We were reminiscing about our school days in Quiz Master Shop Towers a few days ago, and one thing that came up was picking teams (mainly Football) at break time. All of us remembered using exactly the same method:
The two best players were the Captains, obviously. The best player had first pick and the other Captain had second pick, and then they alternated, each picking the best available player from the pool of unpicked players. We all reflected on the ignominy of being the last choice!
Of course, our Quizzing and Puzzling brains started to analyse this method . . .
Is this the fairest way of choosing two teams that will be roughly equal strength?
And if it is not the fairest way, can you devise a better method?
Firstly, it is not the fairest method. If there are 20 players, for example, one team will consist of players ranked 1, 3, 5, 7 and 9, and the other of players ranked 2, 4, 6, 8 and 10. The average ranks of the two teams are 5 and 6 respectively.
A fairer method is for the second best player to have first pick. And here is the neat bit; the Captains now alternate have TWO picks each!
With the example above with 20 players the teams would be players ranked 2, 3, 6, 7, 10 and 1, 4, 5, 8 and 9. This gives two team with average ranks of 5.6 and 5.4, the best that you can achieve. It is not possible to have two teams with an average ranking of 5.5.