In order to prevent batters from hitting a pitch, pitchers must decide on a strategic balance of many different pitch types. While each pitcher has preferred pitches (likely those with which he is most confident), he cannot over-utilize his dominant pitches, or batters will be able to gain a strategic advantage in trying to put the ball into play. We analyze Major League Baseball (MLB) pitch data from 2008 to 2018 in order to determine whether or not MLB pitchers are able to reach the theorized mixed-strategy Nash equilibrium given the pitcher’s skill in utilizing each type of pitch. Our data suggests that MLB pitchers are in fact rational, and succeed in reaching the mixed-strategy Nash Equilibrium.
BaldiniK.GillisM. T.RyanM. E. (2011). Do relief pitching and remaining games create moral hazard problems in Major League Baseball?Journal of Sports Economics, 12(6), 647–659.
2.
BaumannF.FrieheT.WedowM. (2011). General ability and specialization: Evidence from penalty kicks in soccer. Journal of Sports Economics, 12(1), 81–105.
3.
BradburyJ. C.DrinenD. (2006). The designated hitter, moral hazard, and hit batters: New evidence from game-level data. Journal of Sports Economics, 7(3), 319–329.
4.
BuzzacchiL.PedriniS. (2014). Does player specialization predict player actions? Evidence from penalty kicks at FIFA World Cup and UEFA Euro Cup. Applied Economics, 46(10), 1067–1080.
5.
ChiapporiP.-ALevittS.GrosecloseT. (2002). Testing mixed-strategy equilibria when players are heterogeneous: The case of penalty kicks in soccer. American Economic Review, 92(4), 1138–1151.
6.
ColomaG. (2007). Penalty kicks in soccer: An alternative methodology for testing mixed-strategy equilibria. Journal of Sports Economics, 8(5), 530–545.
7.
CoxD. JSosineJ.DalleryJ. (2017). Application of the matching law to pitch selection in professional baseball. Journal of Applied Behavior Analysis, 50(2), 393–406.
8.
DemminkH. (2010). Value of stealing bases in Major League Baseball. Public Choice, 142(3), 497–505.
9.
DowneyJ.McGarrityJ. P. (2015). Pick off throws, stolen bases, and southpaws: A comparative static analysis of a mixed strategy game. Atlantic Economic Journal, 43(3), 319–335.
10.
EpsteinS. (1994). Integration of the cognitive and the psychodynamic unconscious. American Psychologist, 49(8), 709–724.
11.
GauriotR.PageL.WoodersJ. (2018). Nash at Wimbledon: Evidence from half a million serves. SSRN Electronic Journal.
12.
HerrnsteinR. J. (1961). Relative and absolute strength of response as a function of frequency of reinforcement. Journal of the Experimental Analysis of Behavior, 4(3), 267–272.
13.
KahnemanD.KnetschJ. LThalerR. H. (1991). Anomalies: The endowment effect, loss aversion, and status quo bias. Journal of Economic Perspectives, 5(1), 193–206.
14.
LeeY.-S. (2016). Behavior and biased choice: A pitcher’s problem. Journal of International Trade & Commerce, 12(5), 123–134.
15.
ReedD. D.CritchfieldT. S.MartensB. K. (2006). The generalized matching law in elite sport competition: Football play calling as operant choice. Journal of Applied Behavior Analysis, 39(3), 281–297.
16.
RomanowichP.BourretJ.VollmerT. R. (2007). Further analysis of the matching law to describe two-and three-point shot allocation by professional basketball players. Journal of Applied Behavior Analysis, 40(2), 311–315.
17.
ScottD. W. (2015). Multivariate density estimation: Theory, practice, and visualization. John Wiley & Sons.
18.
SeniukH. AWilliamsW. L.ReedD. D.WrightJ. W. (2015). An examination of matching with multiple response alternatives in professional hockey. Behavior Analysis: Research and Practice, 15(3–4), 152.
19.
VollmerT. RBourretJ. (2000). An application of the matching law to evaluate the allocation of two-and three-point shots by college basketball players. Journal of Applied Behavior Analysis, 33(2), 137–150.
20.
WalkerM.WoodersJ. (2001). Minimax play at Wimbledon. American Economic Review, 91(5), 1521–1538.
21.
Weinstein-GouldJ. (2009). Keeping the hitter off balance: Mixed strategies in baseball. Journal of Quantitative Analysis in Sports, 5(2).
