Power matching schedule

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Frater Taciturnus
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Power matching schedule

Post by Frater Taciturnus »

I have been trying to figure out how exactly power matching works so i tried to make a sample schedule. Can someone who actually knows what this is supposed to look like check this? Also if this is your prelim, are teams playoff seeded by card number?


http://spreadsheets.google.com/ccc?key= ... rqTg&hl=en
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Re: Power matching schedule

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Re: Power matching schedule

Post by Stained Diviner »

I have a system that I think is fairer than both of those while still guaranteeing no repeats, assuming that the cards represent seeds.

My third round would have 9 vs 17, 10 vs 18, 11 vs 19, 12 vs 20, 13 vs 21, 14 vs 22, 15 vs 23, and 16 vs 24.

My fourth round would have 5 vs 16, 6 vs 15, 7 vs 14, 8 vs 13, 9 vs 12, 10 vs 11, 17 vs 28, 18 vs 27, 19 vs 26, 20 vs 25, 21 vs 24, and 22 vs 23.

My fifth round would have 1/2, 3/9, 4/10, 5/7. 6/8, 11/21, 12/22, 13/19, 14/20, 15/17, 16/18, 23/29, 24/30, 25/27, 26/28, and 31/32.
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Re: Power matching schedule

Post by jonah »

Can someone explain how these are created?
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Re: Power matching schedule

Post by Stained Diviner »

I write down a grid as follows:
1 32 16 17
8 25 9 24
4 29 13 20
5 28 12 21
2 31 15 18
7 26 10 23
3 30 14 19
6 27 11 22

In the first match, just match up the teams in order.
In the second match, each team plays a team in its own row, matching winners with winners and losers with losers.
In the third match, the first row plays the second row, the third row plays the fourth row, etc. Each team is matched with a team with the same record. The team that won first and lost second (probably the better of the 1-1 teams) is matched with the team that lost first and won second (probably the worse of the 1-1 teams).
In the fourth match, the first two rows play the next two rows, and the fifth and sixth rows play the seventh and eighth rows, again matching teams with identical records and trying to get the best 2-1 teams with the worst 2-1 teams, and the best 1-2 teams with the worst 1-2 teams.
In the fifth match, the top four rows play against the bottom four rows.

If you follow this, repeats are impossible, since you are always going against a team that is in a row or group of rows that you could not have faced before. For example, if you're in the sixth row, then you play your first two matches against different teams from the sixth row, your third match against a team from the fifth row, your fourth match against a team from the seventh or eighth row, and your fifth match against a team from the top four rows. This should make it clear that there are no repeats.

To make the grid, make sure that each team is next to a team that makes their seeds add up to 33, make sure there is a team in the other half of the row that makes the seeds add up to 17 for the top 16, make sure there is a team in an adjacent row that makes the seeds add up to 9 for the top 8, and separate the top four seeds.

I have no idea if that makes sense to anybody but me.
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Re: Power matching schedule

Post by jonah »

It gives me a headache but is essentially comprehensible. The extension to other fields sized at other powers of two looks like something I could readily figure out, but what about fields that aren't powers of two?

Edit: Wait, no; I tried to replicate this and couldn't figure it out. When I get back from school, I'm sure I'll be stopping by NT, so you get to show me then.
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Re: Power matching schedule

Post by ChathamNJ »

So it's basically a simple 2x2x2x2x2 grid, right? All we need is five-dimensional paper.
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Re: Power matching schedule

Post by cvdwightw »

Okay, this should clear everything up.

You start with brackets of 2. For instance, 1-32, 16-17, etc. Typically you want these to add up to 33, but in reality, you can just go through and use like A-FF and match seeds to letters later.

Then you combine brackets of 2 into brackets of 4, such that the teams with identical histories play each other, i.e. if teams 1 and 17 won their first round match, they play each other.

Then you combine brackets of 4 into brackets of 8, such that the teams with identical records in reversed order of wins and losses play each other. By "reversed order" I mean that you take one team's series of wins and losses and flip them, for instance the "reversed order" of a WWLWL team would be LWLWW (and the WWLWL team from each bracket of 32 would play the LWLWW team from the other bracket of 32 in round 6). So in this case, the WW teams play each other, the LL teams play each other, the WL teams play the LW teams.

Then you combine brackets of 8 the same way, i.e. the WWW teams play each other, the LLL teams play each other, the WWL teams play LWW teams, the WLW teams play each other, the LWL teams play each other, and the WLL teams play the LLW teams.

Then you combine your 2 brackets of 16 the same way, i.e. the WWWW, LWWL, WLLW, and LLLL teams play the team with the equivalent history, the WWWL teams play LWWW teams, WLWW teams play WLWW teams, LWLW teams play WLWL teams, LLWW teams play WWLL teams, LWLL teams play LLWL teams, WLLL teams play LLLW teams.

If you have 64 teams, then you combine 2 brackets of 32 the same way; 128 teams, you then combine 2 brackets of 64 the same way.

By continually combining ever-larger brackets, you ensure that each team is playing a team it hasn't played before (since they couldn't have played any of the teams in the bracket you're matching their bracket with).

EDIT: I found a couple of problems with this. I'm creating a better google spreadsheet to illustrate what should actually happen.
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Re: Power matching schedule

Post by cvdwightw »

Okay, spreadsheet is here.

Essentially, this is the format for power matching:

Start with brackets of 2, combine into brackets of 4, then 8, etc.

For the first bracket being combined with another bracket, write a column with the card number and records in order from lowest card number (highest seed) to highest card number (lowest seed). Do the same thing in the adjacent column for the second bracket being combined, only invert the card numbers by record. For instance, when writing bracket 3-1, instead of writing 8-9-24-25 in the right column (when combining bracket 2-2 with bracket 2-1), I flipped the 9 and 24 to write 8-24-9-25; this allows 16 (higher seed of the 2 1-1 teams in bracket 2-1) to play 24 (lower seed of the 2 1-1 teams in bracket 2-2) and 17 (lower seed of the 2 1-1 teams in bracket 2-1) to play 9 (higher seed of the 2 1-1 teams in bracket 2-2).
Dwight Wynne
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UC Irvine 2008-2013; UCLA 2004-2007; Capistrano Valley High School 2000-2003

"It's a competition, but it's not a sport. On a scale, if football is a 10, then rowing would be a two. One would be Quiz Bowl." --Matt Birk on rowing, SI On Campus, 10/21/03

"If you were my teammate, I would have tossed your ass out the door so fast you'd be emitting Cerenkov radiation, but I'm not classy like Dwight." --Jerry
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Re: Power matching schedule

Post by Stained Diviner »

I endorse Dwight's spreadsheet and the idea of five-dimensional paper.

With a number that is not a power of two, you first have to accept that your system is not going to be as good. There are a couple of approaches you can take. One is to start with the top teams playing the bottom teams and then finesse matches when necessary. For example, with 30 teams, after one match you are going to have 15 winners and 15 losers, so you have to make one match in the second round a winner vs loser. The best way to do that may be to have a high seed winner play a low seed loser, so you can pretty much predict the outcome and with high probability believe that, after two rounds, you will have 8 double winners, 14 teams even, and 8 double losers, and then take it from there.

Another approach when you don't have a power of two is to have what I called safety matches. If you have thirty teams, you take whatever teams would have played #31 and #32 that round if there had been 32 teams and have them play each other, with both teams being treated as victors. After one round, you'll have 16 "winners" and 14 losers. After two rounds, you'll have 8 double winners, 16 teams even, and 6 double losers.
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