Handicapping Based on Quantiles
Handicapping to give all players in a tournament the same mean score clearly penalises the more consistent golfers — they are less likely to improve on their mean score enough to win.
In a competition with n golfers of identical abilities, the winning score is the minimum of the resulting n random scores. This minimum has a distribution that is centred on the lower 1/(n+1)'th quantile of the distribution of the individual scores. (A bit more detail about the minimum of a random sample will be given later.)
This suggests that in a competition of 24 golfers, a fairer handicapping would make the lower 1/25'th quantile of all competitors equal.
The diagram below calculates handicaps to make these equal to 70.
Drag the slider to see the distribution of handicapped scores for different golfers. Note that the poorer golfers are given a lower handicap with this scheme so their mean handicapped scores are higher than the mean scores for the better players.
Click on the diagram above 70 on the axis. (Again drag to the left or right to get exactly 70.) Observe that all players now have the same probability, 0.04, of getting a handicapped score of 70 or less.
Simulation of a Handicapped Golf Tournament
The diagram below simulates a tournament with 26 players whose mean scores on a par-70 course are 75, 76, ..., 100, using the handicapping scheme described above. 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.
Click Accumulate then click Play 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 all players have similar probabilities of winning this tournament.