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LostInParadise's avatar

Is this the right way to schedule a seeded tournament?

Asked by LostInParadise (27908points) 3 months ago

I was curious as to how seeded tournaments are set up. As you probably know, these schedules are set up so that top seeded competitors cannot face each other until the final rounds. The top two seeds can’t meet until the finals, none of the top four seeds can meet until the semi-finals, and so on.

I could not find an algorithm, but I found Web sites that create schedules for you. Does this seem right? Link?

I came up with my own scheduling algorithm, which satisfies the seeding requirement, but which I think is better. My algorithm is simple to describe, but a little clunky to do, since it takes several repetitions. The computer program for this is only a few lines.

First write the seeds in order:
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16

Then move the numbers in even positions to the right to get two sub-tournaments:
(1,3,5,7,9,11,13,15), (2,4,6,8,10,12,14,16)

In the same way, each of the two sub-tournaments are divided into
two sub-tournaments, and so on.

The final result is:
(1, 9), (5, 13), (3, 11), (7, 15), (2, 10), (6, 14), (4, 12), (8, 16)
The schedule at the computer site has the first and last seeds facing each other and the second and next to last seeds facing each other in the first round. That does not seem very fair. My algorithm spreads things out. Each of the initial matches has the competitor seeds separated by 8.

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4 Answers

gorillapaws's avatar

@LostInParadise “The schedule at the computer site has the first and last seeds facing each other and the second and next to last seeds facing each other in the first round. That does not seem very fair.”

That’s how is always done (as far as I’m aware). Usually the seeding is based on prior performance. Entering the final tournament as the #1 seed is typically indicative of having a very strong regular season, and entering as the last seed is indicative of having a much weaker season. Part of the “prize” for finishing in the top of your season is that it entitles you to an easier time in the tournament, sometimes you even get a Bye: https://en.wikipedia.org/wiki/Bye_(sports) .

LostInParadise's avatar

Interesting. Apparently everything is set up to benefit the top seeds. I will have to rethink this to see if I can get the same results.

Tropical_Willie's avatar

I’ve seen it done where with 16 teams the first pairings add up to seventeen, (1,16) (2,15) . . . .

LostInParadise's avatar

That is what I finally figured it was doing. I wrote another program. It is not very pretty, but it seems to work. It starts with a sum of 3 and adds 1 and 2. Then it moves to a sum of 5 and puts the 1 with 4 and the 2 with 3. For 16 teams, it will eventually get to a sum of 17.

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