Perfect Rounds and Perfect Brackets:
An Inside Look (2017)

It is well known that there are 9,223,372,036,854,775,808 (or 2**63) possible brackets. If each game is viewed as a toss-up, then each of these brackets are equally likely to occur. However, basketball aficionados know that since 1985, a No. 1 seed has never lost to a No. 16 seed. This means that not all games are toss-ups, and that using some basketball knowledge can reduce the odds of picking a perfect bracket.

What about the odds of a perfect round? The following table estimates these odds values, assuming that each game is a toss-up, or each seed will perform exactly as it has historically.perfomed.

We can use this information to estimate the odds of picking a perfect bracket. If all games are toss-ups, then the odds are 9,223,372,036,854,775,807 (or (2**63)-1) to 1. If all seeds are expected to perform exactly as they have historically, then using the third column in the table, the estimated odds of getting all the seeds correct drops to just over 4.4 billion to 1. If all seeds are expected to perform exactly as they have historically and taking into account the four regions, then using the fourth column in the table, the estimated odds of getting all the seeds correct in their respective regions is just over 106 billion to 1. Note that 4.4 billion to 1.odds is for getting all the seeds correct, though not necessarily in the correct regions. The 106 billion to 1 odds is for getting all the seeds correct in the correct regions, a true perfect bracket.

Round Toss-up Historical Performance, Seeds Historical Performance, Teams
Round of 64 (32 games correct) 4,294,967,295 839 thousand 20 million
Round of 32 (16 games correct) 4,294,967,295 182 thousand 4.4 million
Sweet Sixteen (8 games correct) 1,677,215 1,709 41 thousand
Elite 8 (4 games correct) 65,535 299 7190
Final Four (2 games correct) 1,023 11 143
National Champion (1 game correct) 63 1.5 9
All Rounds (63 games correct) 9,223,372,036,854,775,807 4.4 billion 106 billion

 

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