By Christopher Keyes

Back in January, I was scrolling through the spreadsheet of student applications to our university’s directed reading program. I scanned for topics aligning with my expertise as a grad student in number theory that would be fun to work on with an undergrad in a one-on-one setting. In previous semesters, I chose such bread and butter topics as p-adic numbers and elliptic curves. This time though, what stood out was a student who wanted to learn sports analytics. This wasn’t traditionally offered as a course anywhere at Emory, but it would certainly involve a lot of mathematical content, making it perfect for a DRP!

At this point, it’s relevant to mention that I have been a baseball fan for as long as I can remember. I played every year from tee ball at four years old until high school, and never stopped following the game. Even now, I keep a pair of gloves and a baseball at my desk in the math department in case anyone wants to take a break to play catch, and I have been known to organize the occasional pick up wiffle ball game among the graduate students. All of this is to say that mentoring a student on sports analytics seemed right up my alley.

Still, I hesitated. I knew the game of baseball, but nothing about the wave of advanced metrics that have overtaken the modern game. My relevant mathematical background was also weak, as I haven’t taken a formal class in statistics since high school. Perhaps it would be best to find a student interested in another topic that I already know well. Something safe and familiar, like p-adic numbers and elliptic curves were. Learning about baseball analytics sounded great, but I was lacking some confidence to step out of my comfort zone to learn and mentor something new.

What ultimately convinced me to take this on was reframing it as the opportunity that it was. I had always told my fellow grad students that a DRP was a great way to learn that new topic that you’ve been wanting to learn and grow along with your students. Now it was my turn to take my own advice.

At my first meeting with Ezra, I was up front that I didn’t have much background in analytics or statistics, but that I was willing to learn along with him, which he appreciated. We connected over our shared interest in baseball, exchanging questions we had about the game that we hoped to answer by the end of the semester. For example, Ezra wanted to know “how much more is a single worth than a double?” The double is clearly worth more, since it moves the batter (and likely any baserunners) further along the bases than a single does. But its value might not be literally double that of a single. How should we even go about assigning value to different hits?

This meeting set the tone for the whole semester. I found an open access online course on sabermetrics, the mathematics of baseball, and we started learning about ideas like run expectancy, which gave us the language to answer Ezra’s question about singles and doubles. Along the way we also learned how to use SQL – a programming language for managing databases – to manipulate 150 years of baseball data, and brushed up on the statistical techniques we would need to evaluate each new metric we discovered. We spent our weekly meetings exchanging new questions that puzzled us about the game of baseball or poring over spreadsheets trying to decipher trends and identify outliers hiding in the heaps of historical data.

What surprised me was the profound impact this DRP had on me. In stepping out of my comfort zone to learn something new, I found myself genuinely enjoying every minute of it! One minute I was watching lecture videos or trying practice problems, when I had a question or an idea; before I knew it I had spent an entire afternoon trying to figure out, say, how much a stolen base is worth now, compared to the 1980s. Even the statistical portion of the material – which initially made me so apprehensive about the topic – turned out to be fun. Since (re)learning that the mean is the measure of central tendency that minimizes the sum of squared errors, while the median minimizes the sum of absolute errors, I haven’t shut up about it.

The whole experience has rejuvenated my curiosity and boosted my confidence, permeating my approach to my research. As a graduate student, it’s easy to get discouraged when you find a counterexample to the statement you’re trying to prove, or discover a paper that solves your problem but uses unfamiliar techniques you now have to learn. Lately, I have felt a little bit less discouraged and a little bit more curious to figure out what additional hypothesis I need to add, or more confident in my ability to decipher the unfamiliar. I was originally drawn to study mathematics, and number theory in particular, because I found the questions fascinating. By focusing on those questions that interest me and just seeing where they lead, math feels less serious and more fun.

Chris Keyes is a Ph.D. candidate at Emory University studying number theory. Outside of the math department, Chris enjoys staying active through running, baseball, and ballroom dancing.