NCAA Tournament 2019 Bracket Math for the MDS Model

Another year, another attempt to quantify the 9.2 quintillion outcomes of the NCAA tournament via my MDS Model. As I did last year, I've generated a composite set of rankings similar to what I used to sportsbet in Las Vegas. 

I'm taking a composite of 4 different models, similar to what FiveThirtyEight does, and the same technique as last year: 

• FiveThirtyEight (so I'm including a composite of a composite)
• KenPom (who's ratings are also included in FiveThirtyEight, so they're counted twice)
• Powerrank (created and maintained by Ed Feng)
• Massey Composite (another composite, this time spanning 68 rating systems)

I then use a weighted average of these 4 ratings that reduces outliers by weighting the ratings closer to the median higher. This smooths out the final Aggregate ratings that I then use to project the tournament. That being said, I have a good deal of trust in all of the above rating systems, so I wouldn't expect anything too crazy outlier-wise.

Note: For simplicity, I've taken the highest rated team in each play-in game and included them.

Seed	Team	1st Round	2nd Round	Sweet 16	Elite 8	Final Four	Championship	Champion
	East
1	Duke	100.00%	98.28%	80.11%	58.13%	37.81%	23.02%	13.77%
16*	North Dakota St.	100.00%	1.72%	0.19%	0.01%	0.00%	0.00%	0.00%
8	VCU	100.00%	52.72%	10.84%	4.40%	1.45%	0.42%	0.12%
9	UCF	100.00%	47.28%	8.86%	3.37%	1.03%	0.27%	0.07%
5	Mississippi St.	100.00%	71.93%	35.26%	11.71%	4.84%	1.79%	0.64%
12	Liberty	100.00%	28.07%	7.99%	1.33%	0.29%	0.05%	0.01%
4	Virginia Tech	100.00%	82.67%	51.90%	20.43%	9.82%	4.27%	1.81%
13	Saint Louis	100.00%	17.33%	4.85%	0.62%	0.11%	0.02%	0.00%
6	Maryland	100.00%	63.24%	33.30%	12.12%	4.21%	1.50%	0.52%
11*	Belmont	100.00%	36.76%	14.67%	3.69%	0.88%	0.21%	0.05%
3	LSU	100.00%	77.18%	45.15%	17.98%	6.85%	2.67%	1.01%
14	Yale	100.00%	22.82%	6.88%	1.15%	0.18%	0.03%	0.00%
7	Louisville	100.00%	63.56%	21.80%	11.86%	4.39%	1.66%	0.61%
10	Minnesota	100.00%	36.44%	8.49%	3.48%	0.89%	0.23%	0.06%
2	Michigan St.	100.00%	95.13%	68.98%	49.62%	27.24%	15.29%	8.42%
15	Bradley	100.00%	4.87%	0.73%	0.11%	0.01%	0.00%	0.00%
	West
1	Gonzaga	100.00%	98.16%	77.94%	56.95%	36.19%	20.95%	12.22%
16*	Fairleigh Dickinson	100.00%	1.84%	0.19%	0.01%	0.00%	0.00%	0.00%
8	Syracuse	100.00%	52.65%	11.98%	5.26%	1.77%	0.51%	0.15%
9	Baylor	100.00%	47.35%	9.89%	4.09%	1.28%	0.34%	0.09%
5	Marquette	100.00%	61.83%	29.61%	9.60%	3.69%	1.23%	0.41%
12	Murray St.	100.00%	38.17%	14.01%	3.23%	0.90%	0.21%	0.05%
4	Florida St.	100.00%	77.73%	48.91%	19.61%	9.17%	3.78%	1.57%
13	Vermont	100.00%	22.27%	7.47%	1.25%	0.26%	0.04%	0.01%
6	Buffalo	100.00%	67.41%	30.14%	12.68%	4.93%	1.80%	0.66%
11*	Arizona St.	100.00%	32.59%	9.45%	2.49%	0.60%	0.13%	0.03%
3	Texas Tech	100.00%	85.61%	56.58%	29.81%	14.67%	6.89%	3.26%
14	Northern Kentucky	100.00%	14.39%	3.83%	0.65%	0.10%	0.01%	0.00%
7	Nevada	100.00%	55.72%	20.65%	9.27%	3.46%	1.21%	0.43%
10	Florida	100.00%	44.28%	14.23%	5.62%	1.82%	0.55%	0.17%
2	Michigan	100.00%	91.50%	63.47%	39.22%	21.13%	10.91%	5.68%
15	Montana	100.00%	8.50%	1.65%	0.26%	0.03%	0.00%	0.00%
	South
1	Virginia	100.00%	97.08%	79.91%	60.52%	41.42%	27.37%	16.33%
16	Gardner Webb	100.00%	2.92%	0.49%	0.06%	0.01%	0.00%	0.00%
8	Ole Miss	100.00%	47.66%	8.96%	3.62%	1.18%	0.36%	0.09%
9	Oklahoma	100.00%	52.34%	10.64%	4.54%	1.58%	0.51%	0.13%
5	Wisconsin	100.00%	65.06%	39.24%	14.18%	6.74%	3.03%	1.16%
12	Oregon	100.00%	34.94%	15.92%	3.80%	1.26%	0.39%	0.10%
4	Kansas St.	100.00%	73.61%	37.56%	12.18%	5.29%	2.16%	0.74%
13	UC Irvine	100.00%	26.39%	7.28%	1.10%	0.24%	0.05%	0.01%
6	Villanova	100.00%	59.52%	27.21%	11.61%	4.07%	1.62%	0.54%
11	Saint Mary's	100.00%	40.48%	14.96%	5.08%	1.38%	0.43%	0.11%
3	Purdue	100.00%	83.84%	53.53%	28.10%	12.47%	6.21%	2.67%
14	Old Dominion	100.00%	16.16%	4.29%	0.82%	0.12%	0.02%	0.00%
7	Cincinnati	100.00%	53.51%	18.09%	7.55%	2.30%	0.80%	0.23%
10	Iowa	100.00%	46.49%	14.36%	5.52%	1.52%	0.48%	0.12%
2	Tennessee	100.00%	90.71%	65.40%	40.95%	20.39%	11.31%	5.50%
15	Colgate	100.00%	9.29%	2.15%	0.36%	0.04%	0.00%	0.00%
	Midwest
1	North Carolina	100.00%	97.40%	75.57%	51.86%	32.56%	17.61%	9.22%
16	Iona	100.00%	2.60%	0.31%	0.02%	0.00%	0.00%	0.00%
8	Utah St.	100.00%	52.59%	13.17%	5.41%	1.90%	0.53%	0.14%
9	Washington	100.00%	47.41%	10.96%	4.24%	1.39%	0.36%	0.09%
5	Auburn	100.00%	69.60%	40.97%	17.73%	8.70%	3.53%	1.36%
12	New Mexico St.	100.00%	30.40%	11.99%	3.08%	0.93%	0.22%	0.05%
4	Kansas	100.00%	75.14%	40.04%	16.31%	7.56%	2.87%	1.04%
13	Northeastern	100.00%	24.86%	7.01%	1.34%	0.30%	0.05%	0.01%
6	Iowa St.	100.00%	63.22%	33.30%	15.04%	6.44%	2.44%	0.87%
11	Ohio St.	100.00%	36.78%	14.74%	4.84%	1.49%	0.39%	0.10%
3	Houston	100.00%	82.63%	47.90%	23.09%	10.59%	4.31%	1.67%
14	Georgia St.	100.00%	17.37%	4.06%	0.70%	0.11%	0.01%	0.00%
7	Wofford	100.00%	61.22%	22.60%	10.62%	4.08%	1.37%	0.43%
10	Seton Hall	100.00%	38.78%	10.64%	3.85%	1.10%	0.27%	0.06%
2	Kentucky	100.00%	92.90%	65.48%	41.68%	22.84%	11.31%	5.40%
15	Abilene Christian	100.00%	7.10%	1.28%	0.18%	0.02%	0.00%	0.00%

