ESTIMATING FIELDING ABILITY IN BASEBALL PLAYERS OVER TIME James Martin Piette III A ...

111 Pages·2011·1.63 MB·English

ESTIMATING FIELDING ABILITY IN BASEBALL PLAYERS
OVER TIME
James Martin Piette III
A DISSERTATION
in
Statistics
For the Graduate Group in Managerial Science and Applied
Economics
Presented to the Faculties of the University of Pennsylvania in Partial
Fulfillment of the Requirements for the Degree of Doctor of Philosophy
2011
Supervisor of Dissertation
Shane Jensen, Associate Professor, Statistics
Graduate Group Chairperson
Eric Bradlow, Professor of Marketing, Statistics, and Education
Dissertation Committee
Edward George, Professor of Statistics
Dylan Small, Professor of Statistics
Acknowledgements
Professor Shane Jensen served as the perfect advisor to me. It was a foregone
conclusion upon my arrival at Penn that you would be my advisor. I appreciate all
of your advice on research, video games and baseball, as well as introducing me to
fantasy baseball. I will miss our talks about how Alfonso Soriano and the Nationals’
closers make us cry.
IwanttothankallofmyfellowclassmatesintheWhartonStatisticsdepartment.
Being able to dump my grad school worries on people like Mike Baiocchi, Sivan
Aldor-Noiman, Jordan Rodu, Oliver Entine and Dan Yang helped me over the
bumps in the road towards my Ph.D.
I am fortunate to have had some excellent co-authors, like Blakely McShane and
Alex Braunstein, who pushed me to be a better researcher and writer, as well as
introduce me to the great things that Flipadelphia has to offer.
I am grateful to have shared an office with two of the finest people I know.
I will always be in Kai Zhang’s debt for both his wisdom and kindness; without
him contributing to my first paper, my Erdos number would be ∞. Sathyanarayan
ii
Anand likely knows me better than anyone else, and has provided me with endless
conversation as a roommate. Thank you for keeping me sane, grounded and affable,
while going through the four very trying years of my life.
I appreciate all that my home town friends, Austin Cowart and Alex Sprague,
did for me. Playing video games and sharing great beers stands as some of the most
fun moments in my life, and serve as reminders of who I am and where I am from.
Some of my best years during graduate school were working with and helping
start up Krossover with Vasu Kulkarni, Alex Kirtland and Sandip Chaudhari. I
could not imagine a better way to start my career, working for a company in the
sports industry with three smart, driven individuals who I can also call dear friends.
I would like to thank the people who have always been there with their love and
support: my family. To my sister, mom and dad, I love you all. Without you, I
would have never pursued, much less finished, my Ph.D, missing out on one of the
best experiences of my life. I have always wanted to make you proud, and I hope
that I will continue to do so.
My beautiful, soon-to-be wife Lisa Pham, who has given me nothing but love,
despite the fact that I am a lanky spaz that is easily excitable and loud. This
dissertation literally would not have been written without your encouragement. For
the past four years, anything I have achieved is because you gave me the confidence
to do it. I will always love you, jitterbug and all, with all my heart. And, as I
promised, I will get you a puppy as soon as possible.
iii
ABSTRACT
ESTIMATING FIELDING ABILITY IN BASEBALL PLAYERS OVER TIME
James Martin Piette III
Shane T. Jensen (Advisor)
It is commonplace around baseball to involve statistical analysis in the evaluation
of a player’s ability to field. While well-researched, the question behind how best
to model fielding is heavily debated. The official MLB method for tracking field-
ing is riddled with biases and censoring problems, while more recent approaches to
fielding evaluation, such as Ultimate Zone Rating [Lichtman 2003], lose accuracy
by not treating the field as a single continuous surface. SAFE, Spatial Aggregate
Fielding Evaluation, aims to solve these problems. Jensen et al [2009] took a rig-
orous statistical approach to this problem by implementing a hierarchical Bayesian
structure in a spatial model setting. The performance of individual fielders can be
more accurately gauged because of the additional information provided via sharing
across fielders. I have extended this model to three new specifications by building
in time series aspects: the constant-over-time model, the moving average age model
and the autoregressive age model. By using these new models, I have produced
a more accurate estimation of a player’s seasonal fielding performance and added
insight into the aging process of a baseball player’s underlying ability to field.
