# Baseball Simulation

**Topics:**Markov chain, Baseball, Major League Baseball

**Pages:**396 (39845 words)

**Published:**December 8, 2013

Los Angeles

A Player Based Approach

to Baseball Simulation

A dissertation submitted in partial satisfaction of the

requirements for the degree Doctor of Philosophy

in Statistics

by

Adam Philip Sugano

2008

© Copyright by

Adam Philip Sugano

2008

The dissertation of Adam Philip Sugano is approved.

_______________________________________

Jan de Leeuw

_______________________________________

Rick Paik Schoenberg

_______________________________________

Hal Stern

_______________________________________

Mark Hansen, Committee Co-Chair

_______________________________________

Don Morrison, Committee Co-Chair

University of California, Los Angeles

2008

ii

To my favorite statistician and my Dad, Dr. David S. Sugano, with love and admiration…

iii

TABLE OF CONTENTS

1

Introduction................................................................................................ 1

2

Baseball within a Markov Chain Framework......................................... 5 2.1

Markov Chain Properties................................................................. 6

2.2

Previous Work Modeling Baseball via Markov a Markov Chain.... 8

2.3

The Transition Matrix...................................................................... 9 2.3.1

2.3.2

3

Transition Constraints.......................................................... 13

2.3.3

2.4

Run Potentials...................................................................... 12

Finalized Transition Matrices.............................................. 14

Advantages of Simulation Models................................................... 23

Situational Factors Affecting Transition Probabilities.......................... 25 3.1

Bias and Evolvement of Baseball Statistics.................................... 26

3.2

Measuring Chance vs. Ability......................................................... 28

3.3

The Log5 Method............................................................................ 31 3.3.1

3.3.2

Alternative Methods............................................................ 34

3.3.3

3.4

Extending the Log5 Method................................................ 32

Comparing Simulated Results............................................. 36

Situational Affects........................................................................... 38 3.4.1

Handedness.......................................................................... 40

3.4.2

Home vs. Away.................................................................... 40

iv

3.4.3

3.4.4

4

Streakiness............................................................................ 43

3.4.5

3.5

Clutch Hitting....................................................................... 42

Momentum............................................................................ 45

Conclusions About Situational Affects in Baseball.......................... 46

Batter-Pitcher Matchups in Baseball and Small Sample Decision Making....................................................................................................... 47 4.1

The Batter-Pitcher Matchup: A Simple Binomial View................. 49

4.2

A Hierarchical Model for Batter-Pitcher Matchup Data................. 51 4.2.1

4.2.2

A Probability Model for Batter-Pitcher Matchups............... 52

4.2.3

Results – Kenny Lofton........................................................ 55

4.2.4

Results – Derek Jeter............................................................ 56

4.2.5

4.3

Data for a Single Player....................................................... 51

Results – Multiple Players.................................................... 60

Batter-Pitcher Data from the Pitcher’s Perspective.......................... 61 4.3.1

Results – Tim...

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