The Perfect Bracket

Sunday, March 29, 2009
By Sharad Goel

Million Bucks

Last week I wrote about a “wisdom of crowds” strategy for picking my March Madness basketball bracket. Down to the Final Four, I’m doing pretty well: tied for 2nd in my office pool, and in the 94th percentile of all 2 million brackets submitted on Yahoo! Sports. But doing well still means predicting a lot of games wrong; the current leader on Yahoo! has already missed 6 of 60 games.

As far as I can tell, no one has ever picked all 63 March Madness games correctly. But if you manage to do it, Yahoo! will shell out a cool $1 million. So what do you suppose it would cost them to buy insurance against that perfect bracket? My conservative answer is 28 bucks.

Now for the long answer. If each of the 63 games were decided by a fair coin flip, the chance of picking the perfect bracket is about 1 in 10 quintillion. But that ignores obvious disparities in team strength. Nobody really thinks #16 seed Chattanooga had much of chance to take down top dog UConn. Looking at tournament play from the last five years, the plot below shows the estimated probability of the favorite team winning as a function of the difference in rank between the favorite and the underdog. So, for example, the probability of a #1 seed beating a #16 seed is about 97 percent.

Probabilty of Winning

Thus accounting for team strength, the chance that each of the 63 tournament games is won by the favored team is a mere 1 in 70 billion.  So with this “favorite-team” bracket, you can expect to win about $1 million / 70 billion, or 0.0014 cents. OK, that’s not a lot of cash–but it’s free to enter, so you’re just leaving money on table if you don’t try, right?

Finally, despite the slew of “sure-thing” strategies out there, I’d bet that going with the favorites is about as well as you can do. Since about 2 million people submit brackets, Yahoo! can expect to pay out about 28 bucks.

I don’t know if Yahoo! actually has an insurance policy to hedge against that perfect bracket, but here’s my offer: For a paltry $50, I’ll cover the million dollar prize!

For more on the odds of picking the perfect bracket, check out Carl Bialik’s post.

Illustration by Kelly Savage

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