Math Awareness Month – Q & A with Michael J. Schell

As part of our Math Awareness Month celebrations we asked Dr. Michael J. Schell, about his interests in mathematics and sports. Schell is the Chair and Scientific Director of Biostatistics at the MOFITT Cancer Center in Tampa, Florida, yet he is also the author of Baseball’s All-Time Best Hitters: How Statistics Can Level the Playing Field and Baseball’s All-Time Best Sluggers: Adjusted Batting Performance from Strikeouts to Home Runs. While Schell might spend his weekdays researching cancer data, he likes to spend his weekends watching baseball. Schell has even found that analyzing statistics in baseball has helped him in understanding and analyzing cancer data!

PUP: What are you currently working on?

Michael Schell: I am working on several things: fielding in baseball, and team winning performance over time in all major U.S. sports.  The latter was spurred forward by the Tampa Bays Rays great 2008 season.  For the first 10 seasons, Tampa Bay only won about 40% of their games, and had never been 5 games over .500.  In 2008, they went 97-65, breaking out of their traditional cellar dweller role.

PUP: How is mathematics used in your work?

Michael Schell: I use a branch of mathematics called statistics.  Statistics studies variation in data, and often seeks to determine whether a given result could occur by chance or not.  I frequently model data using regression methods.

During the week, I am involved in cancer research.  Knowledge that I have gained in understanding variation in data from baseball, as well as fitting changes over time have come in quite useful in analyzing cancer biomarker data, where I try to find relationships between levels of proteins in the body with the presence or absence of cancer.

PUP: How can math help us better understand baseball?

Michael Schell: Baseball managers have long known, as just one example, that it is better for the batter to be the opposite handedness to the pitcher.  This is used in setting up lineups, especially where players are “platooned”, and by selecting which pitcher to bring in from the bullpen in a given late inning situation.  In recent years, baseball teams have begun hiring statistical analysts to look for more subtle advantages revealed by statistical analysis.

Baseball can also help math in the sense that the strong knowledge of the game by fans allows them to more easily deal with concepts in math.  Thus sports examples can be an excellent way to learn statistical ideas.  That is why the linkage is being celebrated this year in Mathematics Awareness Month.

PUP: Why do you think we haven’t included outside contexts in ranking baseball heroes before?

Michael Schell: Adjustments to batting average data go back at least to the 1970s, when averages were adjusted for the league average.  My books just expanded upon that by incorporating three additional adjustments: player talent spread (using the standard deviation), ballpark effect, and aging.

There are some technical statistical details involved in doing these adjustments well.  The biggest challenges for me were: 1) adjusting for batting events that vary greatly between players, like home runs, stolen bases, and triples, and 2) estimating ballpark effects without having the home and away data for each ballpark that makes it much easier to do.

PUP: Why is ranking baseball heroes this way important?

Michael Schell: Fans would like to know where their heroes rank among the all-time greats, as it makes their experience of the game more exciting.  Without any adjustment, Tony Gwynn, who retired in 2001, ranks as the 18th best hitter for average in major league history.  All players ahead of him on the unadjusted list were retired by 1960.  After the adjustments made in my books, Gwynn ranks 1st.  Fans are greatly interested in a fairer appraisal, which is only possible through appropriate statistical adjustment.

PUP: What other ways can we use mathematics in baseball besides batting statistics?

Michael Schell: I am using mathematics to look at team winning performance over time.

PUP: How do you find yourself incorporating mathematics in other sports?

Michael Schell: I recently found that expansion teams in the NBA require about 5 years in order to become competitive with existing teams.  Another tidbit: since 1960, the New York Mets are the most inconsistent team in winning percentage in baseball.

Math Awareness Month – Q & A with Andrew Gelman

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.

Math Awareness Month — Q & A with Mason Alexander Porter

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.

Math Awareness Month — Q&A with Dr. Tim Chartier

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.

Math Awareness Month — Q&A with Dr. Mike Huber

As part of our Math Awareness Month celebrations we interviewed previous faculty member of the United States Military Academy at West Point and current Associate Professor of Mathematics at Muhlenberg College, Dr. Mike Huber. Although Huber teaches courses ranging from Statistics to Calculus his real passion is sabermetrics, the computerized measurement of baseball statistics. Huber finds that he is able to relate to students most through sabermetrics because he is able to show that what he is teaching in the classroom is relevant to the students’ passion of sports. He is also the author of Mythematics: Solving the Twelve Labors of Hercules

PUP: What sports are you fond of? (including and beyond baseball)

Mike Huber: I am a general sports fan. I regularly follow baseball at the professional and college levels. I also enjoy watching college and pro football, college basketball, and international soccer (the World Cup and European Cup tournaments). My son graduated from a Division I university with major sports programs and I have been following them ever since he was a freshman. I also helped establish a faculty liaison program at Muhlenberg College, where faculty have a habitual relationship with a team, helping the student athletes with academic-related issues, honor societies, being a fan at the matches/games, etc. I did this for 9 years with Army’s baseball team and now I have been with Muhlenberg’s volleyball team for over 2 years. I travel to away matches and root for the Mules.

