Let's run through it really quick for those who are scratching their heads. College basketball is a thing. Play up to this point in the season has pointed out that some teams are doing better than others. Teams can thus be rank ordered. Best teams play worst teams, middle teams play middle teams, teams that win move to the next level of a bracket. Teams that lose are out. The winner of the whole thing wins college basketball (basically).
You like the idea of brackets but still hate college basketball. I get it. Maybe you wish I was just talking about Star Wars again? PROBLEM SOLVED:
By the way, is anyone but Vader ever going to win something like that? Prove me wrong, Internets, prove me wrong.
Basketball. For what it's worth, a lot more people are going to fill out basketball brackets than Star Wars brackets this year. How many more people? Well, it's hard to find accurate numbers, but it seems that it is a pretty safe claim from the numbers I've seen that the low end is that several million to tens of millions of brackets each year.
Has anyone ever filled out a perfect bracket? Nope. The odds are pretty rough against you, as the cascading contingencies get fairly complex. We could spend the rest of this week just talking about calculating the odds of a perfect bracket (1 in like a lot), but that's not what I want to focus on.
I'm also not going to tell you how to pick a perfect bracket (if I knew I probably wouldn't tell you, and I'd be a lot richer), nor which team is going to be the best upset, etc.
What I want to take a look at is as what the system of brackets is really manifesting. In fact, when we get down to the base of it, it's a lot like a lottery, or horse racing (which I've already talked about here). Sorry is this is starting to feel like a clip-show.
What makes it more like horse racing than a lottery (at least a random lottery) is the odds that are present in each match-up. Until you get to the final four (and even then if you count certain ranking groups) every team that plays against every other team is ranked by the tournament as either a favorite or an underdog. If you know anything about statistics (and nothing about basketball), that means that the safe bet is always the more probable outcome.
At the horse races, there is a favorite in every race. The problem is that your odds are not good for betting on the favorite. In theory, those odds could sometimes drop below 1:1 - for every dollar bet you might get less than a dollar back for a winning bet.
Some of you might not follow horse racing, so let's go back to a lottery and just fix it (figuratively and literally) so that it's a little less random.
For a game like pick 3, there are three boxes full of balls with numbers from 0-9 on them. A ball is drawn from three of these pools in order, resulting in a real three digit number that is the winner (i.e. any number between 000 and 999). Every number (e.g. 333, 148, 042, 611, 500, 007, 554) has an equal odds of being drawn, despite (incorrect) perceptions of dependence between draws (e.g. thinking something like 444 is less likely than something like 435).
So, let's rig this lotto. Let's rig it good.
Instead of there being 10 balls in these draws, let's make things a bit more interesting. Let's put in as many balls of each number in each draw as...well, that number. That means 3 balls that say '3', 5 balls that say '5', 9 balls that say '9'. We've just made a draw of '999' a lot more likely than a draw of '111'. We've also made a draw of '000' or '990' impossible, oddly enough.
So, this is simple, right? Go out and buy a ticket for '999' and sit back and wait for fat sacks of cash. Problem solved?
Well, not quite. Remember, even a rigged lottery really isn't statistically fair. Betting on every horse might get you a cool story, but in the end still costs you money.
Why, you ask? Well, you might have the (relatively) genius idea to go out and buy a '999' ticket, but I'm betting (a good bet, not a lotto bet) that you'd not be the only person with the same idea.
The way the lotto works is conceptually similar to the way horse racing works (which again was covered in that horse racing post). Everyone buys a chance at winning, and it is that cash input that is used as a take after the house takes its share (the rake). If the house didn't take a rake you'd be in a situation where acting on the odds could potentially just help you break even a whole bunch. With the rake in place you're going to end up tending toward a slow drain (again, just like the horse racing charts in that much earlier post).
This is because the take is divided between all the people who shared in the winning of it. If a million people buy dollar tickets, but they all buy a '999' ticket - and that ticket ends up being drawn - then what they are walking away with is a millionth share of a million dollars, less the rake. If the rake is 10% they're walking away with a millionth share of 900,000 dollars, or about 90 cents for every dollar in. That's not a great place to be.
