Mixed strategies in baseball Greg Powell Masters of Applied Econometrics

1. Pitching Strategies in a Hitters Count: Mixed Strategies in Baseball Greg Powell Masters of Applied Econometrics

2. So, where were we? Baseball is Big Business – effective strategies are utmost importance MSNE Unobserved in low incentive games Weinstein-Gould attempting to prove MSNE with respect to his 3 measurables PitchSuccess - (Ball/Strike) OnBase– Batter gets on base via hit/walk wOBA – weighted OnBase We are using the frame work Weinstein-Gould used in a 0-0 count into a 2-1 count. Pitching strategy between two counts IS different, statistically MSNE Game – Pitcher vs Hitter – Conceptual Game

3. 2-1 Count – Hitter Advantage = Better Chance of Getting On Base League Average OBA OBA of in 0.333 in 2009 0.325 in 2010 (ESPN 2011) 2-1 Count is advantage hitter, statistically – 0.397 OBA After the following pitch: Ball 3-1 OBA = 0.671 Strike 2-2 OBA = 0.191

7. Calculating the MSNE Pelfrey ROWS payoff FASTBALL against Hitter (q,1-q): q(0.50) + (1-q)(0.60) Pelfrey ROWS payoff OTHER against Hitter (q, 1-q): q(0.65) + (1-q)(0.45) If Pelfrey is mixing in NE then payoffs to McCann FASTBALL/OTHER must be equal q(0.50) + (1-q)(0.60) = q(0.65) + (1-q)(0.45)0.2q + 0.45 = 0.6 – 0.1q q = 0.5 McCann’s NE Fastball Mix McCann Columns payoff FASTBALL against Pitcher (p, 1-p): p(0.5) + (1-p)(0.35) McCann Columns payoff OTHER against Pitcher (p, 1-p): p(0.4) + (1-p)(0.55) If McCann is mixing in NE then payoffs to Pelfrey FASTBALL/OTHER must be equal: p(0.5) + (1-p)(0.35) = p(0.4) + (1-p)(0.55)0.5p + 0.35 – 0.35p = 0.4p + 0.55 – 0.55p0.3p = 0.2p = 2/3 Pelfrey’s NE Fastball Mix

8. Equilibrium Strategy… Batter McCann Strategy [1/2 Fastball, 1/2 Other] We have proved that in equilibrium the Pitcher must be indifferent between the pitches in his mix, to solve for the batters equilibrium strategy PITCHER Pelfrey Strategy [2/3 Fastball, 1/3 Other]

9. First Analysis – Hitter Specific Strategies on Heterogeneous Dataset Conventional Baseball Theory suggests that pitchers use hitter specific strategies… In a heterogeneous dataset… …can we prove that pitchers use a hitter-specific strategy? YES!

10. First Analysis – Hitter Specific Strategies on Heterogeneous Dataset Initial Multinomial Logistic Regression 72,445 Rows 805 pitcher dummy variable columns 965 hitter dummy variable columns Test the hitter dummy variables Null Hypothesis H0: Hitter 1 = Hitter 2 = Hitter n = 0 Joint insignificance of Hitter fixed effects = pitcher indifference/MSNE

11. First Analysis – Hitter Specific Strategies on Heterogeneous Dataset Major Issues with data size/singular co-variance of dummy variables Series of binomial models with only the hitter dummies Fastball = hitter_dummies + e Changeup= hitter_dummies + e Curveball= hitter_dummies + e etc… Test whether hitter_dummies are jointly significant Jointly significant means hitter-specific strategy

12. First Analysis – Results

13. First Analysis – Results HITTER SPECIFIC STRATEGY: Fastball Curveball Changeup Handedness Issue RH Hitters – Only fastball LH Hitters – Fastball, Curveball, Changeup Why? Already proved a different strategy in 2-1. Hitter anticipating fastball – less fastballs Curveball difficult to throw for strike – less thrown Changeup perhaps the easiest pitch to throw for a strike without throwing a fastball – more changeups “Pitcher must throw a strike to level count”

14. Second Analysis – Model (homogenous data) Testing for indifference/MSNE In a homogenised dataset, within every pitcher-hitter battle… …Can we prove that each type of pitch thrown by a given pitcher to a given hitter has the same effect? YES!

15. Second Analysis – Model (homogenous data) Condensed dataset of 5632 rows of the most populous hitter-pitcher pairs. Similar modeling issues as in the first analysis, ie Singular co-variance , etc Therefore following models run on each of the 3 measures of success: Binomial: Pitch_success = PitcherHitterPitchType + e Linear: wOBA = PitcherHitterPitchType + e NOT ABLE TO BUILD MODEL FOR OBA Joint Test of PitcherHitterPitchType = 0 If insignificantly different from 0 – each pitch thrown with same effect Therefore Indifferent strategy, therefore MSNE employed

16. Second Analysis - Result Pitch Success Binomial Model FAIL TO REJECT Joint Test of PitcherHitterPitchType = 0 Effects Insignificantly different from 0 – each pitch thrown with same effect Pitchers acting indifferently on 2-1 pitch = MSNE!!! wOBA Linear Model Reject Joint Test of PitcherHitterPitchType = 0 Effects Significantly different from 0 No evidence of MSNE with respect to plate appearance Weinstein-Gould’s results are replicated

17. Other Issues Pitchers who continually fall behind 2-1 are the poorer pitchers Poorer control Can’t mix optimally, yet they are indifferent to batter It might be indifference, but it might not be mixing optimally Batters who work counts to 2-1 are more selective and better hitters? Weinstein-Gould proposed examining 0-0 to avoid the dynamics of the previous pitch This research shown that the dynamics don’t really matter within his framework – same result

18. Further Work For publication Examine 1-2 count where the pitchers are ahead in the count Examine Locations Hitters in Majors may actually look for location rather than pitch type… Examine other variables such as: # Outs # Runners on Base Score Etc…

19. Conclusion In 2-1 count Pitchers mix optimally with respect to Pitch Success measure Plate appearance (wOBA) measures probably cannot be estimated without considering many other variables or building a more complex model PROFESSIONALS USE MSNE (OR AT LEAST ARE INDIFFERENT)!