3s vs 4s in Golf: Analyzing the Scoring Advantage

Question
WE USUALLY END UP WITH SOME OF EACH 3'S 4'S AND WE PLAY THE QUOTA POINTS SYSTEM. WE COUNT ALL THREE OR FOUR AS A TEAM, AND PAY OUT FOR THE TEAM MOST OVER THEIR QUOTA. I AM TRYING TO CONVINCE OUR GROUP THAT THE FOURS HAVE AN ADVANTAGE BUT THEY DO NOT SEE IT, WHAT DO YOU THINK?

Answer
Hi Bob,

According to my calculations, the 3s would have a slight advantage. Using the fact that a golfer will shoot lower than his handicap 1 out of 6 rounds, and over his handicap 5 out of 6 rounds, the expected number of points is 8 below quota for a 3some and 11 below quota for a foursome. This assumes a quota of 36 points per player (2 points for par).

To calculate, I used probability theory and the expected outcomes of 0 players shooting lower than handicap, 1 player shooting lower, 2 players, 3 players, etc.

The difference can be balanced by calculating the average quota per player instead of using the totals.

-11/4 = -2.75 per player on average
-8/3 = -2.67 per player on average

Hope this helps.

Best regards,
Ken Tannar
www.probablegolfinstruction.com