fair distribution of table tennis players in roster

Question

Say I have 18 players who have been ranked in order of ability 1-18. I need to make up 6 teams each with 3 players. How do I choose the members of each team such that based on the ranking of the players there has been a fair distribution so that the teams are balanced.

Answer 1

One way would be to ensure the sum of the rankings of players in each team are the same.

Let's say team A has players 1,2,3,16,17 and 18. Team B has 4,5,6,13,14 and 15.

You'd expect 16,17 and 18 to lose all of their matches against Team A, meaning 18 wins for Team B in a round robin. However, 1,2,3 would win all their matches, meaning 18 wins for Team A in a round robin. In 36 matches, the teams would be even. Team C taking players 7 through 12 would also win 18 matches against either team, and lose 18 against either.

This gets a little more complicated if you're not playing a round robin, however.

If each team player plays only one match, you'll want one from 1,2,3 on each team and one from 4,5,6 on each team, etc. If Team A had the top player from 1-3, you'd want Team B to have the top player from 4-6 and Team C to have the top player from 7-9, etc. You'd also want to have each team have only one second best player from each of these subdivisions of the rankings, and each to take one third best from each of these subdivisions.

Note that if you did this, then again you'd find that the sum of the rankings of each team is equal, at 57.