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.