iv
Contents
Title Page i
Acknowledgements ii
Abstract iv
Table of Contents v
List of Figures viii
1 Introduction and Motivation 1
1.1 An Introduction to Baseball and Fielding . . . . . . . . . . . . . . . 2
1.2 The State of Fielding Analytics . . . . . . . . . . . . . . . . . . . . 5
1.3 Spatial Analysis in Sports . . . . . . . . . . . . . . . . . . . . . . . 11
1.4 Related Time Series Techniques . . . . . . . . . . . . . . . . . . . . 13
1.5 Dissertation Organization . . . . . . . . . . . . . . . . . . . . . . . 17
2 Original Bayesian Hierarchical Model 19
v
2.1 Description of the Data . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2 Data Manipulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.2.1 Flyballs/Liners . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.2.2 Grounders . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.2.3 Eligible BIP × Fielder Combinations . . . . . . . . . . . . . 28
2.3 Original Hierarchical Model . . . . . . . . . . . . . . . . . . . . . . 29
3 New Model Specifications 34
3.1 Constant-Over-Time Model . . . . . . . . . . . . . . . . . . . . . . 35
3.2 Moving Average Age Model . . . . . . . . . . . . . . . . . . . . . . 39
3.3 Autoregressive Age Model . . . . . . . . . . . . . . . . . . . . . . . 43
3.3.1 Model Description . . . . . . . . . . . . . . . . . . . . . . . 44
3.3.2 State Sampling: FFBS . . . . . . . . . . . . . . . . . . . . . 47
3.3.3 Remaining Sampling: Gibbs Sampler . . . . . . . . . . . . . 49
4 Results 53
4.1 Calculating SAFE Values . . . . . . . . . . . . . . . . . . . . . . . . 54
4.1.1 Choosing the Parametric Curves . . . . . . . . . . . . . . . . 54
4.1.2 Weighted Integration . . . . . . . . . . . . . . . . . . . . . . 56
4.2 Analyzing SAFE Estimates . . . . . . . . . . . . . . . . . . . . . . 59
4.2.1 General Analysis . . . . . . . . . . . . . . . . . . . . . . . . 59
4.2.2 Model Differences and Specific Players . . . . . . . . . . . . 63
vi
4.2.3 Age Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.3 Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.3.1 Derek Jeter . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.3.2 Vernon Wells . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5 Model Validation 81
5.1 Predicted Deviations . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.1.1 Methods of Calculation . . . . . . . . . . . . . . . . . . . . . 82
5.1.2 Graphical Survey . . . . . . . . . . . . . . . . . . . . . . . . 86
5.2 Comparing to Existing Metrics . . . . . . . . . . . . . . . . . . . . 89
6 Conclusions and Future Work 92
A Kalman Filter 95
B Backward Sampling 97
vii
List of Figures
1.1 Baseball positions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Field of play broken up into the zones needed when calculating UZR 9
2.1 Heatmaps of all in play flyballs and liners . . . . . . . . . . . . . . . 22
2.2 Empirical angle densities for groundballs . . . . . . . . . . . . . . . 23
2.3 Defensive alignments by fielding teams . . . . . . . . . . . . . . . . 25
2.4 Examples of distance to a flyball/liner and angle on a grounder . . 27
3.1 Hierarchy of the Constant-Over-Time Model . . . . . . . . . . . . . 35
3.2 An Example of the Moving Average Age Model . . . . . . . . . . . 40
3.3 A Visualization of the Autoregressive Age Model . . . . . . . . . . 47
3.4 AnExampleoftheSolutionforMissingSeasonsintheAutoregressive
Age Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.1 Histograms of the Posterior Means for Age-Specific SAFE Estimates 60
4.2 SAFE Results for a Group of Fielders under the Original Model . . 64
viii
4.3 SAFE Results for a Group of Fielders under the Constant-over-Time
Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.4 SAFE Results for a Group of Fielders under the Moving Average Age
Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.5 SAFE Results for a Group of Fielders under the Autoregressive Age
Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.6 Position-Age SAFE Estimates . . . . . . . . . . . . . . . . . . . . . 72
4.7 Posterior Means and 95% Intervals on Autoregressive Terms over Time 74
4.8 Acrobatic Fielding Play by Derek Jeter . . . . . . . . . . . . . . . . 77
4.9 Catch at the Wall by Vernon Wells . . . . . . . . . . . . . . . . . . 79
5.1 MosaicPlotofWinningPercentageviaPredictedDeviationsforEach
Ball In Play Type and Position Combination . . . . . . . . . . . . . 88
5.2 Histograms of the Average Ranking of Each Model . . . . . . . . . 90
6.1 Automatic Tracking Data by Field F/X . . . . . . . . . . . . . . . . 94
ix
Chapter 1
Introduction and Motivation
Evaluating a baseball player’s fielding ability using objective means has been an
ongoing problem amongst Major League Baseball (MLB) enthusiasts and profes-
sionals. During the sport’s infancy, the only data available for measuring a player’s
fielding contribution was fielding percentage, an antiquated metric based on data
acquired through subjective means. Thanks to technological advancements giving
way to new data in the past couple of decades, metrics meant to gauge the value
of a fielder have brought a fresh perspective to fielding’s contribution to winning
baseball games. However, most of these tools do not fully utilize the potential that
this new data has to offer, especially with regard to its continuous nature. SAFE,
Spatial Aggregate Fielding Evaluation, is an approach that attempts to fully uti-
lize these continuous measurements. The methods, both frequentist and Bayesian,
to calculate the rudimentary version of SAFE have been highlighted in past work
1