As part of our Math Awareness Month celebrations we asked Dr. Andrew Gelman how his interest in sports has had influence on his career in statistical mathematics.  Although Dr. Gelman noted that he was often picked last in gym class, he continues to be a fan of sports and his credentials in academia certainly make up for his lack of athleticism. Dr. Gelman is currently a Mathematics Professor at Columbia University. His statistical expertise has won him various awards such as the Outstanding Statistical Application award from the American Statistical Association, the award for best article published in the American Political Science Review, and the Council of Presidents of Statistical Societies award for outstanding contributions by a person under the age of 40. He is also the author of Red State, Blue State, Rich State, Poor State: Why Americans Vote the Way They Do.

PUP: What sports are you fond of?

Andrew Gelman: I always preferred soccer, actually.

PUP: Did you enjoy sports or mathematics first as a child?

Andrew Gelman: As a child, I always enjoyed sports, but I imagine I’m not unique among mathematicians in having often been the last kid in the playground to be picked for any team. I remember some very long and unpleasant softball games in 5th grade recess.

PUP: How did you become interested in sports and/or mathematics?

Andrew Gelman: I graduated from college (majoring in mathematics and physics) in 1986, and one of the factors influencing me to go into statistics were the baseball abstracts which Bill James published annually during most of the 1980s.

PUP: Do you find yourself using math while watching or playing sports?

Andrew Gelman: I don’t think my interest in mathematics and statistics has any impact at all in my participation in sports, but it certainly increases my enjoyment in spectator sports.

PUP: What can coaches or athletes gain by having an understanding of mathematics?
Andrew Gelman: I’m sure that coaches and athletes can gain a lot from statistical analysis when coupled with good coaching strategy. Earl Weaver was famous for making the best use of his players, focusing on their strengths rather than their weaknesses, and putting them in the lineup when appropriate. Statistical analysis can give a better idea of what works in what settings, and sophisticated statistical analysis can move us past generalities toward situation-specific recommendations.

As a part of our Math Awareness Month celebrations we talked with Dr. Mason Porter about how his initial interest in baseball led him into a career in Mathematics.  Porter received his doctorate from Cornell University in 2002 and currently teaches courses in applied mathematics at the University of Oxford.

PUP: What sports are you fond of?

Mason Porter: Baseball!!!

Well, I also like playings things like ping pong and frisbee, but baseball was my first love—and I’m not referring only to sports.  I’ve been fanatically following the Dodgers for 30 years, and I’m only 34.

PUP: Does your career in mathematics influence your appreciation for sports?

Mason Porter: Not really. However, my appreciation for sports has occasionally influenced my mathematics;  it is true that my mathematical knowledge makes it pretty easy to understand what the sabermetricians are doing.

I recently coauthored a paper on baseball networks, in which pitchers and batters give a bipartite graph of what can be viewed as mutually-antagonistic interactions.  I have also worked with collaborators on a ranking system for college football, and I wrote a book review (on a book that aims to teach statistics using baseball) for the AMS Notices this year for their Mathematical Awareness Month issue.

PUP: Did you enjoy sports or mathematics first as a child?

Mason Porter: I enjoyed sports first, but baseball statistics are actually one of the things (along with fractals and, more generally, pretty pictures that could be better understood and appreciated with the help of mathematics) that first got me into mathematics.  I learned a few things early that way, and I also would snail-mail baseball card companies when the stats were wrong to see whether it was a reporting error or a calculation error.  Nowadays, I’d look such things up online, but then it required more effort to find an extra source.

PUP: How did you become interested in sports and/or mathematics?

Mason Porter: I probably just caught part of a game on tv, and I was hooked.  It certainly helped that early on (1981) the Dodgers won the World Series, and we had players like Fernando Valenzuela and personalities like Tommy Lasorda (and announcer Vin Scully) that were wonderful.

PUP: Do you find yourself using math while watching or playing sports? How?

