Bracketology: London Style

Written by - Posted 2009-10-11 21:18 in Blog

Let me start by saying I love the London Wiffleball Tournament and I’m going to keep bringing teams as long as I’m able to do so. I like Brian Wheeler and the guys on the Reds, and I know they do a tremendous amount of work with very little support to put on the tournament every year and I’m glad they do.

I don’t want to be one of those guys that complains about things but doesn’t do anything to help fix them. I’ve been on the receiving end of those kinds of complaints too many times to not appreciate that position. That being said, I think that constructive criticism is a good thing, and people who really love things should be able to give the people who run the things they love ideas to help make it better or correct problems that they see.

I’ll keep bringing PWL teams, and I hope the other 56 teams that played this year will continue to come, and some of the 20-30 other teams that didn’t make it this year will come back in 2010. Even if nothing changed, or none of the things that I think would make the tournament better ever happened, I’d still be there. I’m also happy to help in any way I can to make the tournament better. Whether that means donating time, money, or other resources, if there is a room for help, I’m happy to provide it.

The issue that most concerned me this year was the tournament seeding in the double elimination tournament. Sure, I’m an anal stats guy, who likes systems and process, so maybe I’m the only person who was bothered by this. But, the seeding was wrong. It actually punished the top seeds, and I think it’s worth addressing in the future.

This isn’t sour grapes. It wasn’t the seeding that eliminated the Nationals and the Senators from the tournament. I’d be writing this whether we left in round 2 or round 11. Our teams had an amazing time and a spectacular trip and everyone is ready to come back next year. (Assuming we get the bus with DirectTV on it again.)

The seeding might not have meant the difference between any wins and losses for any teams. However, that isn’t the point. This is a situation where perception and accountability are an issue. If the perception is that we have pool play in order to “seed” the tournament, then we need to actually seed the tournament properly based on those results.

2009 London Tournament Winners Bracket [ full size ]

The guiding principles of seeding teams in a tournament, whether based on a regular season, a round robin, or a pool play scenario are always the same. The advantage should go to the best team, who gets to play the worst team available if they continue to win. All real sports that seed teams in tournaments do this. (Tennis doesn’t do this, but 1) tennis is not a real sport, and 2) their seeds are not really seeds based on a previous round or record, but computer generated numbers, and only part of the players are seeded anyway.)

The real principles of this seeding get illustrated in a four team scenario. Team #1 plays Team #4 (the best and the worst), leaving Team #2 to play Team #3. If the top teams were to win, then Team #1 would play Team #2 in the second round. This same principle should apply, and be the end result of your tournament (the semi-finals), whether you have 4, 8, 16, 32, 64, 128, 256, or any number of teams in between.

In order to make sure that happens, you need to setup your schedule of games to be played to work backwards from the #1/#4 matchup and the #2/#3 matchup. For example, with eight teams #1 plays #8, and #4 plays #5. The winners of those two play each other. That way, if the top seeds were to win, it’s #1 playing #4. On other side, #2 plays #7, and #3 plays #6, again with the winners meeting. So, end result, #1 plays #4, #2 plays #3. It’s the same no matter how big you get.

A long time ago some genius developed the brackets above to graphically represent this order of things. According to Wikipedia, the nation’s online encyclopedia of record: “A bracket is the diagrammatic representation of the series of games played during a tournament, named as such because it appears to be a large number of interconnected (punctuational) brackets.” And yes, I’m aware that quoting Wikipedia will weaken my argument, but it’s a risk I’m prepared to take. The bracket lets you see the progression of games and who should be playing each other as they move forward. Genius.

The other thing you need to know about seeding before you start just randomly filling in a bracket is that in order to keep the matchup’s working properly, if you do not have exactly the ideal number of teams in a tournament (basically just continuing to double the number of teams starting from 1 until you reach a number for the teams you have – 2, 4, 8, 16, 32, 64, 128, or 256), you will need to have BYE games. Basically, a bye is an automatic win for the team scheduled against a bye. A 29 team tournament is really just a 32 team tournament bracket, with 3 byes. A 6 team tournament is just an 8 team tournament with two byes. If you have an 8 team bracket, you just write in bye where it asks for the seeding for the seeds #7 and #8, giving teams #1 and #2 automatic wins on those games, and you’ll still end up with the right end result.

