Handicaps in Golf

In amature golf tournaments, competitors often have greatly varying abilities, so the better players are 'handicapped' relative to the poorer players to reduce their chances of winning. Does handicapping give all players the same chance of winning the tournament if they play better than usual?

We will next examine how effectively handicapping can achieve this goal.

Handicapping Based on Mean Score

We initially assume that any golfer's handicap is the difference between that golfer's expected score on a par-70 course and 70. If a golfer's handicap is subtracted from his or her score, the handicapped score should therefore have a distribution with mean 70 on a par-70 course.

The diagram below shows how the distribution of the handicapped scores all have mean 70, irrespective of the ability level of the golfer (i.e. the mean raw score).

Drag the slider to see the distribution of handicapped scores for different golfers. Note that the poorer golfers are more variable, so their handicapped scores have normal distributions with greater spread.

Click on the diagram above 70 on the axis. (Again drag to the left or right to get exactly 70.) Observe that all players have the same probability of getting a handicapped score of 70 or less — exactly 0.5.