The problem is simply that a lot of people are going to make the smartest bet (and not play the lotto? - okay, the second smartest bet) and play in line with the odds. The way to win is to somehow figure out how to get outside of the main pack and still end up with a winning ticket. You can buy '111' tickets over and over until that hits (and you're the only person silly enough to be holding one), but the numbers would suggest that on average you're going to spend more money on all those tickets while waiting for your number to come up. You can also go to Vegas and just slam down Lincolns (I'm assuming none of you are going to Vegas and dropping Benjamins) on the green spot(s) on a roulette wheel (or any spot, really).
You might hit early and get super lucky on the first draw. The moral of that - for hopefully obviously reasons - would be to stop playing the lotto and be happy that you capitalized on noise instead of having the odds capitalizing on you.
Enough with these pretend, odd lotteries, you say? You're here for basketball (or Star Wars)? How does this relate?
It relates because there is a bracket that corresponds to a lotto ticket of '999'. I have filled out that bracket in the past - it makes it a lot easier to watch games and remember who to cheer for. Always cheer for the favorite, and hope they're the favorite for a reason. When you get to the final four make your picks based on records as well as strength of conference. It's...pretty simple.
The problem is that it's simple enough that you can be assured you're not the only one that's through about it. Picking a safe favorites bracket will not make you stand out among the crowd - if you do happen to pick a perfect bracket you're now sharing that prestige with a whole bunch of others (as well as any prize money - several places like Yahoo offer big prizes for registering a perfect bracket).
Let's look at the extreme opposite for a moment. What if instead of picking every favorite you misinterpret the numbering system (biggest number is best number, right?) and instead pick every underdog?
This would be similar to the '111' ticket, but in practicality might closer to a '000' ticket. Such a situation seems so unlikely that in order for it to pay out you might have to do something crazy, like play March Madness longer than the lifetime of the universe. Some of you might be fine with that.
It's also the case that a '111' ticket is easy prey, so you can be assured you'd also not be alone in your strategy. As dumb as you might feel picking that bracket, you can be sure that the law of large numbers gave you at least a handful of partners in stupidity.
So you want to be somewhere in that happy middle ground. A bracket that's not too obvious, but one that is still unique. Not too hard to hit the unique part - estimates of the number of possible brackets are well into the 10+ digits. Again, cascading choices produce exponential growth (well, I got it right that James Madison made it to the final four, and everything else right, but I totally missed that Missouri upset Colorado State! Missouri!)
You can start, then, with a totally safe bracket - the statistician in me would advise it. From there, it's time to add your own pieces of flair to make it yours. Who do you think stands the best chance of being upset? Flip that one for the underdog and you'd just reduced the number of people who have done the same thing. Pick another underdog and the pool has probably again diminished. Now, figure out how far those upsets are going to go along the path to the finals. Figure out what upsets might occur in the Sweet 16 or Elite 8. Pick those.
You're walking a fine line here - it's conceptually similar to the trade-off of type I and type II error. The farther you push away from the most likely bracket the farther you also push away from the group of people playing it safe. The more risks you take the more likely you'd be standing alone with a perfect bracket if you ever hit one. Make sense? Makes sense.
In any case, go and get filling out those brackets! ESPECIALLY THE STAR WARS ONE.
If - though - all this talk about the way brackets are really working has you totally disillusioned on the idea of March Madness, then bracket-less brackets might be fore you. Bracket-less brackets are another cool take on this that actually makes it a lot harder to play it 'safe'. Instead of filling out a bracket you pick a team for each seed that you think will go the fartherst, and get points when they move on. I'm not going to get much deeper into it, because the guys over at Stuff Smart People Like already do a good job at it - they also have a bracket-less bracket contest you can easily take part in here:
Cheers to cross-promotion! Now fill out some brackets!
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