General Question

LostInParadise's avatar

How is the playing schedule created for tournaments where the teams are seeded?

Asked by LostInParadise (27677points) June 23rd, 2017

For example, a tennis or basketball tournament, where the tennis players and basketball teams have a relative ranking. The idea is to set things up so the top two seeds cannot face each other until the finals, none of the top 4 seeds can face each other until the semi-finals, none of the top 8 seeds can face each other in the third to last round, and so on. I did a google search and all I found were bracket charts that you could download.

I came up with a straightforward way of doing this. It takes a bit of repetitive effort, but can easily be programmed into a computer. There is of course more than one way of satisfying the requirements.

Can you come up with a method? Your answer would be represented by a bracket chart. All the seed numbers are written in a line. In the first round, the first two seeds play against each other, as do the second two and so on. In a similar way, winners of consecutive games play against each other in the next round of the tournament.

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2 Answers

LostInParadise's avatar

In case anyone is interested, here is how I solved the problem. I will present the solution for a 3 round tournament. The generalization should be fairly obvious.

Suppose there are only 2 players. Then there is only one game, [1,2].

For four players, think of [1,2] as a possible second round matchup. In the first round, 1 and 2 play 3 and 4. There are two ways of doing this.
I am just going to add 2 to 1 and 2 to get: [1,3][2,4]

For 8 players, think of [1,3][2,4] as a possible second round outcome. In the first round, players 1 to 4 play against 5 to 8. Maintaining the order of the four team result, just add 4 to get [1,5][3,7][2,6][4,8]

funkdaddy's avatar

Your solution isn’t generally how it is done.

The top seeded entry will almost always play the bottom seeded entry, second seed will play the second lowest seed, etc., the only variable is whether or not everyone is reshuffled at some point or not to line up highest and lowest remaining seeds.

That helps to ensure either upsets in early rounds or great matchups in the later rounds, both of which are considered good viewing.

So 8 entries will generally go
[1,8][4,5][3,6][2,7]
[1,4][3,2]
[1,2]

If we go with all favorites.

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