# Bracket Voodoo: Trying, and failing to win a billion dollars

PLAY: Bracket Manager | Bracket Challenge | Round-by- Round | Experts Challenge

This is my entry for the Billion Dollar Bracket Challenge, and as of now I think it is the best possible entry. Let me explain why:

First, let's get one thing out of the way. I do not think this bracket will win me a billion dollars. I could have gone for the billion and had about a one in 300 billion chance of winning it, which in the best case is an expected value of 1/3 of a penny (and that is before we account for the fact that there will definitely be several entries identical to that one). What's more attainable is the “consolation” prize of \$100,000 that is awarded to the 20 brackets with the highest score. That's what this bracket is designed to go after.

So the obvious question then: how do you optimize a bracket to win such a massive pool? In a nutshell: you go out on a limb, way out on a limb. With 15 million people competing for \$2 million, you have just better than a 1 in a million shot at getting a cut of it. Following the masses and picking Florida to win isn't going to do it for you. Four or five million people are going to pick Florida to win in this contest, so even if that does play out, you haven't helped yourself much.

You need to make picks that everyone else is overlooking or dismissing. The metric you need to focus on is the ratio of your pick's probability of winning to the percentage of people that you think will pick them. We'll call that the pick's odds ratio. (To get a good approximation of how many people you think will make a certain pick in a large challenge like this, you can look at who CBSSports.com users are picking.)

The Billion Dollar Bracket Challenge uses the standard 1-2-4-8-16-32 scoring system, which means it awards 32 points for correctly picking the champion, 16 for the finalists, and so on. In the context of this system, especially with such a large number of competitors, it is of ultimate importance to correctly pick the champion, since there is essentially no chance you could finish in the money without doing so. A couple of days ago I ran through the 12 teams with the best shot of winning it all, but for a competition like this throw that out the window. You need to focus exclusively on the odds ratio. Here are the picks to win the championship with the best odds ratio:

We mentioned Villanova, Pittsburgh, and the Iowa/Tennessee matchup yesterday when we were discussing teams you should show some love in your bracket. Villanova is by far the most likely among these teams to win the tourney, with a 5.6% chance of winning versus 1.1% of people picking them. The only problem with that pick is that even if you get it right, you could still be left with about 160,000 like-minded people competing against you to win that \$100,000. Going with one of the other picks listed here would leave you in the running with 10,000 to 30,000 other people. These are still long odds, but better.

Regardless of which of these teams we pick, we would still have to get into about the top .1% of brackets that correctly made that pick to end up in the top 20. So obviously going out on a limb to pick the champion isn't good enough in a contest like this. We need to combine this with another gambit. Given the 1-2-4-8-16-32 scoring system, we would ideally want that gambit to involve picking the other finalist, since we could get the biggest point boost from it (and basically ensure that we couldn't be beaten by anyone that hadn't also correctly picked both of the finalists). That being the case, let's look at the picks to make the finals with the best odds ratio. We see a lot of the same names here:

At this point we took various combinations of these picks and ran them through the bracketvoodoo.com optimization engine, to evaluate their chances of winning this contest, have the engine optimize the rest of the picks, and see if the engine could recommend any improvements. The engine was actually designed to handle pools with 2 to 1000 participants (requisite blurb -- come analyze your bracket today!), so we had to customize it a bit to handle 15 million, and as you can imagine, the analysis took a little longer to run.

In the end, the engine liked VCU over the Iowa/Tennessee winner as its pick. The odds that this gambit plays out are about one in 6500. But we would expect only about 75 people in the pool to have this strategy.

Thus, assuming we correctly pick all the winners in Arlington (a big assumption, I know), we would essentially just need to come in the top 20 out of the 75 or so people that also accomplished that. This bracket would have a 42% chance of doing that. Those are relatively good odds, which is why the rest of this bracket is pretty chalky. All in all then, this comes out to a 1 in 15,000 shot at winning \$100,000 or an expected value of just under \$7. The odds will get a little better if Iowa wins Wednesday night, but regardless of who wins, this is still a solid pick.

The one problem in all of this is that I am violating a cardinal rule of picking brackets -- never tell anyone your picks. This whole analysis is based upon ensuring that if this gambit plays out I will only have to compete against 75 or so other people to win the \$100,000. If anyone reading this plays the same gambit, my odds go down. So please, don't steal my picks.

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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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