Final Four per the MDS Model (2019)

Some decent upsets this weekend have left us with only the best team (per my model) remaining: Virginia, which had a 16.33% chance to win it all at the start, now is up to better than 2 in 5 odds.

Seed	Team	1st Round	Championship	Champion
	Final Four
2	Michigan St.	100.00%	57.98%	28.75%
3	Texas Tech	100.00%	42.02%	17.58%
1	Virginia	100.00%	70.88%	42.49%
5	Auburn	100.00%	29.12%	11.18%

No other 1 seed made it though! So Virginia will have to carry the banner for the 54% combined favorite that all 1 seeds encompassed going into the Sweet 16.

Potential area of concern for Viginia fans: I've only picked the champion correctly twice going into the Final Four, and both times it was Villanova.

Sweet 16 per the MDS Model (2019)

I caught some flack for my model being so chalky going into the tournament, and well, here we are:

Seed	Team	Elite 8	Final Four	Championship	Champion
	Sweet 16
1	Duke	67.55%	40.85%	23.65%	13.52%
4	Virginia Tech	32.45%	13.91%	5.58%	2.20%
3	LSU	32.63%	11.01%	3.91%	1.37%
2	Michigan St.	67.37%	34.23%	18.13%	9.48%
1	Gonzaga	66.97%	39.31%	21.62%	12.03%
4	Florida St.	33.03%	13.65%	5.20%	2.01%
3	Texas Tech	45.10%	20.03%	8.78%	3.90%
2	Michigan	54.90%	27.01%	13.13%	6.46%
1	Virginia	82.75%	52.68%	33.34%	19.30%
12	Oregon	17.25%	4.77%	1.32%	0.31%
3	Purdue	44.18%	17.47%	8.12%	3.33%
2	Tennessee	55.82%	25.07%	13.11%	6.12%
1	North Carolina	64.01%	37.41%	18.68%	9.42%
5	Auburn	35.99%	15.95%	5.79%	2.12%
3	Houston	40.75%	16.80%	6.13%	2.25%
2	Kentucky	59.25%	29.84%	13.52%	6.18%

Virginia is the only team with better than a 50/50 chance of making the Final Four at this point, and no team has even a 1 in 5 chance of winning it all. Interestingly, they are also the only team to see their odds improve from prior to the tournament. The chalkyness of results has left Duke, Carolina, and Gonzaga relatively unchanged. Even so, there is a 54% likelihood that one of the 1 seeds ends up winning it all.

"What are the odds?" Duke and Carolina Will Meet in the NCAA Tournament, and When

Duke/Carolina is arguably the fiercest rivalry in all of college sports. I can understand if you choose The Game (since they did fight an actual war at one point), but results this century don't encompass a compelling argument:

And between North Carolina and Duke, the two schools rank #3/#4 in all-time wins, have 48/42 NCAA tournament appearances, 20/16 Final Fours, and 11/11 championship game appearances (all figures are respective). So it's fairly surprising that we've never met in the NCAA tournament (we met once in the NIT, in 1971).

The committee never puts us in the same region, so the Final Four would be the earliest meeting. And even for the best teams, it's more likely than not that they won't make the Final Four. So this proposition is definitely a long shot, but not impossible; it almost happened in 1991 in the title game. So when is it expected to happen?

I started by gathering the seedings for both us and Dook over the past 20 seasons (we also missed the tournament 3 times...):

	Average	Median	Mode	Max	Min	Standard Dev
Carolina	3	2	1	1	8	2.53
Dook	1.9	2	1	1	6	1.33

We've had more variance, but the most likely seed for both teams is a 2. We also have been on the same side of the bracket only 5 times in this period, or 25% of the time (in other words, 25% of the time we could have met in the Final Four, and the rest of the time would have been in the title game).

Next, I drew a fairly deep sample of the odds a generic 1 through 8 seed makes the Final Four using the past 5 seasons of my model:

Seed	Prob FF
1	28.93%
2	23.73%
3	12.51%
4	10.59%
5	7.67%
6	4.34%
7	2.98%
8	2.20%

Note: I threw out Kentucky's region from 2015. Talk about an outlier: 78.5% to make the Final Four!

So now for the math on an outcome I certainly hope to never see; I actually agree with Coach K, who stated in '91 "that he never wanted the two schools to play in the last game of the season because it would be too devastating for the loser." (Chansky, Blue Blood: Duke-Carolina) 

The Bump (or Lack Thereof) From Winning Your Conference Regular Season

Stemming from my earlier post on whether teams see a bump from winning their conference tournament, I have received demands to follow this up with the same analysis but for conference regular season titles.

I can now recreate the chart from the last post with both types of conference titles considered:

Year	Champion	Conference	Conf Tourney	Conf Reg Season	>= 1	Both
2018	Villanova	Big East	1	0	1	0
2017	North Carolina	ACC	0	1	1	0
2016	Villanova	Big East	0	1	1	0
2015	Duke	ACC	0	0	0	0
2014	Connecticut	AAC	0	0	0	0
2013	Louisville	Big East	1	1	1	1
2012	Kentucky	SEC	0	1	1	0
2011	Connecticut	Big East	1	0	1	0
2010	Duke	ACC	1	1	1	1
2009	North Carolina	ACC	0	1	1	0
2008	Kansas	Big 12	1	1	1	1
2007	Florida	SEC	1	1	1	1
2006	Florida	SEC	1	0	1	0
2005	North Carolina	ACC	0	1	1	0
2004	Connecticut	Big East	1	0	1	0
2003	Syracuse	Big East	0	1	1	0
2002	Maryland	ACC	0	1	1	0

8/17 won their conference tournament, 11/17 won their conference regular season, 15 /17 won at least 1 of these, and 4/17 won both.

I can see how far each team progressed similar to last time as well:

Finish	Count	%	Cumul %
Missed	1	1.0%	100.0%
First Round	5	4.9%	99.0%
Second Round	22	21.6%	94.1%
Sweet 16	18	17.6%	72.5%
Elite 8	25	24.5%	54.9%
Final Four	13	12.7%	30.4%
Championship	8	7.8%	17.6%
Champion	10	9.8%	9.8%
Total	102	100.0%	100.0%