20 Golf Players

Date: 04/11/97 at 12:01:25
From: Mark Mullen
Subject: Variance in average team handicaps

There are twenty players with golf handicap between 6 and 32. 
(6,6,8,9,10,11,13,15,15,16,18,19,21,23,26,27,29,30,31,32).

The problem is to divide the twenty players into four teams of five 
players each, with the variance in the average team handicaps being 
no more than one or two.

Is there a mathematical formula that can be used to do this rather 
than using trial and error, as is done every spring?

Date: 04/11/97 at 15:48:52
From: Doctor Steven
Subject: Re: Variance in average team handicaps

This simple method should get a close enough approximation to the 
minimum variance of the means.  

Start by placing the golfers in order, listing them down one column 
and then going up on the next column and so on and so on.

For your golfing problem we get this arrangement (with the first row 
being the first team, etc, etc):

 6   15   15   27   29;  Average Handicap: 18.4
                    
 6   13   16   26   30;  Average Handicap: 18.2
                    
 8   11   18   23   31;  Average Handicap: 18.2
                    
 9   10   19   21   32;  Average Handicap: 18.2
 

Variance of Averages: .01    Standard Deviation of Averages: .1

This method should land fairly close to the optimal strategy (and it's 
probably a lot less work!).  Hope this helps.

-Doctor Steven,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/