If you do not have an ideal number of teams you cannot just apply the “best plays the worst” philosophy for just those teams, and ignore the fact that you have byes. For example, in the six team scenario, if you say you don’t want to have byes, and you just have #1 play #6, #2 play #5, and #3 play #4, that works out fine for the first round and is pretty balanced. However, round two is where you have your problem. Now you have three teams left, #1, #2, and #3. So…you’re now in trouble because three teams can’t play each other at the same time.

Instead, you have to use the 8 team bracket, and just put in a bye for teams #7 and #8. So it would work like this. #1 plays BYE (no #8), #4 plays #5 and the winners play each other. Again, balanced out having #1 playing #4 in the second round. On the other side, #2 plays BYE (no #7) and #3 plays #6, again with the winners meeting. Basically, it should always end the same way assuming all the top seeds win.

The number of byes you have in the first round always depends on the number of spots you have away from the ideal number of teams. If you have 13 teams, the bracket you’d use is a 16 team bracket. Your top three teams would get byes in the first round.

Fortunately, since this way of seeding brackets has been done for probably hundreds of thousands of years, you most likely don’t need to only use the 4, 8, 16, 32, 64, 128, or 256 team bracket and write in the byes. Odd numbers of teams are so common, these brackets are already created for you for the most part. (Especially for 32 teams and under, google it.) However, you never know, you might need a 236 team bracket, and can’t find one pre-prepared on the internet. No worries, just use the 256 team bracket, and write in byes for the top 20 teams. It will make sure your end results are the same, and your match-ups are fair and balanced.

Properly Seeded 58 Team Bracket (London Seeds in Red / Proper Seeds in Black) [ full size ]

This gets us to the London Wiffleball Tournament 2009 bracket. They got the principles of a couple of things right. The best team plays the worst team. They had 58 teams, and #1 played #58, #2 played #57, and so on. In principle, that’s right, that the best plays the worst. They also placed the #1 seed and the #2 seed at opposite ends of the blank 64 team bracket they were using. That is also the correct philosophy.

However, there were two critical flaws that followed, which caused match-ups to be completely unbalanced for the rest of the tournament. First, as we just learned a 58 team tournament is really a 64 team tournament with 6 byes. Assuming you want #1 to meet #4 and #2 to meet #3 which I all generally thing we agree is a good and balanced thing to have. Second, they put #1 and #2 on opposite sides of the bracket, but then they failed to put the #3 and #4 teams on the right sides (ie – #4 closer to #1 and #2 closer to #3). They then also put them in the bracket directly next to the #1 and #2 teams, meaning that #1 and #3 would meet in the second round, as would #2 and #4. First of all, those teams should NEVER meet if the top seeds win. But, if they swapped it had #1 meet #4, and #2 meet #3, that still shouldn’t happen until the 5th round, not the 2nd round.

The third major flaw that was made was a direct result of the first flaw, and further exacerbated the problem. With not entering in the byes in the proper places, they had six blank lines at the bottom of a bracket designed for 64 teams. They actually ripped those six lines off the page, which actually would have caused the #2 seed to a play a game in round one, but have a bye in round two AND round three because half of their bracket was missing.

Everything kind of made sense in round one. Again, having best play worst works, and is even fair if you’re just doing it for one round of games and you’re done. But if you have a bracket, and want to play until you have one team left, or much, much worse, have a double elimination tournament, the seeding very quickly makes no sense.

For example, in a properly seeded 58 team tournament, here is who the top seed would face each of the rounds assuming always that the top seed won each game.