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

Mike Huber: Absolutely. About ten years ago I wanted to model rare events in baseball (hitting for the cycle, pitching a no-hit game, and turning a triple play). Having an understanding of different distributions (Poisson, exponential Weibull, etc.) allowed me to fit the data to a cumulative distribution function and then determine a goodness of fit. It seemed to me that no-hitters followed a Poisson process and may have followed a memoryless criteria, but I was able to “prove” so knowing the mathematics. Most of my sports-related scholarly research has centered around baseball.

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

Mike Huber: Sports probably came first. Having two brothers very close in age to me, I was always outside. We played Little League baseball, pick-up basketball and baseball games in the back yard and then at the neighborhood field, touch football (then tackle football) and even bowling. Our neighborhood had youth leagues and we played beginning at age 7 or 8.

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

Mike Huber: My father taught me how to read box scores and keep score myself, and I recall memorizing the statistics in the Sunday sports section of the paper when I was about 12. I started showing an aptitude for mathematics in the 6th grade and I remember reading as many books as I could find at the library dealing with baseball players and their statistics. I tried to link mathematics projects to sports while in college and graduate school and I continue to do so now as a professor.

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

Mike Huber: Yes; I will often jump on the internet and look up data during a baseball game. Here’s an example: Last season, the New York Yankees opened their new stadium in the Bronx, after having spent LOTS of money in off-season trades. Fans expected an offensive barrage of power and runs. The first homestand of the season was against the Cleveland Indians, and in the second game at the new stadium, the runs arrived. Unfortunately for the Yankees, it was the Indians who won, 22 – 4. I immediately searched online for such occurrences in the past. How often had teams scored 20 or more runs in a game? Since 1901, when the American League joined the National League, there have been just over 172,000 Major League games. In 224 of those games (about 0.13%), a team has scored 20 or more runs in a game. This is a rare event. I then fit an exponential distribution to the data and performed some analysis on the outcomes. Hopefully, I can now make some predictions on future events. I wrote a paper (with a colleague at West Point) and the Annals of Applied Statistics is publishing it soon.

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

Mike Huber: Believe it or not, some of the more successful Major League managers have a background in mathematics. Earl Weaver was one of the first managers to keep split statistics on pitcher-batter matchups (in the 1970s). Tony LaRussa keeps a laptop in the dugout. Davey Johnson was a math major in college. The Society of American Baseball Research (SABR) offers many different methods to evaluate or compare players. All teams have statisticians or public affairs individuals who make data available to coaches. Athletes are keenly aware of their stats; their agents are probably even more aware of them.

PUP: How has your interest in sports and math translated in the classroom?

Mike Huber: By conducting research and publishing scholarly books and articles, the students see that what I’m teaching in the classroom is relevant to their passion of sports. I’ve been fortunate to meet former ballplayers, including members of the Baseball Hall of Fame, and I’ve brought them to campus to meet the students; or, I’ve taken students to meet ballplayers. I regularly collaborate with the Bart Giamatti Library staff at the Baseball Hall of Fame, and I involve students in my research. I hope to continue involving students in sports-related research in the future.

PUP: Any interesting anecdotes about your work involving sports?

Mike Huber: Several years ago, I met Mr. Tony Morante, the director of tours at Yankee Stadium. He asked me to investigate a story surrounding Mickey Mantle. On May 22nd, 1963, the New York Yankees hosted the Kansas City Athletics in a night game at Yankee Stadium, before a crowd of 9,727. According to John Drebinger of The New York Times, “Mickey Mantle belted one of the most powerful home run drives of his spectacular career.” In the next paragraph, Drebinger continues, “First up in the last of the 11th with a score deadlocked at 7-all and a count of two balls and two strikes, the famed Switcher leaned into one of Carl [note: Fischer’s first name was Bill] Fischer’s fast ones and sent the ball soaring. It crashed against the upper façade of the right-field stand, which towers 108 feet above the playing field.” Mr Morante wanted to know, “How far would Mantle’s mighty smash have traveled, had it not smacked the upper façade?” Factoring in the wind, drag, Magnus force, humidity, assumed bat speed, trajectory of the ball, and other factors, I was able to develop a model for the distance traveled. The New York Times for May 23 provided weather records for the night before: the temperature at 11 PM was 61 degrees, with 39% humidity, winds blowing from the west at 8 miles per hour, and a steady barometer of 30.05 inches. Combining this with Magnus force charts found in Robert K. Adair’s The Physics of Baseball, I determined a maximum predicted distance for Mantle’s mammoth drive of 536 feet. Mr. Morante incorporated that information into his tours. Coincidentally, the great Mickey Mantel hit 536 career home runs, so his home run would have traveled one foot for each career home run!