Mason Porter: I use some simple on-the-fly statistics when watching baseball games because most announcers often say asinine things. I’m also into sabermetrics, which creeps into broadcasts more these days.

I do use some of this when playing fantasy games as well, though my track record isn’t all that great.  However, I did do well enough once to get an autographed Nolan Ryan baseball.

When playing, it makes a lot more sense to use physics rather than math!  Although they are obviously (to me… I’m sure pure mathematicians would yell at me for this) two sides of the same coin, it’s more sensible to think in terms of physics when it comes to the action.  I have definitely thought in those terms when playing ping pong, pool, and Frisbee.  I have more skill at those than at baseball, though I do like to play.  For ping pong, the magnus force is really important—and, embarrassingly, I only found out that that was what was going on there after messing up the relevant physics on a project concerning vortices in Bose-Einstein condensates.

Also, putting various types of spin in pool shots, and of course angles in pool, ping pong, and Frisbee.  For baseball, I would say I just try to make up for lack of natural ability by baseball knowledge rather than science.  For example, I am an opposite-field hitter, which is exceptionally rare in softball—but the right fielders are usually very poor fielders in softball, so I have developed my batting stance to hit things there naturally.

PUP: What can coaches or athletes gain by having an understanding of mathematics?

Mason Porter: I’m not sure what athletes can gain.  Coaches could certainly make use of statistics that correlate more strongly with winning.  As a trivial example, on base percentage is much more important than batting average, yet there are still many examples of so-called 300 hitters who get lots of playing time even though they don’t get on base via walks, don’t hit for power, and aren’t good fielders.  The magic .300 still blinds a lot of people.  And then there are more sophisticated quantities (RUE,etc.) that can also help in making decisions about personnel and playing time.  Also, keep in mind that it’s not just coaches who should use such considerations—others are deciding who the organization drafts, what free agents are signed, etc.

As part of our Math Awareness Month celebrations we asked Mathematics Professor, Dr. Tim Chartier, about how he incorporates his love for soccer and other sports with his passion for mathematics. Chartier is a professor at Davidson College where he specializes in numerical analysis and partial differential equations, and even taught a class on how to produce mathematical brackets for March Madness. He has been recognized by the Mathematical Association of America in 2007 when he received the Henry L. Alder Award for Distinguished Teaching by a Beginning College or University Mathematics Faculty Member.

PUP: What sports are you fond of?

Tim Chartier: In terms of sports that I am fond of analyzing mathematically, I enjoyed learning about the recent research into soccer. I learned about the research on soccer when I was investigating applications for a numerical analysis textbook I’m co-authoring. When I bumped into the work, I was captivated by the results and motivated to dig deeper and deeper into their work. In the end, I wrote a short expository article on the work which was prompted by an encounter with a student who responded quite enthusiastically when I talked about the work. I believed strongly that other students would respond similarly. I have found this to be an excellent example for Calculus, Differential Equations, Numerical Analysis or Modeling classes.

I have also conducted original research in sports ranking. We have applied our research to football, ice hockey and basketball. This academic year will be especially memorable as it was the first time I taught a class, “How to create mathematically-generated brackets of the NCAA Division I Men’s basketball tournament”. March was even more maddening as we watched our brackets compete in the class pool! In particular, our brackets were submitted to the ESPN Tournament Challenge in which close to 5 million brackets were submitted. One student produced a bracket (entirely generated from math) that scored in the top 99% of that competition!

As an individual, I do enjoy soccer, although these days my games are with my son who is in first grade and my daughter who is in pre-school. I also enjoy running and mountain biking. Growing up outside Philadelphia, I played considerable amounts of basketball although largely half court games or games of HORSE in which my arsenal of trick shots was handy.

PUP: Does your career in mathematics influence your appreciation for soccer and other sports?

