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The 3-0 Count Dilemma

While it might not appear so, baseball games constantly portray economic thought, such as in the mathematical model of game theory. There are many ways game theory takes place, but a classic example is the prisoner’s dilemma. Imagine a police officer is interrogating two suspects of robbing a bank together. The police officer has some evidence to put them in jail, but a confession would go a long way. Each suspect is contemplating confessing to the crime. If both suspects keep quiet, they will each receive five years in jail. If one suspect confesses and the other keeps quiet, the one who kept quiet will receive 20 years in jail while the suspect who confessed will receive just one year. If both confess, they each receive 10 years in jail. The logical choice for each suspect is called the dominant strategy. The end result, or the combination of each suspects decision, is called the Nash Equilibrium. By using game theory, we come to the conclusion that each suspect should confess to the crime, meaning they will each get 10 years in prison. I won’t go much into why this is the case, but feel free to research more about game theory and the Nash Equilibrium on your own.

What does this have to with baseball? We can think of each pitch as game theory, with each suspect as the pitcher and batter. Instead of confessing to a crime, the pitcher is contemplating throwing a ball in the strike zone while the batter is contemplating swinging. While the prisoner’s dilemma has a Nash Equilibrium, not only does a pitch to a batter not have a Nash Equilibrium, but the combination of decisions is constantly changing. If the batter’s dominant strategy is to swing, then pitchers will throw more balls outside the batter’s reach. If the pitcher’s dominant strategy is to throw a ball, then the batter will take more pitches.

We could observe this thought process for every pitch thrown. However, let’s look at one type of pitch: 3-0 counts. If you are the batter, it might seem obvious to take the pitch. The worst-case scenario is you end up with a 3-1 count. If you are the pitcher, it might seem obvious to throw an easy strike. You do not want to walk the batter, and you know the batter doesn’t want to swing and risk giving you an easy popup to get out of good count. So I guess the batter should take every pitch and the pitcher should throw the ball right down the middle every time. Read the rest of this entry »

How the Nationals Outsmarted Paul Goldschmidt in the NLCS

The NLCS had a weird feel to it from the get go. The Nationals’ pitching was stupendous, balls hit off the bat that sounded like towering home runs were dying on the warning track, and of course, the Cardinals bats never woke up. This was a bit unexpected considering the club’s monster first inning in Atlanta during game 5 of the NLDS. We were all waiting for the Cardinals offense to appear, but it never showed up, as they only scored six runs in a four-game sweep by the Nationals.

Nobody could seem to get anything going offensively. Instead of searching for answers for all the Cardinal batters, let’s just look at one. While Paul Goldschmidt had his worst season offensively with a .346 wOBA, he is still the thunder in the St. Louis lineup. How exactly did the Nationals pitch to Goldschmidt, and why couldn’t he succeed in the series?

On one hand, the Nationals pitchers were outstanding. They were putting pitches right on the edge of the plate and mixing their pitch selection well. When you have Max Scherzer, Stephen Strasburg, and Patrick Corbin in your starting rotation, your opponent is going to have a difficult time. Additionally, Anibal Sanchez had a great game. Meanwhile, Goldschmidt went 1-for-16 with nine strikeouts in the series. He did seem to experience a little bit of bad luck with a few hard hit balls. In Game 4, he hit a ball 101.4 mph that went 340 feet, and he had another two hard-hit outs in Game 2. One traveled 316 feet that was hit 95.9 mph off the bat, and another traveled 284 feet that was hit 108.1 mph. That may not make him feel tons better about his performance given the nine strikeouts.

It is not surprising that Anibal Sanchez was able to succeed in his three times facing Goldschmidt in Game 1. Sanchez used the cutter and sinker well in that game. While his sinker generated an unimpressive .387 wOBA this year, his cutter was lethal with a .260 wOBA. Goldschmidt had a .350 wOBA against sinkers and a .317 wOBA against cutters. Those numbers are going to add to some underwhelming results. Sanchez utilized the sinker and cutter well and put them in difficult locations against Goldschmidt. During the second at-bat, Sanchez generated similar results. Read the rest of this entry »