SIAM News Blog

A Mathematical Journey to Football

By Eric Eager

My love of numbers has always accompanied my love of sports. As a kid, I could recite the Pythagorean theorem as well as I could recount the number of catches that Jerry Rice made in each season of his hall-of-fame career. My childhood is annotated by my hometown Minnesota Vikings’ heartbreaking losses. I knew all of the stats during any game and could recite those of others. This penchant served me well as I progressed in both my athletic and academic endeavors. I chose mathematics as my undergraduate major, a subject that came naturally to me and neatly coexisted with my love for playing and watching football as a college student at Minnesota State University Moorhead.

When it became noticeably clear that my career would likely not involve sports, I began taking the time to appreciate the beauty of mathematics and the learning thereof. I was hooked by real analysis, abstract algebra, differential equations, and the idea that math was a living, breathing thing that could model the world with the guidance of people like me. As a result, I opted to pursue my Ph.D. at the University of Nebraska–Lincoln (UNL).

At UNL, I grew to love all aspects of professional applied mathematics — from modeling to data analysis and simulation to theorem proofs. I developed models that led me into the discipline of mathematical biology, where I studied under world-class researchers and tackled important problems in population ecology, environmental biology, and gene regulatory networks. I also enjoyed conducting cutting-edge research about the scholarship of teaching and learning, and I mentored two Research Experiences for Undergraduates groups while in Lincoln. This work then took me to the University of Wisconsin–La Crosse, where I founded the Math Bio Working Group and received multiple grants from the National Science Foundation to mentor undergraduate research at the interface of mathematics and biology. I was actively accomplishing the goals I had set when I decided to become a mathematician many years earlier. 

Eric Eager (left) of Pro Football Focus (PFF) previews Super Bowl LIV between the Kansas City Chiefs and the San Francisco 49ers in Miami, Fla., with Soren Petro of Sports Radio 810. Photo courtesy of Soren Petro.
In 2015, my world changed. While in the middle of my academic career as a mathematician, I agreed to help a company called Pro Football Focus (PFF) collect and analyze data for the National Football League (NFL) and college football. PFF found its way into my world through my weak interests in fantasy football and the plight of my favorite team, the Kansas City Chiefs. The organization was collecting and analyzing data in a way that I had never seen. “Moneyball for football,” I thought. I was already watching these games religiously, so I figured that getting paid to do so would keep everyone in my family happy. My mother thought I was wasting my time.

At the time, researchers were doing little in the way of mathematical or statistical analysis with this type of information. This fact surprised me but ended up being extremely advantageous. I knew that nearly all of the NFL teams were paying PFF for its services; here was an opportunity for me to use my skills as an applied mathematician to finally make a difference in the game I loved so much. I was learning more about football and data science than I ever thought possible and pushing my professional capabilities forward with each day.

By 2018, my colleague George Chahrouri and I had developed enough quality football-based machine learning models for PFF CEO Neil Hornsby and former Cincinnati Bengal and PFF majority owner Cris Collinsworth to offer us the job of a lifetime: the opportunity to work full time in football as data scientists for the world’s most prominent football data company. While it was not easy to leave my position at UW–La Crosse, especially because I had just earned tenure the previous year, it was a risk I decided to take.

Now almost three years later, I have held several different roles at PFF as the company continues to grow. From data scientist to Vice President of Research and Development, I have consulted with teams on the use of our data to evaluate players, coaches, and front office members. I have also mentored other employees who have grown to do the same thing. When PFF moved from a data provider to an analysis company, our group began to build machine learning models for fantasy football and simulators for gambling. Our dashboards and contract projections help pair agents with rising professional prospects, and our text and video content provide alternatives to traditional sports media. I have been lucky enough to appear on NFL Network and frequent talk radio shows in almost every major media market in the country to discuss fantasy football, gambling, and the NFL draft. PFF’s work has been featured on NBC Sunday Night Football as well as the TODAY show. In fact, MSNBC’s national political correspondent Steve Kornacki used our simulation to analyze the playoff picture in the same engaging way he analyzed the electoral map during the 2020 U.S. election season.

My typical workday is never typical, and my mathematics training routinely comes into play through the habits of mind that are necessary to navigate the competitive and ever-changing world of sports analytics. While PFF’s data set was already immense when I began working with the company in 2015—and even more so when I joined full time in 2018—the data we use to better understand the game of football continues to grow in both rows and columns each day. Staying up to date with the newest methods of generating insights from this data is no different than being privy to the latest theorems or models in mathematical biology. I therefore spend much of my time reading the work of other analysts, including those within and outside my group, to determine whether I can integrate any of their ideas into my models. Does incorporating the continuity of a team’s offensive line reduce the errors in our fantasy football projections? Can adding the speed of a pass rusher’s first move off the line of scrimmage help sharpen our ability to employ machine learning to evaluate his talent level? What is the best way to utilize subject matter expertise to communicate our findings to stakeholders and ensure that the information will be used?

Throughout the course of both my own education and that which I gave my students, the narrative always remained that one can do anything with a mathematics degree. There were times where I questioned such a notion, but ultimately my career path has convinced me that it really is completely true. The marketplace for sports analysts is quickly evolving but far less rigid than most. With so much public data readily available, your resume is the insight that you present to the world; do not be afraid to get started and share your work!

Eric Eager is the Vice President of Research and Development at Pro Football Focus (PFF), a worldwide leader in data and analytics. Prior to joining PFF, he was an applied mathematician who studied mathematical biology, ecology, and the scholarship of teaching and learning.

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