Statistics and Mathematics of Baseball (spring 2000)

  • Course Instructor: Kenneth Ross

    General description

  • For many, a great appeal of baseball is its emphasis on statistics. This seminar will analyze some of the statistics used with an emphasis on methods from the theory of statistics. Batting averages, streaks and other records will be studied. Criteria for membership in the Hall of Fame will be examined. Examples of Simpson's Paradox will be studied. Also, the mathematical theory of elementary "game theory" will be interpreted in terms of baseball.
  • Prerequisites
  • College algebra and an interest in understanding how ideas of statistics and mathematics can be applied to questions about baseball.
  • Course requirements and grading criteria
  • Students in the class will be evaluated in several different ways. There will be regular homework and several quizzes. Class participation, both written and oral, will also count. There will be two texts; see below. There may also be reading assignments in other books or articles. References that students will need access to will be put on reserve in the mathematics library. Also, I can loan copies of books that I own.
  • Each student will be expected to complete a term project, which will involve a substantial investment of time and energy. It may involve some outside reading; see the references. Each project will have a written component and may involve a presentation to the class as a whole.
  • Texts
  • Michael J. Schell, Baseball's All-Time Best Hitters: how statistics can level the playing field, Princeton University Press, 1999. $22.95. Available from amazon.com for $16.07 plus shipping and handling. "This book makes a significant contribution to baseball statistics and will also have the side-effect of getting readers interested in statistical reasoning and in how statistics can be used to clarify comparisons."
  • Michael Hogan, Baseball's Complete Players, McFarland & Company, Inc., Publishers, 2000. Available from amazon.com for $24.95 plus shipping and handling. This book provides ratings of total-season performance for the greatest players of the 20th century using the HEQ (an acronym for Hoban Effectiveness Quotient, pronounceable as "heck") rating system. This system is intended to present the fan with a simpler, yet accurate way to measure, in a quantitative manner, how good a season a player had. I have a copy.
  • Other Books on Baseball
  • Bill James, All-Time Baseball Sourcebook, STATS, Inc., 1998. This huge book has 2,653 pages and weighs about 7.5 pounds. It has more than enough for any amateur. More statistics are in the authorŐs All-Time Handbook. I have a copy.
  • Bill James, Major League Handbook 1999, STATS, Inc., 1998. All about 1998 with projections for 1999. I have a copy.
  • Bill James, The Politics of Glory, MacMillan, 1994. History of, and statistical analysis of, the choices made for the Hall of Fame. I have a copy.
  • Gerald W. Scully, The business of major league baseball, The University of Chicago Press, 1989. Identifies the many economic pressures exerted on the game today and measures their effects both on the field and in the ticket office. Out of print, but I have a copy.
  • Paul M. Sommers, ed., Diamonds are forever: The business of baseball, The Brookings Institution, Washington, D.C., 1992. "Exhibits the power of economics to predict and explain social behavior and its capacity to be fruitfully applied in diverse worldly contexts. It is a splendid book about a splendid sport. I have a copy.
  • Other Books
  • John L. Casti, Searching for certainty: what scientists can know about the future, William Morrow and Company, 1990. Chapter 1 is on chance and predictions; Chapter 4 is on random walks and stock market prices.
  • Edward Packel, The Mathematics of Games and Gambling, Mathematical Association of America, 1981. I have a copy.
  • John Allen Paulos, A Mathematician Reads the Newspaper, Basic Books, 1995. This book consists of many very short stories about issues recently in the news.
  • M. Stewart Townend, Mathematics in Sport, Ellis Horwood Limited and John Wiley & Sons, 1984. A British book on sports, with emphasis on the physical aspects. Baseball is hardly mentioned. I have a copy.
  • Journal Articles JRM = Journal of Recreational Mathematics
  • Albert, Jim, The Home-Run Hitting of Mike Schmidt, Chance, Vol. 11, No. 3, 1998, 27-34.
