## Sunday, December 18, 2022

### Handicapping a Skins Game for Par Threes

A group of players participate in a gross skins game and net skins game. There is a wide range of handicaps with players receiving 0, 1, or 2 strokes on a par three.  In the net skins game, nothing irritates the low handicap player as much a seeing his natural birdie tied by a bogey made by a player receiving two-strokes.   To right this injustice, the low handicapper suggests that players only receive one-half of their handicaps strokes on par three. That is, a player receiving two-strokes would only get one-stroke.  The player receiving one-stroke would only get one-half a stroke.

What are the implications of going to the “0ne-half Rule”?  A rigorous analysis would require scouring tons of data and using a simulation model to estimate which golfers win and which golfers lose under the different handicap rules.  Even then, the result would be imperfect since results of skins games depend upon the mix of players[i], a hole’s difficulty, its stroke allocation, and the abilities of players (e.g., long hitter, short hitter).  The importance of this problem does not call for that much work.

In this post, a more slothful approach is taken.  It is assumed three players play a par three with the scoring probabilities of each player shown in Table 1.  There are 36 possible outcomes each with its own probability of occurring.  For example, the probability of all three players making par is (.6 x .2 x .1) .012.

Table 1

Scoring Probabilities

 Gross Score Player 1 (0 strokes) Player 2 (1 Stroke) Player 3 (2 Strokes) Birdie 0.1 0.05 0.0 Par 0.6 0.2 0.1 Bogey 0.3 0.6 0.5 Double Bogey 0.0 0.15 0.4 Average Score 3.2 3.85 4.3

For each outcome, one of three players earns a skin or there is no skin.  A player’s probability of winning a skin is the sum of the probabilities of occurrence where he wins a skin.  Table 2 presents these probabilities for three handicap rules (no handicap, full handicap, one-half handicap).

Table 2

Net Skin Probabilities

 Handicap Rule Player 1 Player 2 Player 3 No Skin No Handicap .505 .055 .020 .420 Full Handicap .030 .117 .435 .418 ½ Handicap .196 .353 .198 .253

If the competition was only net skins, the ½ Handicap Rule would appear to be best.  The No Handicap Rule gives the low handicap player a big advantage and the Full Handicap Rule gives the high handicap player a big advantage. But the competition under consideration has both a net skin pool and a gross skin pool. Table 3 presents the probability of each player winning at least one skin.

Table 3

Probability a Player Wins At least One Skin

 Handicap Rule Player 1 Player 2 Player 3 Full Handicap .52 .23 .45 ½ Handicap .60 .39 .21

These numbers do not represent the actual probabilities in a skins competition.  With many more players than the three used in the example, the actual probabilities will be much lower.  The probabilities in Table 3, however, do indicate the relative advantage of each type of player.  The Full Handicap Rule appears to best in terms of equity and simplicity of administration (1/2 strokes can be confusing).  Moreover, this analysis was done for par three holes which the high handicapper typically finds the easiest (i.e., scores the least over par).  Therefore, applying the Full Handicap Rule over all holes would tend to equalize the chances of all types of players earning at least one skin.

In the long run, this type of skins game is an annuity for the low handicap player and he should not begrudge the high handicap player who chips in for a three and wins a skin.

[i] www.ongolfhandicaps, “Why You Win (or lose) in Skins,” June 25, 2012.