This is a review of the bootstrap simulation research conducted by Timothy Chan, David Madras, and Martin Puterman.
There are two categories of golf competitions. In a stroke play competition the player with the fewest strokes wins the game. In match play, the player who wins the greatest number of holes wins the game. As each golfer is unique, having a unique set experience and expertise, a handicap system has been devised in order to put players at a more even level with each other, in order to create fairer competitions.
A handicap indicates how well a person plays compared to par when they are playing their best. At the end of a competition that uses handicaps, the players’ handicap is subtracted from their score and the person with the lowest score at that point wins the match. In a match play game the process is more complicated in that the strokes a player ‘gives’ their opponent depends not only upon their own handicap but also on the ranking of each hole.
This research looks at whether the current handicap system allows for a truly fair game or if another approach could be more effective at providing each player with the same probability of winning the match. Data was collected from four casual stroke play tournaments held at the Shaughnessy Golf and Country Club in Vancouver, Canada including the player’s handicap and their scores on each of the 18 holes.
The data was graphed which indicated that the players’ handicaps and performance were equivalent. The graph also indicates that the net score for those with middle to high handicaps were more varied than the net score for those with a low handicap.
In order to calculate the over-all win percentages a bootstrap simulation approach was used. The 73,512 matches were sampled with replacement a total of 10,000 times. Following this, the win percentage was determined at each handicap differential using the same method.
Theoretically, the current handicap system should give each player a 50% chance of winning. This simulation calculated that the better player actually won 53% of the time indicating a bias in the current system towards the player with the lower handicap.
Three possible changes to the system are proposed: create three new hole rankings, change the holes to which the handicap differential is applied, and vary the number of extra strokes given to the weaker player. Giving an additional 0.5 strokes to the weaker player created the fairest outcome of all the scenarios.
Information from bootstrap simulation provides analysts with an additional tool in determining likely outcomes of different matches, as the current system appears to favour the better player. Golf courses and tournaments could use this information to develop a handicap system that is fair to all players, allowing for an optimal level of competition.
Analytics Used: Distribution Graph, Bootstrap Simulation
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