Download Fourth Down Decisions in NFL Football, a Statistical Analysis

CALIFORNIA STATE UNIVERSITY, NORTHRIDGE
FOURTH DOWN DECISIONS IN NFL FOOTBALL
A Statistical Analysis
A thesis submitted in partial fulfillment of the requirements
For the degree of Master of Science in Mathematics
By
Jennifer Alison Wright
August 2007
The thesis of Jennifer Alison Wright is approved:
Carol Shubin, Ph.D.
Date
Mark Schilling, Ph.D.
Date
Larry Clevenson, Ph.D., Chair
Date
California State University, Northridge
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Acknowledgements
I would like to thank Dr. Clevenson, my committee chair, for the hours that he has worked by my side on
this project. He introduced a topic that I very much enjoyed and had fun with. Also, I would like to thank
him for his patience; especially concerning topics of football. I have worked with Dr. Clevenson on other
projects and it has always been a pleasure.
I would also like to thank my committee members Dr. Schilling and Dr. Shubin. They have been a
wonderful help in reviewing my work. Dr. Schilling has been one of my professors in statistics and
regression. He is a busy man but always takes a moment to answer a question and play a game of croquet
(crochet). As for Dr. Shubin, she has helped me since I started CSUN. Her work in the NASA CSUN/JPL
PAIR program and other projects has helped me, as well as many other students. Through her continued
support and encouragement she has helped me obtain my masters.
There are many other people to thank at CSUN. In many ways, the math department has felt like a family.
After working up to a Master degree in Mathematics I have met, had classes with, or spent time with all the
professors in the department. Many of the professors, staff and fellow students have contributed to my
personal growth and development here at CSUN.
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TABLE OF CONTENTS
Signature Page ...……………………………….…………………………………………………………….ii
Acknowledgements …………………….……………………………………………………………...…....iii
Abstract ….…………………………………………….…………………………………………….……….v
Section One – Introduction, How is football played? ......................................................................................1
Section Two – Data Collection …………...……………………………………….…………………………3
Section Three – Expected Points Model ………………………………………….………………………….7
Section Four – Probability of a Successful 1st Down Conversion ……………………………….…………13
Section Five – Field Goal Success ………………………………………………………….………………16
Section Six – Field Goal vs. First Down ……………………………………….…………………………..18
Section Seven – Punts ……………………………...………………………………….……………………23
To Punt or Not to Punt ...…………………………………………………..……………………...25
What Could Have Been? ………………………………..………………………………………...27
Section Eight – Punt vs. First Down Table ……………….……………………………………….………..31
Section Nine – Extra Yards ………………………………………………………………………………...34
Bibliography ………………………………………………………………………….…………………….38
Appendix A – Logistic Regression ………………………………………….……………………………...39
Appendix B – Field Goals vs. First Downs ……………………………….……………………………..…41
Appendix C – Punts vs. First Downs ……………………………………….……………………………....46
Appendix D – Expected Points, Tables and Graphs ……………………….…………………………….…51
Appendix E – Probability of 1st Down Success, Tables and Graphs …...…………………….………….…59
Appendix F – Other Tables ……………………………………………………………….………………...65
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ABSTRACT
Fourth Down Decisions in NFL Football, A Statistical Analysis
By
Jennifer Alison Wright
Master of Science in Mathematics
The teams in the National Football League demonstrate different strengths, weaknesses, and styles of play.
Some are clearly more powerful offensively, and they also differ in their style, the run-pass balance.
Defensive strength also varies greatly from team to team. Nevertheless, most teams make the same fourth
down decisions out of the choices of punting, attempting a field goal, or going for a first down.
Usually, the choice between the three possible 4th down decisions is easily narrowed down to two. For
example, if the team is too far from the goal line to attempt a field goal, the choice is either to punt or to go
for a first down. When close enough to attempt a field goal, punting is not considered; then the team
chooses between attempting a field goal and attempting to get a first down. The statistical analysis of these
choices is the subject of this thesis.
We seek models to answer these questions:
1.
From a given yard line with a new first down, what is the expected number of points? A new first
down occurs whenever a team takes possession for the first time, or has just gained the ten yards
necessary from a previous new first down to be granted another first down and ten yards to go.
New first downs inside the opponents’ ten-yard line are called first and goal-to-go. These are also
considered part of the same model.
2.
What is the probability an attempt at a new first down is successful, as a function of the yards
needed for success?
3.
From a given yard line, what is the probability a field goal attempt is successful?
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With the answers to these questions, we can compare the expected gain (or loss) from two different
decisions. When the difference in expectations is not close to zero, then the choice between these two
decisions is clear. One would choose the decision with the higher expectation.
The performances of five different teams, during the 2005 season were studied to find models to address
these questions. The teams were selected to represent teams both strong and weak offensively and
defensively, and another was picked as both offensively and defensively average.
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