The circular constant figures in the Gaussian normal curve, yes, but be careful about how you apply the law of large numbers in a small tournament pool.
Perhaps [Wisconsin industrial engineering professor Laura] Albert McLay’s most important advice came at the end of her blog post: “It’s random.”

Doing your research might help you win in a smaller pool, but the more people get involved, the more likely it is “that someone will accidentally make a good bracket with a bad process,” she wrote.

This is the frustration amateur bracketologists know all too well: You can spend hours making well-researched predictions, but it feels like the office pool’s winner will always be someone who barely put any thought into his or her picks.

“A good process yields better outcomes on average but your mileage may vary any given year,” Albert McLay wrote.
Yes, and in the large national competitions, perfect brackets are rare, even with a goodly number of entrants correctly forecasting the final four and the champion.

That observation in the second paragraph is an example of a blind squirrel finding a nut.  With as many tournament pools as there are, there will be a lot of nuts and a lot of lucky blind squirrels.

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