  • Albert, Jim and Patricia Williamson, Using Model/Data Simulations to Detect Streakiness, submitted to American Statistician.
  • Albright, Christian, A Statistical Analysis of Hitting Streaks in Baseball, J. American Statistical Association, Vol. 88, No. 424, December 1993, 1175-1183.
  • Comments on the previous paper, same journal issue. by Jim Albert, pages 1184-1188, and by H. Stern and C. Morris, pages 1189-1194.
  • Berry, Scott, The Summer of '41: A Probability Analysis of DiMaggio's Streak and Williams' Average of .406, CHANCE, Vol. 4, No. 4, fall 1991, pp. 8-11.
  • Berry, Scott, Modeling Acceptance to the Major League Baseball Hall of Fame, CHANCE, Vol. 13, No. 1, winter 2000, pp. 52-57.
  • Berry, Scott, Does "The Zone" Exist for Homerun Hitters?, preprint.
  • Boswell, Thomas, Welcome to the World of Total Average Where a Walk is as Good as a Hit, Washington Post, 1980. This is a very interesting sales pitch for the Total Average as the ultimate measure of baseball players' offensive power. I'd love to see an update that takes into account players of the past twenty years.
  • Bradley, Michael J. Building Home Plate: Field of Dreams or Reality? Mathematics Magazine, 69, # 1 (1996), 44-45. Are the official specifications for baseball's home plate consistent with the laws of geometry, or is it impossible to build such a five-sided figure?
  • Carbonneau, Danielle E. and Paul M. Sommers, Measuring Competitive Balance in Major League Baseball, (JRM), Vol. 28(3), 1996-97, pp. 161-165.
  • Cassuto, Leonard and David Grant, Babe Ruth and the Politics of Greatness: Is the Pen Mightier than the SABR?, preprint.
  • Cooper, H., K.M. DeNeve, and F. Mosteller, Predicting Professional Sports Game Outcomes from Intermediate Game Scores, CHANCE, Vol. 5, Nos. 3-4, 1992, 18-22.
  • Cornish, Andrew, Charles Fiedler, Brian S. Foss, and Paul M. Sommers, Eye-pothesis Testing: Another Look at the 1986 World Series, JRM, Vol. 19(4), 1987, 241-246.
  • Disco, Matthew D., Felix Paulick, and Paul M. Sommers, Some Differences Are Like Night and Day, JRM, Vol. 24(2), 1992, 94-96.
  • Durland, Dan W. and Paul M. Sommers, Collusion in Major League Baseball: An Empirical Test, Journal of Sport Behavior, Vol. 14 (March 1991), No. 1, 19-29.
  • Erickson, Jill E., Elizabeth A. Loring, Lisa B. Seiden, and Paul M. Sommers, The Boys of Summer are the Chis of Spring, JRM, Vol. 19(3), 1987, 161-163.
  • Gould, Stephen J., The Streak of Streaks, CHANCE, Vol. 2, No. 2, spring 1989, 10-16.
  • Groenveld, Richard A. and Glen Meeden, Seven Game Series in Sports, Mathematics Magazine, Sept-Oct 1975, 187-192.
  • Heath, Steven H., The Mathematics of the Baseball Boxscore, UCTM Newsletter, March 1988.
  • Heath, Steven H., Babe and Big Train, The Baseball Research Journal, 1988, page 40.
  • Heath, Steven H., An Analysis of the Walter Johnson Shutouts, Baseball Quarterly Reviews, Vol. 4, 1989, 1-17.
  • Heath, Steven H., One Hundred Twenty Outs -- No Runs, Baseball Quarterly Reviews, Vol. 6, 1991, 1-24.
  • Heath, Steven H., Ty Cobb vs Walter Johnson, Baseball Quarterly Reviews, Vol. 7, 1992, 129-148.
  • Heath, Steven H., The Big Train and AL Batting Champions, A Review of Baseball History, no date, 129-131.
