Abstract
Club golf competitions are regular events arranged by golf directors (or professionals) for club members. Player skill levels are measured by their USGA or R&A handicaps and it is the job of the director to use the handicaps to organize teams that are, in some sense, fair. The handicap system is limited in that it does not take the variance of players’ scores into account. In this paper we propose two optimization models that employ the handicap distributions from a prior study [1]. The first model directly computes team probabilities to win a single hole, and the second derives team probabilities to win from those of the players. The computational complexity of both models grows exponentially with the number of players. Using scenario optimization, with approximations, the second model is shown to give very good results for up to \(40\) players in reasonable computer time. Also, the solution of a real problem shows that common assumptions about the structure of fair teams are not necessarily correct.
Keywords
- Golf Director
- Disability System
- Player Skill Level
- Handicap Players
- Team Scores
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Siegbahn, P., & Hearn, D. (2010). A study of fairness in fourball golf competition. In S. Butenko, J. Gil-Lafuente, & P. M. Pardalos (Eds.), Optimal Strategies in Sports Economics and Management (pp. 143–170). Heidelberg: Springer.
Kaspriske, R., et al. (2007). Golf Digest’s Complete Book of Golf Betting Games. New York: Random House Digital Inc.
Glover, F., & Woolsey, E. (1974). Technical note—converting the 0-1 polynomial programming problem to a 0-1 linear program. Operations Research, 22, 180–182.
Watters, L. J. (1967). Reduction of integer polynomial programming problems to zero-one linear programming problems. Operations Research, 15, 1171–1174.
Grasman, S. E., & Thomas, B. W. (2013). Scrambled experts: Team handicaps and win probabilities for golf scrambles. Journal of Quantitative Analysis in Sports, 9, 217–227.
Dear, R. G., & Drezner, Z. (2000). Applying combinatorial optimization metaheuristics to the golf scramble problem. International Transactions in Operational Research, 7, 331–347.
\({\text{ FICO }}^{\text{ TM }}\) Xpress Optimization Suite 7.6. http://www.fico.com (2013).
http://www.usga.org/handicapping/articles_resources/Men-s--Handicap-Indexes/. Retrieved from December 2013.
Acknowledgments
We would like to thank two golf directors, Tom Parsons, National Golf Club, Pinehurst, NC, and Philip Ankrim, Gainesville Country Club, Gainesville, FL, for their comments and suggestions during this study.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Appendix
Appendix
See Tables A.1, A.2.
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Pavlikov, K., Hearn, D., Uryasev, S. (2014). The Golf Director Problem: Forming Teams for Club Golf Competitions. In: Pardalos, P., Zamaraev, V. (eds) Social Networks and the Economics of Sports. Springer, Cham. https://doi.org/10.1007/978-3-319-08440-4_10
Download citation
DOI: https://doi.org/10.1007/978-3-319-08440-4_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-08439-8
Online ISBN: 978-3-319-08440-4
eBook Packages: Business and EconomicsBusiness and Management (R0)