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Old Tue Mar 19, 2013, 03:32pm
MD Longhorn MD Longhorn is offline
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Quote:
Originally Posted by grunewar View Post
The odds of you filling out a perfect bracket this year are a staggering 1 in 9.2 quintillion. That's a nine with 18 zeroes or 9,223,372,036,854,775,808 if you're not into the whole rounding thing.

How big is that?

• That's one billion, 9.2 billion times.

• It's 500,000 times more than our $17 trillion national debt.

• You'd have a better chance of hitting four holes-in-one in a single round of golf.

The 1 in 9.2 quintillion number is straight mathematics. It figures out how many possible ways the 63 game results on your bracket could be filled out. (Two to the sixty-third power.)
I've seen this math before, and honestly, it's quite inflated. Statistics classes in me coming back to mind...

The assumption there is that each game has exactly a 50% chance of hitting either result. But that's not true at all. Take the 1-seed vs 16-seed games as the extreme example. I suppose the chance of a 1 seed losing is not exactly zero, but it's damn close. Take as a given (near 100%) that the picker will pick 4 1-seeds to win, and 4 1-seeds do actually win, your odds of a perfect bracket become 16 times greater ... a mere 576.46 quadrillion to 1.

For each set of matchups, the odds are not 50-50, and for each of those that are not, if you also assume that the picking people mirror somewhat the actual odds (and not 50-50), the odds of the overall package improve.

(For an example of that, consider 4 games with 75% odds, say, 4 4-13 matchups:

The odds of getting these 4 correct are not 1 in 2^4 (1/16 = 6.25%) but rather 15.2587891%. 2.44 times greater than expected. Those 4 games change the overall odds to (just) 236.25 quadrillion.)

Do that for each round of matchups, and the odds of a perfect bracket are actually MUCH greater than 9 quintillion.
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