So the first round percentages didn't change much this year but here is a question to discuss:
Will a #13 or lower ever win a second weekend game?
I certainly hope we don't see it this year as the only remaining #13 or below is Purdue's opponent, #15 St Peters. In the previous 37 tournaments (1985-2021 not incl 2020):
- #13 seeds made the S16 six times and went 0-6.
- #14 seeds made the S16 twice and went 0-2.
- #15 seeds made the S16 twice and went 0-2.
- #16 seeds have yet to make it out of the first weekend.
This year's example is a pretty good indication of why it hasn't happened yet. St. Peter's already knocked off bluest of blue blood #2 Kentucky in the first round and a decent Murray State team in the second round and their reward is #3 Purdue. St. Peter's obviously had to play at least close to their ceiling to win those first two games and how long can they keep that up?
St. Peter's is currently riding a nine-game winning streak. Prior to that they lost three out of four to such luminaries as Siena, Iona, and Rider. On February 20 St. Peters walked out of Siena's gym as a team barely over .500 (12-11) and decidedly NOT on anybody's NCAA Tournament radar. They haven't lost since. They won their last four regular season games to finish 16-11/14-6 then charged through the MAAC Tournament to hit the NCAA Tournament at 19-11 and obviously they beat #2 Kentucky and #7 Murray State so they are now 21-11.
To answer my own question, I think we will see it eventually but not in the way that I initially thought was most likely. My initial thought was that eventually two #13 or below seeds would bump into each other in the S16 and one of them would have to win. Upon looking into the numbers, that may never happen. Including St. Peter's this year, the #13's and below have made it to the S16 11 times. There have been 592 S16 teams (16*37) so #13 seeds and below make up 1.86%. My initial thinking was ok, 2% is roughly one in fifty so there should be something like a one in 2,500 (50*50) chance of two #13's and below running into each other in the S16, right? Well actually no. It is worse than that.
Note from above that the #13's have more S16 appearances than the #14's, #15's, and #16's combined. That limits the chances of two #13's or below meeting in the S16 because the only potential #13 or below opponent for a #13 is #16 and none of them have ever made it.
Thus, the more likely meeting of two #13's or below in the S16 would be a meeting of a #14 and a #15 (in what, by chalk, would be the #2/3 game). Two #14's and three #15's (including St. Peter's) have made the S16 out of 148 chances for each seed. Multiplying the 2/148 chance of a #14 being there by the 3/148 chance of a #15 being there we get a 6/21,904 or roughly one in 3,651 chance of a meeting of two #13's or below in the S16. Even with four chances per year that is statistically a once every 913 year occurrence.
Therefore, my suspicion is that the more likely method for a #13 or below to win a second weekend game is for a #13 to get lucky and get a #8 or #9 and beat them. Statistically, if a #13 makes it to the S16 their likelihood of opponent is:
- 85.71% #1
- 10.14% #8
- 4.73% #9
- 0.00% #16
Rounding that off and expressing it a different way, in 20 trips to the S16 a #13 would face (on average):
- 17 #1 seeds,
- 2 #8 seeds, and
- 1 #9 seed.
The chances of a #13 taking out a #1 are near zero but I would guess that a #13 has around a one-in-three chance of beating a #8 or #9 seed so given enough trips to the S16 by #13 seeds they should eventually get through to the E8 possibly with a path of #4, #12, #8.
