Perfect Rounds and Perfect Brackets:
An Inside Look (2020)

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 lost to a No. 16 seed only once (in 2018), while the No. 8 - No. 9 game teams are evenly matched. This means that not all games are toss-ups, and that using some basketball knowledge can improve 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.performed.

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 and taking into account the four regions, then using the third column in the table, the estimated odds of getting all the teams correct in their respective regions is just over 17 billion to 1, a true perfect bracket.

Round Toss-up Historical Performance, Teams
Round of 64 (32 games correct) 4,294,967,295 751 thousand
Round of 32 (16 games correct) 4,294,967,295 70 thousand
Sweet Sixteen (8 games correct) 1,677,215 2.1 thousand
Elite 8 (4 games correct) 65,535 870
Final Four (2 games correct) 1,023 50
National Champion (1 game correct) 63 5
All Rounds (63 games correct) 9,223,372,036,854,775,807 17.3 billion ©  2019 - The Board of Trustees of the University of Illinois.
All Rights Reserved.