NCAA Tournament Paths

(The below was inspired by Ryan Bach's work at basketballgeek.com, and particularly, the explanation here.)

Let's assume the NCAA Women's Final Four has two brackets:  Team A vs. Team B and Team C vs. Team D.

Team A beats B 51 percent of the time.
Team A beats C 65 percent of the time.
Tema A beats D 100 percent of the time.

Team B beats C 65 percent of the time.
Team B beats D 100 percent of the time.

Team C beats D 100 percent of the time.

Question: Which team has the greatest chance of being declared national champion?

If you look at A, B, C and D altogether, A is the best team.  Team A's chances of beating either B, C or D one-on-one are greater than 50 percent in each case.  However, let's calculate the probabilities.  Remember, to win the National Championship, a team has to defeat not just the opponent in its own bracket but the winning opponent from the opposite one.

Team win success = (Beat opposing team in own bracket) * (Beat first team in other bracket*(prob of meeting first team) + Beat second team in bracket*(probability of meeting second team))

Team A:  (.51)*(.65*(1) + .65*(0)) = .3315
Team B:  (.49)*(.65*(1) + .65*(0)) = .3185
Team C:  (1)*(.35*(.51) + (.35*(.49)) = .35*(.51 + .49) = .35 * 1 = .35
Team D:  0

Using strict probability, you should put your money on Team C to win it all - and Team C is only the third strongest team!  The fact that C's path to the finals is a cakewalk is a big boost in its chances for final success.  The probabilities add up to 100 percent across all four teams.  Team C, believe it or not, has the best chance of winning the tournament.

For the #1 through #4 seeds for the most part, the first win in that six game hypothetical path to the championship is a very simple one - by the time you get to the prospective opponents which are  #13-#16 seeds, you're seeding the tournament with low-major conference champions that might not otherwise qualify. In some cases, those teams aren't even the best teams in their own conference.  The record of seeds #1 through #4 in the first round is an astonishing 266-6 since 1994 in the NCAA Women's Tournament.  That's a 97.8 percent win probability.

The #8 and #9 seeds have it the worst.  In order to reach the Sweet Sixteen, not only does that team have to beat a team that's virtually its equal in the first round, but must then beat one of the top four teams in the country in the second.  The record of #8 and #9 seeds in the second round?  4-64, or 6.25 percent.   Whereas the #10 and #11 seeds have gone to the Sweet Sixteen eight times.   Part of the reasons for that have a lot to do with path dependency.

What does all of the above mean?  Very simple.  Getting to the NCAA Finals doesn't depend entire on how good your team is matched one-on-one versus any other -  it also depends a great part on "who you play".  The road to the NCAA Finals is a long one...but not if you end up in the express late.  If the half of the 64-team bracket that doesn't have your favorite team is experiencing a lot of upsets, you can be forgiven for feeling good inside.