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Shaw on Tournaments
04/12/06
by Shaw

With all of the talk about the NCAA tournament finally dying down, you might be happy to have a rest from it... if so, I can promise that this might be our last column that mentions the 2006 NCAA. The reason you're seeing this column a full week and a half after the tournament ended is that we have quite obviously been busy with the methodical destruction of your patience by drawing out our Celebrity Animal Steel Cage Match tournament--and by the way, kudos again to you all for selecting Lorenzo as the winner, I really hate that stupid Spuds dog and I would have been loath to use him to represent this site in any way--and I have been busy with what some call "work" and I call "an annoying interruption of my reading time."

That's the reason for the timing of this column. The existence of this column was actually sparked by Clay. (This should not shock you as, generally, sports-related columns are few and far between from Shaw.) We were talking about the construction of the Animal Tournament Bracket, and Clay started authoratitvely baby-stepping me through the seedings of the bracket, explaining that there should be a 1-8 game, a 2-7 game, a 3-6, etc. and I stopped him, saying, "Yeah, I get it, in the 8 team field all the first round matches add up to 9." This halted our conversation for a few seconds, as Clay thought about the mathematical implications of what I had said. I added, "Then, of course, in the 16 team field, they all add up to 17." His response was inaudible, but it was clear that he had never thought of it that way. Of course, I have never thought of it any other way. I always assumed that everyone thought of it this way. Since I now know that to be false, here is the way I present tournament brackets--the Mathematician's approach to bracketology:

Rule 0: If there's no play-in game, then the number of teams has to be a power of 2 (i.e. 32, 64, 128, etc.)

Rule 1: In the first round, the first plays the worst. And if you assume all the higher seeds advance, the next round should have the top remaining seed play the bottom remaining seed.

Rule 2: If you cut out a proper slice of the bracket (meaning you take out something that also looks like a bracket) then this smaller piece should also satisfy Rule 1.

And that's it. Given just those three rules, anyone can make a tournament bracket, as big as they want. And notice that by rule 2, if the top is always playing the bottom and you always assume the top seeded people win, then the seeds in each piece of the bracket will add up to the same number, which is why the NCAA bracket is set up so if the top seeds win, the second round will be 1-8, 2-7, 3-6, 4-5, all adding up to 9, and the next will be 1-4, 2-3, all culminating with a 1-2 match in the finals. If you hated high school math, tune out for a second--this means that if there are 2ⁿ many teams, there will be n rounds, and in the k^th round, the seeds in each matchup will add to 2^(n-k+1)+1. Note that the NCAA tournament has 64 teams, but each separate region basically has its own 16-team tournament, so in the first round the seeds add up to 2^(4-1+1)+1 = 2⁴+1 = 17, and in the second round, that's 2^(4-2+1)+1 = 2³+1 = 9 --Okay, tune back in, slackers. The whole point of this system is to make sure that the later games are the more exciting ones. Anyone involved in making brackets for professional sports should surely know this, right?

Actually, no.

Incredibly enough, while explaining this to Clay, I had a flash, not quite a memory, but a miniscule kernel of a memory... I remembered watching the 1995 Wimbledon. This was a standard summer activity; as a 16 year old in upstate NY there was not much to do on summer break, so mostly my friend Japes and I would ride our bikes to the summer camp where we worked for the morning, and then either come home and play tennis with our friend Smells, or during Wimbledon and the US Open, we would watch tennis all afternoon on TV. Also prevalent among our summer activities were our vaguely homoerotic pool wrestling matches, but I shall leave that topic for another day. I remembered this specific tournament because it was the first time in the Open Era that any Grand Slam tournament had gotten to the point where the last four remaining players in both the men's and women's brackets were also the top four seeds. I also remember being confused as to why the brackets didn't look exactly the same as each other. This brief byte of memory also included the names of all eight of the players involved, so you would imagine that verifying the brackets would not be so hard using the Internet. You would be wrong... it took me an embarassing 60 minutes to find a credible source to back up my suspicions... but the confirmed brackets vindicate me.

Here were the final four women:

No problem, right? Just like the NCAAs, and just like my formula, 1 plays 4, 2 plays 3, all add up to 5.

But then, and this image is seared into my brain, this was the men's semifinal setup:

Amazingly, this is wrong. The 1 seed should absolutely be set to play the 4 seed in the semifinal. The Wimbledon seeding committee actually made the bracket for this tournament incorrectly. To this day, I can't fathom why they did this. But this is at least one piece of useless knowledge that has finally come to some use in my lifetime. You don't know how good it feels to get this off my chest.

By the way, Graf beat Sanchez-Vicario in the women's final, and Sampras beat Becker in the men's.

In order to end this column with something other than a proof of some bad mathematical goings-on in Britain, let me close with a few thoughts, DJ-style, about this year's NCAA tournament: one rant, one rave, one rumination.

Rant: Fuck Duke... normally I would bleep out my own curses, but how could GW have gotten more screwed in this tournament? Regardless of their losing to LSU, most people thought Duke was the best team going into this tournament, and to put GW, who had been ranked 6th until the A-10 tournament, as an 8-seed to face Duke in the second round, in North Carolina... well, fuck that. I would have taken George Mason's draw any day... playing Wilmington in their home state is a sight worse than a neutered MSU team in the first round.

Rave: I may get ostracized from the board of this website for saying this (which would make updating the site interesting), but I have to salute women's NCAA basketball for making this year's tournament a hell of a lot more exciting in the final rounds than the men. And I'm not just saying that because my school won the whole thing, just look at the scores. No one (except maybe DH Gator 27) wanted to watch Florida play UCLA at all, but people especially didn't want to watch Florida win by like 30.

Rumination: Here's a frightening thought. As I was watching the women's Final Four, in typical male fashion, I had a favorite Maryland player early in the tournament and spent most of the game paying attention to her moreso than the team. Only after the final game had ended and the ceremonies were underway did it occur to me that my favorite player, Shay Doron, looks just like my ex-girlfriend. The resemblance was confirmed by almost everyone I asked. I thought I was a pretty open-minded guy, but does this mean that I officially have a type?

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