The Golf Director Problem: Forming Teams for Club Golf Competitions

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.

Appendix

See Tables A.1, A.2.

Table A.1 Distributions of par $4$ scores by handicap

Table A.2 Fractions of golfers with handicaps 1–28 [8]