Fashioning fair foursomes for the fairway (using a spreadsheet-based DSS as the driver)

Abstract

Golf teams at most public universities derive much of their support for player scholarships from external donors. Relationships with current and potential donors are often created and maintained via annual golf tournaments that pair donors with varsity players and team coaches in a scramble format tournament. This paper introduces a new spreadsheet-based DSS tool for optimizing the formation of teams for multi-round, unique-team, golf scramble tournaments. The DSS uses mixed-integer programming to create unique teams for each round of play while considering the handicaps of all teams and individual players to ensure a reasonable level of fairness in the tournament.

Introduction

Golf has become one of the most popular recreational sporting activities in the world, providing young and old alike with a forum for socializing, networking, exercising, and experiencing the thrill of victory and (perhaps more often) the agony of defeat. To allow competitors with varying skill levels to play against one another on a fair and competitive basis, most amateur golf competitions employ a handicap system where players with lesser skills have their scores adjusted downward by a certain number of strokes—representing their “handicap.” In this way, the winner of a tournament may not be the best overall golfer, but the person who played the best given his or her skill level.

When played in a team format, one typical golf tournament is a “scramble”, comprised of four-person teams. In this type of tournament, players are first rank-ordered into four equally sized “flights” based on their handicaps. Next, one person from each flight is selected to make-up each team. (This helps prevent any team from being loaded with exceptionally good or poor players.) On each hole, each team member hits a tee shot (the first team stroke); the best ball location is chosen and each team member hits from that position (the second team stroke). This process is repeated until a ball is in the hole. The number of team strokes determines the score on each hole. (Another common name for this type of tournament is “captain's choice.”) Handicaps are not used for scoring purposes in a scramble format. Thus, a “fair” competition occurs when the total handicap for each team is approximately equal.

Random assignment of players from each flight to teams ensures some measure of equity in each team's ability. Optionally, the assignment of players to teams can be formulated as a relatively easy mathematical programming problem with the objective of balancing the total handicap of each team. Balancing team handicaps provides a psychological benefit by creating a sense of fairness as well as an operational benefit by creating teams likely to play at somewhat similar speeds.

Recently, a more complex variation of a golf scramble tournament was brought to our attention by the assistant golf coach of the first author's university. This university's golf team holds an annual tournament involving its coaches, varsity players, and benefactors. It is a three-day, three-round event where the organizers desire to ensure no two people play together more than once and, for each round, all teams have approximately the same handicap. To complicate matters, they also have side-constraints to ensure that certain people play together once (e.g., each scholarship player plays one round with the benefactor who provided the scholarship) and other constraints to prevent certain people from playing together at all (for a variety of reasons). Each player's total team score over the tournament determines the winner and final rankings for the tournament.

We describe this interesting and difficult scheduling problem and discuss a novel spreadsheet-based decision support system (DSS) to solve it. Prior to the creation of the DSS, the assistant golf coach would spend hours trying to find a feasible solution to the problem using a spreadsheet. The proposed system not only locates feasible solutions but also can optimize the problem on various objectives using readily available software. The proposed mixed-integer programming (MIP) DSS delivered in an accessible software package (Microsoft Excel) provides an important decision support tool for decision makers like the university golf coach. This DSS is relatively inexpensive to implement and does not require substantial training. It can be easily explained, allowing the decision maker to begin using it quickly.

In the game of golf, the player chooses the most appropriate club for a shot based upon the environment. For example, when teeing off, it is generally the custom to use some sort of driver or iron, and when putting the ball, the golfer uses a putter. Maximum performance requires the right club choice for each shot. Additionally, the quality of clubs used matters less than the skill of the golfer. So, if a golfer lacks skill, his or her game will not greatly improve with the purchase of the best clubs. We draw the reader's attention to these points because they relate to our choice of DSS tools in two ways: First, this research meets a unique need of an actual decision maker—the university golf coach. While we acknowledge there are some very excellent alternative tools and techniques for solving this problem, the one proposed in this paper meets (and exceeds) the needs of the decision maker. Second, the objective function in this DSS is based upon human performance (golf handicap). Consequently, while the model may find the optimal solution for fair team assignments, the players may still perform better or worse than usual, creating landslide victories or agonizing defeats. The proposed DSS cannot prevent such outcomes but should help the golf coach plan the best golf tournament he can with the tools at his disposal.

The remainder of this paper is organized as follow: Section 2 reviews the literature on operations research in sports and presents some background on college sports funding and the impetus for this research. Section 3 presents the mathematical formulation of the problem considered here. Section 4 discusses the problem implementation and solution using a spreadsheet-based DSS. Section 5 provides an example showing the benefits of using the DSS in the context of an actual instance of this problem. In Section 6, we report on additional computational testing that provides insight about how our proposed solution methodology performs on larger instances of this problem. Finally, Section 7 provides implications and conclusion.