chris: (mobius-scarf)
2010-03-27 00:58
Entry tags:

World Cup Bracketology

Someone at work suggested that word has gone around that I blog. This felt weird to hear at first, but on further reflection it's not much different from the fact that there are quite a few of us on Facebook offering up status updates - this is just a bit more verbose. If you're from where I work and reading this, hello! (Don't be a stalky stranger; please tell me that I'm wearing odd socks next time you see me at work.) The definitive version of my blog is at Dreamwidth, but if you're sufficiently bored then you might care to look through the silly things I've said over the years at LiveJournal. You've all known that I'm a raging geek for years so I'm more than happy to own and stand up for what I've written, though much of what I've written is now rather old and some things change over time. Not many, though.

A big feature on the annual American sporting calendar is March Madness, a tournament between the best college (i.e., university) basketball teams. (Parallel contests exist for men and women.) Simplifying at the cost of a little accuracy, the US is arbitrarily split into four regions, each of which is nearly-spuriously associated with a geographic name. A committee determines and produces a ranked order of the 16 best college basketball teams in each region. A single-elimination (i.e., knockout) competition takes place in each region, with the draw predetermined by strict seeding order: the first round features the number 1 ranked team vs. the number 16 ranked team, the number 2 seed vs. the number 15 seed and so on, the second round may feature number 1 vs. number 8, 2 vs. 7 and so forth. The four winners of the regions then play each other in semi-finals and a final to determine a national champion. This takes place over about three weeks or so. It's a huge deal, akin to the FA Cup over the course of three weeks; compare with Wimbledon, except that all the teams are supported rather than "just the British players".

Part of the paraphernalia of the event is the Bracket Contest, a form of competition in which participants attempt to predict the result of every game in the tournament. You know who the 64 initial teams are and you can work out who is going to be playing whom in later rounds, so you predict the results of 63 matches. Predicting all 63 results in advance, not least who is going to be playing at each point, is legendarily, astronomically difficult. We're talking, very roughly, "winning a big lottery jackpot from a single ticket twice running" difficult here. Just how difficult is difficult? Do you like big numbers? )

Bracket Contests are very common. Book of Odds quotes a source suggesting 40 million brackets are filled out every year, and that ESPN had over 4.6 million submissions in 2009. (The best score was 58/63.) Now that's not going to be 40 million people with one bracket each, but that's still millions or maybe tens of millions of players. This is a Farmville sort of number, let alone a World of Warcraft sort of number, and probably less than an order of magnitude from a poker or a Tetris sort of number. Heck, the President plays (video), and the video starts with the Barack-et including a pick of #1 Kansas over #9 Northern Iowa, like just about everyone else. Which proved to be wrong.

So a recent interesting story is this claim that someone managed to pick the first two rounds entirely correctly, going 48/48. I don't much care for the hook that the story uses, but given that ESPN claims to have had 4.78 million entries this year of which only four were 47/48 for the first two rounds, a perfect entry is a rarity. If you believe the claims that perfection for the first two rounds is 13.46 million to 1 against, then even 4.78 million shots at perfection all miss 94% of the time. It is said that the existence of Bracket Contests make March Madness a rare sporting contest that becomes less followed the closer it gets to the final, simply because people take less interest when they know their bracket is out of contention.

In conclusion: Bracket Contests are big news and fun. They're also pretty exclusive to March Madness. Why shouldn't the rest of the world enjoy Bracket Contests at a sporting event they'll be following... like this year's (association football) World Cup?

The World Cup has a pretty well-defined structure which makes it amenable to running a Bracket Contest, of sorts. The finals take place in two stages; the first stage sees eight groups of four teams compete in parallel round robins, to generate eight first-placed teams and eight second-placed teams. These teams then fit into a completely deterministic bracket, from which it is possible to identify all the potential matches in the remainder of the competition. This makes it ideal fertile territory for a Bracket Contest, and I don't think there are many of those taking place. (I thought this was a genuinely original idea, but hats off to TourneyTopia for getting there first - and, quite possibly, lots of other people of whom I am not aware.) We then ask, for values of "we" equal to "I", what the probability of a perfect World Cup bracket is.

Some slightly smaller numbers. In conclusion: somewhere between about 1 in 15 thousand and about 1 in 15 billion. )

I do think that bookmakers or newspapers could run quite engaging, and very simple to understand, "fill out your World Cup bracket" contests: one point for each team filled in correctly, first in terms of which teams make it from the group stages to the correct place in the final sixteen, then in terms of which teams make it through each round of the knockout stages. Bearing in mind the probability figures I quote are all overestimates, one should be able to offer 10,000/1 against a perfect bracket with consolations of 100/1 for placing all 8 winners and all 8 second places correctly and 10/1 for placing only all 8 winners correctly, and still make money on it. Alternatively, a newspaper might be able to run the competition and offer bonus prizes safe in the knowledge that they are moderately unlikely to be paid out - or, at least, could probably be reinsured against fairly easily.

Part of the reason why I'm in the mood to think about such things is that not so long ago I encountered the The Wizard of Odds web site, written by the epnoymous wizard (real name Michael Shackleford) himself. It has scads of information about gambling games, particularly their practical implementations found in Las Vegas. The author is the titular Wizard, who has a career path that I would have idolised twenty years ago: he qualified as an actuary, then put his mind towards analysing casino games and made a career out of it, both from consulting work and as a university professor passing on his knowledge. There's probably only room for one of him in the world; I'm glad he exists, for the commitment he has demonstrated to getting very large volumes of high-quality information out there at no charge to the reader.

I am terribly favourably predisposed towards him because of his writing style, which (quite correctly) focuses on expected value, near to exclusion of anything else, sometimes even to the fifth significant digit. The style is generally very unemotional, but when there is emotion, it's generally very direct, delightfully earnest and un-self-conscious. (Case in point.) By chance in 2005 the site found itself top on Google for "Is my boyfriend cheating on me?" and he has wound up answering relationship questions amid the gambling questions ever since, approaching them in a very similar fashion, though his advice is sometimes a bit on the, well, xkcd side. He keeps out of his own writing to such an extent that it's charming when he allows himself a very occasional self-deprecatory anecdote. I even give him points for being a Settlers of Catan player, though these points may just be paying off debt from his October 2004 assertion that "Risk is the greatest board game ever made". There's no accounting for taste, of course, and it may well just be what he grew up with.

Lastly, if any of the game design people around here have ever thought of turning their hands to designing casino games (because, as far as I'm concerned, there isn't a terribly high bar to beat) then the good wizard has a list of articles about this. Seems to me that I would probably enjoy attending a games event devoted to home-brewed gambling games, were such a thing ever to exist, at least as much as I would enjoy playing existing games in a casino. Could there be a gap in the market there for people who want a little more variety with their gambling, and might be prepared to pay for the privilege?