  • Heath, Steven H., One on One with the "Babe" American Leaguers vs Babe Ruth the Pitcher, to appear.
  • Kaigh, W.D., Forecasting Baseball Games, CHANCE, Vol. 8, No. 2, spring 1995, 33-37.
  • Kepner, James L., On the probability that the better team wins the World Series, College Math. Journal, 16 (1985), 250-256.
  • Levin, M. Binomial baseball, College Math. Journal, 12 #4 (1981), 260-266.
  • Meeden, Groeneveld and Glen, Seven Game Theory in Sports, Mathematics Magazine 48 #4 (1975), 187-192. Finds a probability model for the number of games played in a "best of seven" series.
  • Raymond, Kevin R. and Paul M. Sommers, Baseball's Designated Hitter: A Retrospective, JRM, Vol. 28(4), 1996-97, 287-288.
  • Sandefur, James T. The Baseball-Card Collector's Query, Mathematics Magazine, 69 #4 (1996), 243-248. The issue is this. You are collecting baseball cards. Assume all are equally likely. You make two piles, one of the first copies obtained and one of all the duplicates. Typical question asks how long will it take for your pile of duplicates to be as high as your pile of originals?
  • Schilling, Mark F. The Importance of a Game, Mathematics Magazine, 67 # 4 (1994), 282-288. Often when listening to broadcasts, one hears a statement such as ``This game is the most important game of the series.Ó The article analyzes this concept from a probabilistic perspective by defining two distinct notions of importance, ``conditional importance'' and ``a priori importance.'' This provides a means of quantifying the relative significance of the games within a contest.
  • Seligman, Dan, The baseball enigma, Forbes, Nov 15, 1999, 176-178. Neoclassical economic theory tells us that pay should reflect the value of worker output. The theory doesn't work terribly well in the major leagues. Why? I have some copies available.
  • Short, T. and L. Wasserman, Should We Be Surprised by the Streak of Streaks? CHANCE, Vol. 2, No. 2, spring 1989, page 13.
  • Sommers, Paul M., An Empirical Note on Salaries in Major League Baseball, Social Science Quarterly, Vol. 71 (December 1990), 861-867.
  • Sommers, Paul M., Career Length and Playing Position in Major League Baseball: Any Connection? JRM, Vol. 19(4), 1987, 247-251.
  • Sommers, Paul M., The Golden Boys of Summer, 1987, JRM, Vol. 21(3), 1989,161-165.
  • Sommers, Paul M., The Influence of Salary Arbitration on Player Performance, Social Science Quarterly, Vol. 74 (June 1993), 439-443.
  • Sommers, Paul M., Are There Pay Differentials in the Major Leagues? Some Ballpark Figures, JRM, Vol. 23(4), 1992, 281-284.
  • Sommers, Paul M., Home-Field Advantage in the World Series: Myth or Reality? JRM, Vol. 28(3), 1996-97, 180-184.
  • Sommers, Paul M., Pitcher Perfect: All Tall Talk? JRM, Vol. 28(3), 1996-97, 177-179.
  • Sommers, Paul M., Probably the Greatest Hitter Who Ever Lived, JRM, Vol. 26 (1), 1994, 32-35.
  • Sommers, Paul M., Ticket Prices and Player Salaries in Major League Baseball, JRM, Vol. 26(4), 1994, pp. 274-276.
  • Sommers, Paul M., Sultan of Swat and the Runs Test, preprint.
  • Sommers, Paul M. and Noel Quinton, Pay and Performance in Major League Baseball: The Case of the First Family of Free Agents, The Journal of Human Resources, Vol. 17 (summer 1982), 426-436.
  • Vargo, Louis G., A Nonparametric Model for Series Competitions, Mathematics Magazine, Vol. 50, No. 1, 1977, 25-27.
  • Warrack, Giles, The Great Streak, CHANCE, Vol. 8, No. 3, Summer 1995, 41-43, 60.
    Back to home page.