Billion Dollar Bracket Challenge Revisited
About five years ago, Brian Burke – of Advanced NFL Stats – wrote a post in this forum on modeling win probability in college basketball, demonstrating that Brian Burke can do more than just talk football and stats! Before the tournament started, Dave Collins – host of the Advanced NFL Stats podcast (where he interviews football writers, analysts, and researchers) – contacted me about more college basketball related research from the Advanced NFL Stats people. The specific research comes from Brad Null at Bracketvoodoo.com . What follows is an update from Brad:
Its no surprise that the Billion Dollar Bracket Challenge didn’t make it through the first weekend of the NCAA Tournament. As we discussed previously, there was about a 1 in 500,000 chance of anyone winning the challenge this year.(These odds could actually vary by up to a factor of 10 from year to year based on relative strengths of teams and the exact tourney seeding, so when thinking about future years, just take this as a guideline.) To go into a little more depth, here are round by round estimates of the odds anyone would have survived through each round of the Billion Dollar Bracket Challenge:
Odds anyone survives 

1st 32 
1 in 2 
1st weekend 
1 in 200 
to Elite Eight 
1 in 9,000 
to Final Four 
1 in 80,000 
To Championship 
1 in 250,000 
Billion $ 
1 in 500,000 
As we know now, no one in the BDB Challenge survived the first round. Apparently, one person on Yahoo did, but he didn’t register with the Challenge. Some might think that this year’s bracket busting is just a function of the fact that this year’s tournament has been even more chaotic than usual, but in fact, it really hasn’t been.
The likelihood of a bracket is the probability that every pick in the bracket actually wins. We ran 100,000 simulations and the median likelihood through the first two weekends was 1 in 170 trillion, (meaning that if we played this tournament 170 million times we would expect to see this set of outcomes once). So far, this year’s actual bracket (made up of the winning picks so far) has a likelihood of 1 in 120 trillion, which is in the 45th percentile. This means that 55 percent of the time we would have actually expected a more chaotic tournament than we have seen thus far. To see the point, here is a comparison of the likelihood of the actual bracket versus the 10^{th} percentile, median (50^{th} percentile), and 90^{th} percentile outcomes by round (percentiles for the actual bracket by round are in parentheses)
Likelihood of various results for NCAA Tournament 2014
1^{st} 32 
1^{st} Weekend 
To Elite Eight 
To Final Four 

10^{th} Percentile 
1 in 270,000 
1 in 3 billion 
1 in 500 billion 
1 in 5.9 trillion 
Actual 
1 in 1.9 million (36^{th}) 
1 in 27 billion (34^{th}) 
1 in 5.8 trillion (38^{th}) 
1 in 120 trillion (45^{th}) 
50th Percentile 
1 in 4.9 million 
1 in 80 billion 
1 in 13 trillion 
1 in 170 trillion 
90th Percentile 
1 in 210 million 
1 in 5 trillion 
1 in 860 trillion 
1 in 10 quadrillion 
You can see that through the first couple of rounds, the actual bracket was about 3 times more likely to come true than the median expected bracket. In fact, it was only this last weekend that the real life bracket became a little more chaotic (thanks a series of minor upsets by UConn, Kentucky, and Wisconsin). Nonetheless, this is a far cry from the relative chalkiness and madness of our sample 10^{th} and 90^{th} percentile brackets respectively.
Let’s cut back to the Billion Dollar Bracket:
Warren Buffett has stated that he wants to offer the challenge again next year, and he wants it to be more attainable. The tables above offer some insight into how attainable certain subchallenges might be, so in case Mr. Buffet is reading, here are a couple of suggestions for making the challenge more attainable and exciting:
1) Reward everyone that picks the first round correctly. Give everyone that does this $1 million. There would be about a 50% chance you would have to pay this out. And to limit your exposure, you could cap this to be split amongst everyone who accomplishes this. This might be wise, as it is very possible that hundreds or thousands of people would accomplish this. But this could make things even more interesting. Say the first round is very chalky (think the results this year, but without Mercer and Dayton winning). In that case, let’s just say you might have 100 people splitting $1 million. You could give them all an offer to take their cut ($10,000) or let it ride. Talk about drumming up excitement!
2) Offer $1 million to whoever makes it the farthest. And provide a live ticker keeping track of how many people are still alive and what their cut is. Or even give everyone the opportunity to pull out at any point in time and take his or her cut of the million (or some percentage of his or her cut – so there would be a penalty function). Then you could keep track of how much money was left on the table and what could have been…
3) Start after the Thursday and Friday games, let people pick their brackets, but any pick they get wrong in the first round just gets replaced by the team that beat them (so all those Duke fans would have been riding Mercer all the way). Smart entries in this contest could get on the order of 1 in 20 million odds of making all 31 picks correctly. So Buffett could offer $100 million for anyone that correctly achieves this and still have an expected value of paying out less than $10 million. With Buffet’s fortune, we think he could still sleep at night with those odds.
4) Up the Stakes! Of course Mr. Buffet could still offer the billion for picking the whole thing, but since everyone now knows what a long shot that is, might as well make it even more enticing. How about $10 billion? More zeros, more fun.
– Brad Null
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Brad Null (@bradnull) 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.