Journal of Heuristics

, Volume 9, Issue 4, pp 353–370 | Cite as

A Robust Heuristic for Batting Order Optimization Under Uncertainty

  • Joel S. Sokol


Baseball teams are faced with a difficult scheduling problem every day: given a set of nine players, find the optimal sequence in which they should bat. Effective optimization can increase a team's win total by up to 3 wins per season, and 10% of all Major League teams missed the playoffs by 3 or less wins in 1998. Considering the recent $252 million contract given to one player, it is obvious that baseball is a serious business in which making the playoffs has large financial benefits. Using the insights gleaned from a Markov chain model of baseball, we propose a batting order optimization heuristic that performs 1,000 times faster than the previous best heuristic for this problem. Our algorithm generates batting orders that (i) are optimal or near-optimal, and (ii) remain robust under uncertainty in skill measurement.

Markov chain baseball batting order optimization 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Berry, S., C.S. Reese, and P.D. Larkey. (1999). “A Sports Time Machine.” INFORMS Cincinnati, May 1999.Google Scholar
  2. Bukiet, B., E.R. Harold, and J. Palacios. (1997). “A Markov Chain Approach to Baseball.” Operations Research 45, 14–23.Google Scholar
  3. Cook, E. (1964). Percentage Baseball. Cambridge, MA: MIT Press.Google Scholar
  4. Cover, T.M. and C.W. Keilers. (1977). “An Offensive Earned-Run Average for Baseball.” Operations Research 25, 729–740.Google Scholar
  5. Cramer, R.D. (1977). “Do Clutch Hitters Exist?” Baseball Research Journal 6, 74–79.Google Scholar
  6. Cramer, R.D. (1980). “Average Batting Skill Through Major League History.” Baseball Research Journal 9, 167–172.Google Scholar
  7. D'Esopo, D.A. and B. Lefkowitz. (1960). “The Distribution of Runs in the Game of Baseball.” SRI Internal Report.Google Scholar
  8. Efron, B. and R.J. Tibshirani. (1993). An Introduction to the Bootstrap. New York: Chapman and Hall.Google Scholar
  9. ESPN. (1998, 1999). “ESPN Major League Baseball Web site.” Scholar
  10. Freeze, R.A. (1974). “An Analysis of Baseball Batting Order by Monte Carlo Simulation.” Operations Research 22, 728–735.Google Scholar
  11. Grabiner, D. (1993). “Does Clutch Hitting Exist?” Unpublished.Google Scholar
  12. Grabiner, D. (1997). “Can You Protect a Hitter?” Unpublished.Google Scholar
  13. Howard, R.A. (1960). Dynamic Programming and Markov Processes. Cambridge, MA: MIT Press.Google Scholar
  14. James, B. (1984). The Bill James Baseball Abstract 1984. New York: Ballantyne Books.Google Scholar
  15. James, B. (1985). The Bill James Historical Baseball Abstract. New York: Villard Books.Google Scholar
  16. James, B. (2002). Win Shares. STATS, Inc.Google Scholar
  17. Lindsey, G.R. (1959). “Statistical Data Useful for the Operation of a Baseball Team.” Operations Research 7, 197–207.Google Scholar
  18. Lindsey, G.R. (1961). “The Progress of the Score During a Baseball Game.” American Statistical Association Journal 56, 703–728.Google Scholar
  19. Lindsey, G.R. (1963). “An Investigation of Strategies in Baseball.” Operations Research 11, 477–501.Google Scholar
  20. Neft, D.S. and R.M. Cohen. (1990). The Sports Encyclopedia: Baseball. New York: St. Martin's Press.Google Scholar
  21. Pankin, M.D. (1978). “Evaluating Offensive Performance in Baseball.” Operations Research 26, 610–619.Google Scholar
  22. Pankin, M.D. (1991). “Finding Better Batting Orders.” SABR XXI, New York.Google Scholar
  23. Pankin, M.D. (1993). “Subtle Aspects of the Game.” SABR XXIII, San Diego.Google Scholar
  24. Stern, H.S. (1997). “A Statistician Reads the Sports Page: Baseball by the Numbers.” Chance 10, 38.Google Scholar
  25. Thorn, J. and P. Palmer. (1984). The Hidden Game of Baseball: A Revolutionary Approach to Baseball and Its Statistics. Garden City, New York: Doubleday.Google Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Joel S. Sokol
    • 1
  1. 1.School of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA

Personalised recommendations