# Madness of march: Fun facts!

Some fun facts about the Sweet 16 in the 2021 NCAA tournament:

• The average seed of a team in the Sweet 16 this year is 5.875.
• The only seeds not represented in the Sweet Sixteen are 9, 10, 13, 14, and 16.
• This means there are 11 unique seeds represented in the Sweet Sixteen.  There have only been 11 unique seeds in the Sweet Sixteen twice before: 1986 and 1990.  In 1990, the Sweet Sixteen was missing the 9 seed and 13, 14, 15, and 16.  In 1986, the 9, 10, 13, 15 and 16 seeds were missing.
• The seeds 1-8 are represented in this years Sweet Sixteen.  That has only happened five times before in 1986, 1990, 2000, 2004 and 2008.  In 2004, the seeds 1 through 10 were all represented.

• There are 9 teams in the Sweet Sixteen  with a seed of 5 or higher (i.e. teams that “shouldn’t have made it”).  This has happened only 4 times before in 2018, 2000, 1990, and 1996.
• There has NEVER been a Sweet Sixteen  (going back to 1985) with 4 teams seeded 11 or higher.  This year we have two 11’s, a 12, and a 15.  Three teams with a seed of 11 or higher have made the Sweet Sixteen (1985, 1986, 2011, 2013).
• In 1999, there were 5 teams with a double digit seed in the Sweet Sixteen , the most ever.  This year there are 4.
• The sum of the seeds in the Round of 32 was 210 this year.  That is tied for the second highest ever (in 2016 the sum was 215 (TEN double digit seeds won their first round game!) and in 2012 the sum was 210).

• The sum of the seeds in the Sweet 16 is 94.  The second highest ever was in 1986 at 89.  The lowest sum of the seed in a Sweet Sixteen was 49 in 2009.  (Note the lowest possible is 40).

• Here is a density of the seeds in the Sweet 16.  The black line is 2021.  The flatter this estimate the more “madness”.  A high peak on the left with a heavy right skew would indicate a very “chalky” year tournament.

• Finally, here are the empirical CDFs of past tournaments with 2021 in red.  The more “madness” the lower this curve will be.  (I think the area under this curve would be an interesting way to measure the “madness” of a tournament.

Cheers.