Appendix: Sabermetrics in the Classroom — A Primer
What follows is an educational primer, the purpose of which is to assist in the teaching and learning of sabermetrics in a more formal context — that is, in the classroom. We share with you our techniques and approaches and give our pedagogical views. We invite you to adapt anything contained in this primer to your specific educational situation. This would apply to both lecture-hall classes and one-on-one individual studies.
Please feel free to contact us at the following e-mail addresses:
We would be happy to provide guidance and respond to questions or concerns.
This primer is divided into the following sections:
a. Review and Overview of Sabermetrics Courses
b. Prerequisites for Courses on Sabermetrics
f. Data Mining and Course Aids
g. Outside Speakers and Panels
i. Sample of Assessment Instruments: Some Supplemental Problems, Projects, and Examinations
As we mentioned in our acknowledgments, we believe that the first course on sabermetrics was offered in the 1988 Winter Session at Seton Hall University. If it was not the first course, it was certainly
one
of the first. The 1-credit course appealed to students for a number of reasons. First, it gave the student a convenient and economical way to obtain that odd credit needed to satisfy a 130-credit requirement for graduation, when most courses were for 3 credits. Also, since it was about baseball, it was a sort of novelty. This course, listed as MATH 1011, is still taught at Seton Hall. Since Winter Session classes are no longer offered at this institution, the course is taught during two Saturdays each spring semester: an 8-hour session in March followed by a 4-hour session in April. The course enjoys a great deal of popularity.
Since in the spring of 1996, MA 488 has been the course number for the 3-credit sabermetrics course which has been offered every year at the United States Military Academy at West Point. As is the case with all 3-credit courses at West Point, forty contact hours are required.
Since we three authors are most familiar with the MATH 1011 and MA 488 courses, this primer reflects our experiences with them. When necessary, because of a divergence of approaches due to the difference in the number of credits, we specify either MATH 1011 or MA 488, as appropriate.
Finally, we have mentioned that other schools also offer sabermetrics courses. Bowling Green State University and Tufts University, for example. We suspect that other schools will be offering similar courses in the near future, believe this because of the many issues which presently surround the national pastime, including economic, ethical, social and cultural concerns.
(B) Prerequisites for Courses on Sabermetrics
For MATH 1011, the prospective student was expected to have a working knowledge of arithmetic, algebra and a bit of descriptive statistics (mean, standard deviation, etc.). A basic four-function calculator, with a square-root key, was also required before the availability of personal laptop computers. In times past, student accessibility to a data source (
Total Baseball
, for example) was also a requirement. Presently, of course, the Internet is used, taking advantage of a plethora of Web sites (see our References section). Students of any major are permitted to take this course, provided he or she obtain approval from an academic advisor.
Regarding the MA 488 course, all students would have passed the four core mathematics courses required of all cadets. These courses include a semester of mathematical modeling, one year of calculus and a semester of probability and statistics. The cadets are also well versed in computer skills and trained to use spreadsheets, such as Excel, and computer algebra systems and statistics packages, like Mathematica and Minitab
.
Our experience has taught us that unless a student has a great interest in baseball and a desire to really learn more about the game, it is a mistake for him or her to take a course on sabermetrics. The course is not a trivia course; no student is ever asked to round out the Chicago Cubs infield of Frank Chance, Johnny Evers and Joe Tinker. But, unless there is a passion for the game, and its history — not to mention an appreciation for the essential role of numbers in baseball — the student will soon be bored to tears and wishing to drop the course. Should the student know about Harry Steinfeldt, all the better.
(C) Course Objectives
We start with the Bill James definition of sabermetrics:
the search for objective knowledge about baseball.
This is the
overarching
goal and objective in a course on sabermetrics: to teach the student how to search, measure and assess and draw conclusions.
We strive to teach the student how to reason in a sabermetrical fashion, using as many independent measures and instruments as possible. At the end of the course it is hoped that the student will be able to: 1) frame questions in a well defined manner; 2) if necessary, make reasonable assumptions; 3) use appropriate measures in a critical and proper way; 4) draw reasonable and plausible conclusions; and 5) realize any limitations drawn from the conclusions.
As we have emphasized in this book, to draw sabermetrical conclusions is not the same as proving a mathematical theorem.
(D) Course Content
The following bulleted list refers to MATH 1011. Note that all but the last two bullets refer to the March session; the final two to the April class.
• A diagnostic test to determine the BQ (Baseball Quotient) of the students; this is not graded
• A discussion of the history of baseball, with special emphasis on the development of the statistical measures used in the past
• A short review of algebra and descriptive statistics
• A thorough exposition of the “runs created” school popularized by Bill James
• A thorough exposition of the “linear weights” school, developed by John Thorn and Pete Palmer
• Introduction to other measures such as total average, the total power quotient and the weighted pitcher’s rating
• A demonstration of data mining using the Internet
• Determination of a course project (must be approved by instructors)
• Topics for open notes examination.
