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This case presents a dilemma that professional golfers face when having to choose a target point for landing the ball. Key to this case is to acknowledge uncertainty as reflected in less-than-perfect accuracy. Thus the ball will land in a "cloud" around the intended target. On such a cloud, some spots (e.g., the fairway) are better than others (e.g., sand bunkers or rough). There is therefore a conflict between advancing the ball as close to the hole as possible, while at the same time reducing the chance of being in trouble on the next shot. The idea is to find a sweet spot between these two competing goals. To operationalize this problem, we use data from the Professional Golfers' Association (PGA) tour to estimate the average number of shots to complete the hole as a function of (i) distance to the hole, and (ii) type of surface (fairway, rough, recovery, sand, or the green). The case comes with a companion Excel spreadsheet, UVA-QA-0953X, which shows a map of a classical hole in the PGA Tour (the 10th at the Riviera Country Club in Los Angeles). This Excel file also displays a heat map of a bivariate normal around any chosen target, and a heat map with the average number of strokes to complete the hole. Students' goal is to understand the model and use it to find a good target.
- Reinforce the notion of expected value, which in this case takes the form of expected number of strokes to complete the hole. - Introduce the main elements of dynamic programming—states, alternatives, transition probabilities, rewards, and value-to-go—in a visual and palpable way. - Showcase one more application of analytics to the world of sports. - Show how raw data can be used to feed the inputs of a decision model. In this case, we use data to assess accuracy (transition probabilities), as well as to evaluate each landing position (the value-to-go). - Familiarize students with the use of normal and bivariate normal distribution. - Illustrate the value of having a minimally credible working model as a starting point, which then serves as a steppingstone to create more complex and realistic versions.