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Bracket Voodoo: Why you won't win the billion-dollar bracket

By Brad Null | Bracketvoodoo.com

Warren Buffett will play you a tune, but you're not getting his billion. (Getty Images)
Warren Buffett will play you a tune on his sweet ax, but you're not getting his billion. (Getty Images)

Want to win a billion dollars? Warren Buffett and Quicken Loans will write you a check -- all you need to do is pick the perfect March Madness bracket. Though you may have done pretty well in your office pool last year, don't start googling “private islands for sale” just yet (too late?). I'm here to break the bad news. You are not going to win this money.

Last year, though a seven-figure total of people participated in bracket games at CBSSports.com, not one got even the first 32 picks correct, let alone the entire bracket. (Curiously, the last perfect bracket was busted when Indiana beat James Madison on Friday evening). Yet, to win the billion, you would effectively have to get these 32 picks right not once, but twice in a row!

So, what are the odds of picking the perfect bracket? To start with, if you pick every game at random (say flip a coin) then you would have a 50 percent chance of getting each pick correct. You would then have to make 63 correct picks. (Although there has been some confusion about this among the media, it appears that Buffett and Quicken Loans are -- like most bracket games -- giving you the four first-round games for free.) This is equivalent to the odds of flipping heads 63 times in a row, which is 1 in 9,223,372,036,854,775,808. This is just over 9 quintillion or 9 pentillion, depending on whom you ask -- the number is so large that people don't even agree on how to say it. One thing everyone can agree on: these are not good odds.

Looking at it another way, you and a billion of your closest friends could choose to divide and conquer by each entering about nine-billion different brackets into this contest. That way, you could enter every combination and assure you would win the prize. Then, for all of your hard work, you would each take home at most $1 (less if someone else happened to get the winning bracket). This won't buy you a pina colada, let alone a private island.

But of course, you know better than to pick the bracket at random. You'd put your bracket-picking skills to work, just like you did in the office pool. You know a 16 seed has never beaten a 1 seed in the men's tournament. You know there are clear favorites to win the Round of 64, and you know the favorites to win the whole tournament. So what if you used that information to pick the one out of 9 quintillion possible brackets that was most likely to come true? What are the odds that your bracket plays out exactly as you planned it?

Well, this is another way of asking: what is the most likely outcome of the tournament? While this is a difficult question to answer precisely, one good approximation for this is to just assume that the favorite wins every game.

Using bracketvoodoo.com's proprietary NCAA Tournament prediction system, we can calculate the probability of the favorite winning 63 consecutive games pretty easily. Bracketvoodoo ran this analysis for the 2013 Tournament (see our picks here), and according to the calculations, the probability that this bracket would have played out was a little worse than 1 in 80 billion.

On the plus side, a favorites bracket is over 100 million times more likely to win the billion dollars than a completely random bracket (and 100 octillion times more likely than the bracket where all of the underdogs win -- for those of you keeping score at home). Unfortunately, it still doesn't look like you should quit your job and pack for that move yet. In fact, if you and 1 million of those friends identified the 1 billion most likely bracket outcomes (so you each manually enter 1000 of them), you would collectively give yourselves less than a 1 percent chance of taking home at most $1000 each. (I say "at most" because there is a chance that if one of these outcomes pays off you would actually have to split the prize!)

So am I telling you not to bother entering a bracket? Actually, I'm not. Because what is more interesting about this competition is that Quicken Loans is doling out $100,000 each to the top 20 brackets they receive. (That's real money!) If we assume 10 million brackets are entered, then that's 20 cents per bracket, which is a lot better than the fraction of a cent you get on average going for the perfect bracket. Even if 100 million brackets are entered, the average payoff in the top 20 competition is better. But what's even more exciting about going for the top 20 prize is that if you pick your bracket so as to maximize your chances of winning this type of competition, you can generally improve your odds by about a factor of 10. (Since we still don't know various details, such as the scoring rules Buffett and company will be using, this estimate is approximate.) And of course, you're also going to need a bracketing philosophy for beating your friends, and the world, in CBSSports.com's bracket games.

Now, be warned: the bracket you should enter to maximize your chances of getting in the top 20 is very different from the bracket you would enter to maximize your chances of picking the "perfect bracket." And if you visit this space next week, I'll give you some tips on how to build this type of bracket. That is, if you're not busy planning your new life in the tropics.

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Brad Null is the founder of bracketvoodoo.com, the world's most advanced NCAA Tournament bracket analysis and optimization engine. Try it out now at bracketvoodoo.com

 
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