavily.

Clearly, the fastball is the pitch to throw. But, I decide instead to get "cute" (baseball parlance) and throw a curve, a pitch that for whatever reason you happen to expect. As it crosses the plate, the pitch hangs, and continues hanging until it re-enters the troposphere somewhere near the Navy Yard Metro, a massive blast. I made the wrong decision, right?

Not according to Matthew Lichtman, co-author of The Book - Playing the Percentages in Baseball. Lichtman reasons that because you guessed curve, 90% of the time, I'd have you fooled with the fastball. With the curve, the numbers just happened to line up in your favor on this occasion.

So why don't I simply throw my great fastball 100% of the time? This question, he argues, is the crux of game theory in the pitcher/batter matchup:

we cannot decide beforehand (or at any time) that we are going to throw a particular batter ANY given pitch (in this case a [fastball]) 100% of the time. We can’t! Eventually he will be looking [fastball] and will "crush" the pitch 100% of the time, which will be a huge mistake. Huge! Even if he is a stone cold idiot, eventually a manager or coach or scout will tell him emphatically, "Hey moron, when you get 2 strikes, pitchers ALWAYS throw you a [fastball], so do me a favor look for one and forget about the [curve]. Assume that you are taking ‘[fast] ball batting practice’."

In essence, game theory in the pitcher/batter matchup is about optimizing one's options in an effort to keep the opponent off-balance. For this reason, no matter how good any pitch of mine may be, I should not throw it all the time, every time. Unless, maybe, I am Mariano Rivera.

ii). Getting into Count and Pitch-Specific Game Theory

Matt Swartz takes a comprehensive look at game theory in the pitcher/batter matchup over five pieces at The Hardball Times. Using simple assumptions and a normal form (the latter is game theory jargon), Swartz concludes that in full counts, as between pitchers with great out-pitches and average out-pitches, "the pitcher with the fantastic out-pitch [in his model, an out-of-zone, unhittable curve ball] should throw it less often than the pitcher with the average out-pitch in full counts!"

Again, this seems counterintuitive. In his prime and in a full count, Barry Zito had every reason to throw his ridiculous 12-6 curve ball. So why shouldn't he?

...if batters were responding optimally, they would know how unhittable these pitches were and keep the bat on their shoulder more often. To entice the hitters to be willing to take a hack, pitchers should throw more fastballs. When they [subsequently] throw curveballs, batters will be caught off guard.

The batters, on the other hand, should take more pitches, knowing that swinging too much in these counts will only encourage the pitchers to throw the hook. If they keep the bat on their shoulder more often, the pitcher is likely enough to give them a fastball when they do swing. Therefore, pitchers with great curveballs may actually get more called third strikes on fastballs than pitchers with mediocre curveballs.

The above goes for the pitcher with the great curve ball and average heater. Against the pitcher with an average fastball and average curve, on the other hand, the batter has no reason to expect either pitch: they're both average. For this reason, the average pitcher need not (on the basis of pitch strength) adjust his approach to throw a fastball like the hurler with the great curve.

Swartz adds more complexity to the scenario by looking at multiple pitchers across different counts. It's serious stuff - just look at some of these formulas:

V(g) = (-1)*(q) + (1)*(1-q) = 1 – 2q

V(b) = (1.5)*(q) + (-1)*(1-q) = 2.5q – 1

This work adds a layer - well, layers - of math to support different decision making strategies.

Keeping the above in mind, it is easy to see how Stephen Strasburg or Gio Gonzalez or Drew Storen succeed: they can stack multiple high-quality pitches to further disturb the batter's ability to guess what is coming. With two above-average offerings, the batter has no reason (again, based on pitch strength) to expect either pitch. Lethal.

But even these pitchers can fall into usage patterns which undermine these strengths. For example, if Gio constantly goes to a low curve on two strike counts, batters will ultimately stop offering. So, his best strategy is to mix a variety of two-strike pitches in over the course of the year (or even a game).

iii). Actual Examples of Game Theory at Work

Thanks again to Jeff Sullivan's work at Fangraphs, we can see how game theory applies to the last pitch of the 2012 season. His article is worthy of a full read.

Sullivan first shows that Sergio Romo, the San Francisco Giants closer, throws sliders at a high rate very effectively, and fastballs much less so. He then recounts how Tim Wakefield's fastball, although really pedestrian by radar gun measurements, was often an effective pitch because hitters did not expect it.

Sullivan then sets the stage: Romo versus Miguel Cabrera, the American League MVP, in the bottom of the ninth of Game 4 of the World Series. A one-run lead with Cabrera at the bat can disappear quick, and Romo unlimbered a volley of exceptional sliders to start the showdown, five in all.

With the count 2-2,

[t]here was every reason for Cabrera to be expecting a slider. There was every reason for Romo to stick with his slider, because he could afford another ball, and because the slider has been his reliable weapon for years. There was every reason for Posey to call for a slider. And this is where we get into game theory. Because there was every reason for one thing, Sergio Romo saw an opportunity to try another thing. We don’t know how often it would’ve worked, given a million repetitions, but we know how it worked the one time. It ended a World Series.

(emphasis mine). Sullivan notes that, importantly, Romo shook Buster Posey off to a fastball immediately before the pitch. Supporting his point, he includes a .gif of the pitch, a 88.9 MPH fastball located middle-middle:



Perhaps surprisingly, use of game theory - in some form or another - actually dates back over 100 years. Christy Mathewson recounts such a tale in Pitching in a Pinch.

"Cy" Seymour, formerly the outfielder of the Giants, was one of the hardest batters I ever had to pitch against when he was with the Cincinnati club and going at the top of his stride. He liked a curved ball, and could hit it hard and far, and was always waiting for it. He was very clever at out-guessing a pitcher and being able to conclude what was coming.

For a long time whenever I pitched against him I had "mixed 'em up" literally, handing him first a fast ball and then a slow curve and so on, trying to fool him in this way. But one day we were playing in Cincinnati, and I decided to keep delivering the same kind of a ball, that old fast one around his neck, and to try to induce him to believe that a curve was coming. I pitched him nothing but fast ones that day, and he was always waiting for a curve. The result was that I had him in the hole all the time, and I struck him out three times....

He soon guessed, however, that I was not really mixed them up, and then I had to switch my style again for him.

Of note, Seymour was a career .303/.347/.405 hitter, and belted 2 HR's off Mathewson. OK, this is getting long. I'll wrap up.

iv). Conclusions

While an exact strategy for all counts and circumstances may never be found - for the better, in my view - game theory can be used by both pitchers and batters to maximize their ability to succeed. Additionally, the application of game theory in the pitcher/batter matchup can take many forms.

  • In some cases, it can mean simply not throwing one pitch too much generally.
  • In another, it can mean going to a below-average offering in a certain count to achieve positive results, when the opponent has reason to expect something different.
  • In still others, it can mean sequencing pitches to "set up" another pitch. Romo, for example, stuck with the same five pitches before going to a different, and successful, sixth. Mathewson, on the other hand, worked several different pitches without success, then stuck with just one for a while to get the results he wanted.

Succinctly, and at the risk of sounding incredibly obvious: the best pitch to throw is the one the batter least expects...unless you are facing one man:

There was the story that Robin Roberts told me about how one time he was so frustrated against Musial -- Stan hit .383 and slugged .679 against Roberts in more than 200 plate appearances -- that he actually threw Musial something resembling a knuckleball. "I just ran out of things to throw him," he explained.

"Did it work?" I asked.

"Nah," he said. "He lined it to right for a single."

Rest in peace, Mr. Musial.