Math CentralQuandaries & Queries


Question from James, a teacher:


I like to run a 9 team flag football tournament where each team is guaranteed 3 games prior to playoffs. All games must have playoff implications and must not be a consolation game.


How many teams make the playoffs? Suppose you have two teams that have each lost two games and they play each other next. Is that game supposed to have playoff implications? It could work if all teams make the playoffs and the season just determines some kind of ranking (that will have to admit ties).

It is not possible to have each team play exactly three games because the total number of games would be (9 x 3) / 2 = 14.5. I think it can be done if some team plays four games and the rest play three, or in all other situations where an even number of teams play three games and the rest play four games. It is possible to make a schedule where all teams play four games.

You'll need to decide on tie breaking mechanisms. For example: first consider head to head games, then points for minus points against, then toss of a fair coin.

I don't know if this helps.

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