Math Meets Football: One in 600 Billion

Why do football players make terrible pilots? Because they always break the plane before a touchdown!

Obligatory math-football joke? Check. Now let’s get to business.

I’m John Urschel, NFL offensive linemanpublished mathematician, and self-proclaimed mathlete. If you don’t believe me, just check my Twitter handle, @MathMeetsFball. There’s nothing I love more than crunching numbers, except maybe crunching defensive linemen on the football field. The Players’ Tribune has been kind enough to give me my own column, where I will talk about any and everything football with — you guessed it — a mathematical spin.

For my first column, I’d like to go back to my roots and talk college football. Rest easy, Coach Mora, we’re not talking playoffs. Not yet, at least.

More specifically, I’d like to begin by covering a topic very close to my heart: academics in college football. As a former winner of the Campbell Trophy (also known as the “Academic Heisman”) and Sullivan Award (given to the nation’s most outstanding amateur athlete), I’ve always taken the student-athlete ideal quite seriously.

It is commonly said that football players at the top universities are not student-athletes, but simply attend university to play football, and little else. While that debate may never be one that is truly settled, I decided to do a little digging in order to perhaps further the conversation. For this piece, I investigated how the distribution of student majors at two big-time college football programs, with two distinct reputations, compares to that of their respective general student populations.

First, I looked into the distributions of academic majors at one of the top teams in the SEC West, Auburn. Why pick on them, you ask? Am I a closet ‘Bama fan? No, I am not. In fact, I chose them because, of the top five teams in the SEC West, neither Mississippi State nor Alabama bothers listing its students’ academic interests, and Ole Miss and LSU give only vague information. Auburn, to its credit, gives very clear information about actual majors, instead of just general colleges, or even worse, nothing at all. I want everyone to note that I did just say something nice about Auburn. It happened. Unfortunately, after gathering the data and running the numbers, that’s just about the only good thing I can say.

What I did is as follows: I recorded the academic major and school of every upperclassman (junior or above) scholarship player on Auburn’s roster. In addition, I recorded the college distribution of the entire upperclassmen student population at Auburn during the Spring 2014 semester. Then I compared the two. Below are facts and figures illustrating the distribution of academic colleges for football players vs the general student population.

I don’t think it takes a degree in advanced mathematics to see that these are two very different data sets. (However, for those of you more mathematically inclined, the corresponding Chi-Square test gives a p-value of .0001. Yes, I know some of the expected values are less than five. No statisticians, I didn’t use a Fisher’s exact test instead. These things happen.)

But let’s not be too quick to judge. Perhaps the football players at Auburn happen to be drawn to the humanities? If only. When I performed my analysis, I found something particularly fascinating. There was a clear outlier when it came to academic majors. A stunning 23 out of the 48 upperclassmen student athlete football players are enrolled in public administration. Logically, it must be a fairly common major, right? This is where things take a turn for the worse. As of last spring, only 88 of the 11,402 upperclassmen in the whole university were majoring in public administration! The odds of something this extreme happening by chance is about one in three undecillion. For those of you not familiar with your large numbers past trillion, that is a digit 3 followed by thirty-six zeros! Yes, 1 in 3,000,000,000,000,000,000,000,000,000,000,000,000. That’s roughly equivalent to you flipping a coin and landing on heads 125 times in a row.

But with that said, fair or not, Auburn is known for being more of a football factory than an institution that educates its football players. So to get a more balanced look at this phenomenon, I also performed the same analysis for Stanford, a school that most would agree is more academically inclined.

Interestingly, all of the underclassmen football players were undeclared. This is the norm at Stanford, where majors are declared by junior year. For the purposes of my analysis I removed all the undeclared students at the university. These were my results:

Better (p-value of .0658, although the low number of colleges has a large effect on this), but still not quite right. But at least they don’t have over a quarter of their students majoring in one subject, right? Wrong. Of the 64 students with a declared major, 17 of them are majoring in “science, technology, and society,” an interdisciplinary major at Stanford. Unfortunately, I don’t know how many Stanford students are currently enrolled in the major. Believe me, it’s not from lack of effort. Stanford does not list any enrollment statistics by major past 2009-2010, and the Department of Science, Technology, and Society did not take too kindly to my interest in this information (come on Stanford, get on Auburn’s level!). However, I think we can be safe in assuming the enrollment is still in the same ballpark. The total enrollment in 2009-2010 was 99 out of the 3265 undergraduate students with declared majors. The odds of this happening by chance are about 1 in 600,000,000,000 (six-hundred billion), roughly equivalent to flipping heads 40 times in row, and far less likely than winning the California State Lottery jackpot.

What is the cause of this phenomenon that happens to plague both Auburn, a top SEC team known exclusively for football, and Stanford, a team known for extremely strong academics? It could be a number of things. Perhaps it is a case of sheep following the proverbial flock, football players just trying to get by, or, dare I say, something much less benevolent.

I don’t pretend to have these answers. What I do have is the numbers. And there’s more where that came from. Stay tuned.