  • Rd 1 – #1 vs. BYE (no #64)
  • Rd 2 – #1 vs. #32
  • Rd 3 – #1 vs. #16
  • Rd 4 – #1 vs. #8 (seeing a pattern here?)
  • Rd 5 – #1 vs. #4
  • Rd 6 – #1 vs. #2

Assuming that the top seeds won out in the 2009 London Tournament seeding, here is who the #1 seed would have played.

  • Rd 1 – #1 vs. #58
  • Rd 2 – #1 vs. #3
  • Rd 3 – #1 vs. #5
  • Rd 4 – #1 vs. #9
  • Rd 5 – #1 vs. #17
  • Rd 6 – #1 vs. #2

So, as you can see, the first game is kinda right (should be bye, but at least it’s balanced, best vs. worst.) But the trains really get off the tracks rounds 2 through 5. Basically two of the top three teams meet in the second round, guaranteeing that one of the top three teams is in losers’ bracket ahead of 12 other teams that were worse (lower seeded) than they were. The games actually get EASIER as the rounds go on from round 2 to round 5, until the final round 6. This is definitely not the intended result or desire of seedings. In fact, it would be more fair to just randomly assign teams to spots (draw them out of a hat) than it would be to seed them this way. You are PUNISHED with round 2 and 3 games if you are a higher seed. You intentionally get tougher games under this model. So, why would you want to be a top seed?

Under this model, the last four teams left in the tourney are #1 and #17 on the top half of the bracket, and #2 and #12 on the bottom half. It should be #1 and #4, along with #2 and #3.

In order to get some sense of the strength of schedule with the improper bracket, I did an analysis of the teams that the top 16 seeded teams would play under both the standard seeding system and the one used for the 2009 London Tournament. Under the London bracket, the #2 seed has the easiest schedule. (Though, this is partly due to the bracket being cut off in the middle, and the #2 seed getting two byes in the middle of the tournament.) The #12 seed has the second easiest schedule, followed by seeds #1, #9 and #16. In this case, there is still some reward to being top two seed, but a smart team would aim for a #12 or #16 spot.

I know what some of you are going to say. “It doesn’t matter what your seed is, a good team can win a tournament from anywhere.” I don’t disagree. A good team can win games regardless of where they get seeded. And, I’m not sure the results of three games played against opponents in your pool at 8:00 AM the morning before the tournament starts are a real indication of your seed anyway.

However, if that’s the case, then let’s randomly seed all the teams in the tournament. You can’t say the seeds don’t matter, but then play three games to determine what the seeds are. If the tournament organizers said teams would be seeded randomly, I’ll accept their decision and come play. Personally, I think the teams should be seeded, but I don’t run the tournament and I don’t make the rules. However, if the organizers say that teams are going to be seeded, and those seeds are based on the results of the pool play, then the seeding has to be done right. The advantages have to go to the top seeds, not the random 12th seed.

You can also make the case that there is little difference between the seeds. That may be the case in the middle of the bracket, but if the #1 seed is lined up to either play the #3 team or the #32 team in the second round, you can bet there is a LOT of difference between those two games. It’s unfair to both the #1 and the #3 to meet in the second round. One of them is going to the losers’ bracket after round two, when they should coast until round 5.

This could have just been a snafu at this season’s tournament. I definitely remember byes in the 2007 rain out tournament, though I’m not sure about the 2008 tournament. And, I don’t think it was an intentional mistake. Once it was done, it was just too late to correct. (For those of you who seem to think that the tournament was intentionally seeded wrong to the benefit of the local London teams, you guys are idiots. It’s clear a system was followed based on pool play, regardless of where your team was from, albeit a wrong system.)

Look, the tournament is supposed to be fun, and it is. The tournament is also supposed to be semi-competitive, and it is. Not everything has to be perfect. But, I guess I think some things should be prioritized to be right more than others. I feel like this is one of them.

Despite being cold, windy, cold, and windy, it was a great tournament. I was excited to be there and I’m already excited and planning to be heading back next year. Thanks to Brian and all the Reds for putting it on and please let me know if the PWL can help in anyway.

comments powered by Disqus