• Course project and briefing
The sequence of the topics above is roughly followed in the MA 488 course as well. However, because that course is weighted for three credits, and because we have many more contact hours, we not only delve more deeply into such topics as data mining, but we explore other topics and use computer technology much more. For example, the cadets might be asked to simulate the following situation: given a batter who hits .400, and has exactly 4 at-bats in each game, how often will he hit safely in 57 or more consecutive games? One can very quickly simulate hundreds of seasons using a random number command in Excel
.
Furthermore, one can tweak the parameters, such as varying the number of at-bats per game and increasing or decreasing the .400 batting average.
Other topics like clutch play, “streakiness” and ranking great teams of the past are also covered. In-class assignments, projects and examinations are also administered. See Section I below (A Sample of Assessment Instruments) for some examples of these course requirements.
A certain amount of lecturing is unavoidable. Still, we encourage much dialogue, and questions are always welcome, giving the course a seminar flavor. Often we use PowerPoint displays and afterwards have the presentations accessible to the students via the course home page.
Finally, we invite departmental colleagues to address our class if their research interests can be applied to sabermetrics. For example, it can be shown that the distribution of the occurrence of no-hitters can be closely modeled as a Poisson process with a particular exponential distribution studied in statistical analysis, using the assumption that these rare events are memoryless.
(E) In-class Dynamics
In addition to the imparting of knowledge, the opportunity exists to share opinions, perspectives and memories via classroom exchanges. While a course on sabermetrics focuses primarily on the hitting, pitching, running and fielding aspects of major league Baseball, we often have auxiliary discussions which may suggest a project topic for which a particular student may have a special interest. For example, we have had projects submitted concerning the Negro Leagues, women in professional baseball, elections to the Baseball Hall of Fame and the escalation of salaries — all researched from a sabermetrical perspective.
We have instituted many pedagogical changes over the twenty years we have taught sabermetrics courses. The most radical changes have been due to technology. The innumerable Web sites, in addition to split statistics, such as an individual’s batting average for day games versus night games, have provided so much data that we often have to filter out extraneous information to address specific questions.
We have found that serious students not only enjoy a course on sabermetrics, but they are generally self-motivated. Once they learn a specific measure which can be applied to an area in which they have an interest, they will often attempt to expand and improve the specific model. In addition, further research may lead them to some very technical sources. For example, in a 1977 article titled “An Offensive Earned-Run Average for Baseball” which appeared in the journal
Operations Research
, authors Thomas Cover and Carroll Keilers use such concepts as “Markov Chains” and “Negative Binomial Distributions” to develop their statistical analysis.
Naturally, as instructors, we strive to present a complete picture of the pertinent material in a simple, clear manner, without compromising the underlying mathematical integrity. We also try to put the development of this material within the rich historical context which major league baseball possesses. Above all, we attempt to provide an atmosphere where we can “talk baseball.”
(F) Data Mining and Course Aids
As we have indicated above, the Internet is by far our main source of data. Because most of our students have grown up in this computer age, they are most adept in surfing the Web. Many of them are also skilled in importing data into Excel spreadsheets.
In times past, we used various editions of
Total Baseball
and the
Baseball Encyclopedia
to obtain raw statistical totals.
The Hidden Game of Baseball
was, and still is, often referenced, both for its exposition of linear weights and for its insights into the historical development of many of the instruments used in sabermetrics. The same was and is true regarding various
Baseball Abstracts
editions written by Bill James.
Should other hard copy references be required, we encourage our students to use university library book lending programs.
No formal text is required in MATH 1011. We currently use
Curve Ball
in MA 488. Both courses have handouts as supplemental reading.
(G) Outside Speakers and Panels
Over the years we have invited a number of outside speakers to address our classes. For MATH 1011, this has usually taken the form of a panel of baseball fans; individuals who have been following the national pastime since the 1950s. They would share memories about such players as Willie Mays and Mickey Mantle while addressing such questions as whether or not Pete Rose should be inducted into the Hall of Fame. Other questions posed by the students might relate to such topics as free agency, inter-league play and the use of steroids or other banned substances.
We have been privileged to host many guests for our MA 488 sabermetrics class at West Point. Some of these have been:
• Robert Brown, former Yankee third baseman, eminent cardiologist and past President of the American League.
• Steve Balboni, former first baseman with the Yankees, Royals and Mariners, and member of the 1985 World Series champions.
• William Jenkinson, member of SABR, noted expert on long home runs and recent author of
The Year Babe Ruth Hit 104 Home Runs.