Over the course of his career, Patrick Corbin has developed one of the best arsenals in the league. He has a decent curveball and changeup, good two-seam and four-seam fastballs, and one of the best sliders in the game. Combine that with a slightly deceptive delivery and elite command and you get his toolbox – what he has to work with as a pitcher. How he and other pitchers choose to use their toolboxes can be key in determining their success in the major leagues.
Theoretically, every situation has its own optimal distribution of pitches where neither the batter or pitcher can gain an advantage called a Nash equilibrium. Not only are both the batter and pitcher trying to estimate this point, but where their opponent is relative to it. With each interaction being a zero sum game, there is always an edge to be gained by trying to counter what the opponent is doing. This leads to a sort of guessing game dance around the Nash equilibrium point. Pitch sequencing is different from determining a plan of attack, as it describes the strategic ordering of the aggregate strategy to stay ahead in the mental game.
For example, let us look at Trevor Bauer pitching to Aaron Judge in the 2017 postseason. On Bauer’s Youtube series, ‘Breaking Point’, he says “the plan going into this game was to basically just throw him as many breaking balls as possible to get him out.” That reflects the aggregate strategy they had for Judge: Attack with breaking balls, specifically low and away, late in counts. To help set that up, Bauer started him in the first at-bat with two fastballs high and inside to make Judge think that was the plan of attack. Knowing it was not only Judge’s first at-bat of the day but also of the series, fastballs were thrown not just to succeed in the given count, but to induce better results both later in the count and series. In this way, sequencing is going from outcome distributions to pitch selections in trying to manipulate the hitter without being predictable.
Where things get difficult is quantifying the exact effect. Aaron Judge did struggle that series against the Indians; was that luck or Cleveland pitchers being one step ahead of him? How did Bauer’s decision to start him with fastballs affect Judge that at-bat? That game? That series? It becomes quite a rabbit hole problem the more you zoom out, but let’s take a look at what an analysis would look like.
Around a month ago, I made a video about Patrick Corbin and his curveball. In researching for that video, I flirted with sequencing analysis hypothesizing fastballs would generate more swings and misses following such a slow pitch. However, I found fastballs following his curveball had a statistically significantly lower whiff rate than fastballs thrown following another pitch**. The slow curveball was effective when deployed by Corbin in 2019, but if it in fact has a negative effect on fastballs, then it would suggest a reduction of curveball usage when behind in counts and fewer succeeding fastballs, all else being equal. This example has its limitations, but it shows how a sequencing analysis could be done and the insights that could be derived from them.
Humans are bad at randomizing so until pitchers master calculating Nash equilibriums and bring random number generators to the mound, this element of sequencing will be a part of the game. Despite all the scouting going into crafting a plan of attack, either the batter or pitcher will have an advantage on any given pitch. Big data and artificial intelligence provide avenues to a better understanding of the human element than any human can comprehend. Baseball may ultimately be moving toward a game where trash cans and apple watches are not the primary concern. Nevertheless, until we reach the baseball equivalent of an orwellian dystopia, teams will continue pouring resources into gaining insight and game-theoretical masterminds will continue pitching better than their toolboxes should allow.
** = With Corbin only throwing his curveball against right handed batters in certain counts (0-0, 1-0, 0-1, 1-1), the samples of fastballs being compared were constrained to pitches following these conditions. The whiff rates were then adjusted based on count and pitch type due to Corbin having both four seam and two seam fastballs. After these constraints and adjustments, the expected whiff rate was .204 while 50 swings and five whiffs were observed. When treated as a binomial, this yields a p-value of .0418 and is thus significant at the .05 level.