Tim Chartier: The research in soccer underscored the influence of computational fluid dynamics in modern sports. If I am watching sports, be it an Olympic competition, a NASCAR race, or the Tour de France and an announcer mentions some innovative apparatus (suit, car design, or helmet) that increases an athlete’s speed, it is not uncommon for me to smile or even mention that mathematics made that possible! If I’m in the company of others, this can spark interesting conversations about applications of math and even capture the attention of a self-declared math-hater.

As another example, we can look to NASCAR. I live in Davidson, North Carolina. The town immediately north of Davidson houses many of the NASCAR garages. As such, a variety of my friends work in that industry. A few years ago, I learned that one friend who specializes in shocks uses the mathematical software Matlab in his job almost daily. I use Matlab in both my mathematical modeling and numerical analysis classes. Students generally have been very interested to learn that the software they use in class enhances a professional sport connected to our area. In fact, one student worked for a NASCAR team right after graduating from Davidson College and was hired, in part, for his skills in Matlab programming, which he used in his job.

PUP: Did you enjoy sports or mathematics first as a child?

Tim Chartier: This is difficult to answer. My mother notes that even as a young child, I liked games with numbers whereas my sister preferred games with words. I remember enjoying math in elementary school. However, I was also an avid fan of kickball! I grew up in a neighborhood where large numbers of children would gather daily to play conventional sports and games of our own invention.

PUP: How did you become interested in sports and/or mathematics?

Tim Chartier: My interest in soccer grew from the playground. Many of my friends played soccer, and I wanted to play with them at recess. In time, this grew to playing on school teams during my secondary education.

My interest in studying mathematics actually grew from my interest in the performing arts. Throughout high school, I performed throughout the Philadelphia area in puppetry and in college performed widely in puppetry and mime. During college, I studied math and computer science so I could find a job in those fields if the performing did not lead to full-time employment. The more I studied math, in particular, the more I wanted to learn. While I would eventually attain a doctorate in math, I continued to perform at national and international levels throughout my studies.

PUP: Do you find yourself using math while watching or playing sports? How?

Tim Chartier: Many people with whom I play sports comment that I use math to play. I often find angles that are apparently not as obvious to someone else. In basketball, I often would estimate the effect of a spin on ball’s bounce off the backboard. In soccer, I would often try to position myself as to reduce or eliminate the best angles of approach of my competitor. Frankly, many athletes probably do this. My friends often laughed as I would talk about it as angles and in mathematical ways. I do remember once in cross country trying to estimate how much longer my stride was to the lead runner directly in front of me. I tried to compute how long it would take to catch him if our rates stayed constant. I laughed later (having come in second and never catching that runner) that it didn’t work as it was cross country and the terrain didn’t allow for constant rates.

PUP: What can coaches or athletes gain by having an understanding of mathematics?

Tim Chartier: College football coaches already probably try to understand how to best optimize their chances for high ranking with the BCS ranking. Of the various ranking methods of the BCS, two are based in linear algebra. Clearly, winning all the time would be the best way to have a high ranking but that isn’t always possible. Further, players may need rest or even playing time to create a more robust line-up, an understanding of how these schemes work can help with coaching decisions.

The research on soccer demonstrated that the new stitching of soccer balls impacts how the ball flies through the air. I presume that athletes learn this effect through an understanding of the mathematics and physics involved or possibly intuition gained by trail and error. The insights of this work can play an important role for ball manufacturers as they may be able to design balls customized to differing levels of play.

I believe that athletes use mathematics all the time. Ice hockey would be difficult to play if one did not think about angles. Short track speed skating would be harder to win without thinking the effects of acceleration and velocity. Golfers must estimate the effect of wind resistance on a ball in order for some chip shots to land on the green. These examples are simply applications of Calculus. While one may not necessarily have deep understandings of mathematics for these applications, it also wouldn’t hurt. When it comes to those who design the modern equipment of sports – the aerodynamic cars of NASCAR, soccer balls for the World Cup, suits for Olympic swimmers, and the hulls for competitive sailboats, mathematics and computation play a vital role in success in the sport.