Simulation of a Handicapped Golf Tournament
To investigate whether all players in a handicapped golf tournament have the same chance of winning, we will simulate a tournament with 26 players whose mean scores on a par-70 course are 75, 76, ..., 100. These players therefore have handicaps 5, 6, ..., 30.
The black crosses on the scatterplot on the left below show the scores achieved by each player and the red circles are their handicapped scores. (The horizontal axis is the ability level of the golfer, as measured by the mean of that player's score distribution.)
The winner's score is highlighted on the scatterplot. The winner's ability level is also shown as a cross on the right of the diagram. Click Accumulate then click Run Tournament a few times to build up the distribution of the winner's ability. Hold the mouse button down over the button until the tournament has been played 200 times.
Observe that players with higher mean score (i.e. worse players) are more likely to win the tournament.
Explanation from the model
This result could have been foreseen from our model. If there are several golfers in a competition, all with mean handicapped scores of 70, the winner is likely to have a handicapped score below 70.
Although weaker golfers have the same mean handicapped score as better golfers, their scores have greater spread, so they are more likely to achieve a very low handicapped score. The poorer players therefore have a better chance of winning the competition.
The diagram below again shows the distribution of handicapped scores for players of different abilities.
Click on the normal curve at 65 to display the probability of getting a handicapped score of 65 or less. Now drag the slider and observe that weaker players have a greater probability of getting a low handicapped score.