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March 22, 2006
The Numbers Guy looks at the NCAA tournament
The Wall Street Journal's Carl Bialik examines the promotions that offer huge prizes to someone who can fill out a perfect NCAA bracket.
A look at the odds of winning shows why companies are willing to risk such valuable loot. Filling out a perfect bracket means predicting the outcome of 63 games. If each game were a true toss-up, that would mean your chance of perfection is a mere one in two to the 63rd power, or one in nine million trillion (yes, million trillion -- there are no tidy terms for numbers this large). Put another way, you are about 60 billion times more likely to win the multistate Powerball lottery.
The rest of the article goes on to describe some of the strategies for improving your odds (1 vs 16 games really aren't toss-ups). If you like college basketball and probability, you'll like this article.
My take on the situation is that there is usually one game (sometimes more than one) that almost nobody would have picked. The Iowa/Northwestern State contest would fit the bill. Or, how about Bradley over Pitt? George Mason over NC? Wichita State over Tennessee? Take your pick. Now suppose that 100 million people correctly picked the first round games involving Bradley, Pitt, George Mason, NC, Wichita State, and Tennessee. They regard the 4 games above as toss ups and choose them randomly. The expected number of contestants who would still be in the running for a perfect bracket would be 6.25 million. And there are still 53 games to pick!
So in other words, start with 100 million people who have already picked a couple of upsets, give them the courage to give a 50/50 chance to a clear underdog in 4 other games and you'll still cull the herd by about 94% in just 10 games out of 63.
My secret to filling out the bracket is to always have a couple of 10 seeds win in the first round, put one high seed in the Sweet 16, put Duke in the Final Four, and never ever go against Gonzaga in the first round no matter what their seed. That should improve your odds to one in several billion.
By Friday afternoon my bracket was in shambles, by the way (Duke and Gonzaga notwithstanding).
UPDATE: Katie Newmark (A Constrained Vision) also cites the article.
Posted by William Polley at March 22, 2006 10:00 PM
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Comments
It's dang near a crapshoot anymore. I did pick Wichta State correctly, but that's about it. At least as far as correctly picking brackets, there's "too much" parity between teams in the tournament (relative quality has improved) and "random events" are more important in determining outcomes of games these days.
What's driving the parity... are the "mid majors" getting better or the traditional powers getting weaker?
Posted by: Phil at March 23, 2006 7:09 AM
I've heard it said that more college players going pro earlier is weakening the stronger programs. Personally I don't think that explains much of it. The "bracket busters" have helped give the mid majors some wins and some national media exposure which must help the recruiting. I think that is of some significance.
Posted by: William Polley at March 23, 2006 3:12 PM