Some quick reactions:

• North Carolina seems to have the toughest route, but also has the lowest rating in my model of the 1 seeds. These two combined factors result in the lowest probability of the 1 seeds of reaching the Final Four (32.56%)
• Of course Virginia has the lowest chance of winning their first game out of all the 1 seeds (97.08%)!
• The fan base that has the best right to complain is Michigan St: they're #4 overall, yet get #2 Duke in the Elite Eight, and only have a 27.24% chance of reaching Minneapolis

The top 12 teams in the tournament are as follows:

Rank	Team	Rating
1	Virginia	95.38
2	Duke	94.78
3	Gonzaga	94.23
4	Michigan St.	93.03
5	North Carolina	92.71
6	Michigan	91.94
7	Tennessee	91.40
8	Kentucky	91.05
9	Texas Tech	90.22
10	Purdue	89.35
11	Virginia Tech	88.43
12	Florida St.	88.10

5 of these top 12 are ACC, which is a real testament to the strength of the conference. The Big 10 has 3, the SEC has 2, and the Big 12 only has 1.

A word of caution about straight up copying the above: in most pools you want to gauge "contrarian" picks relative to the overall pool. My suggestion would be to use the above probabilities as a guide ("I'm just a guide"), and make contrarian picks that have a good chance of happening (like picking a champion that has solid odds but isn't necessarily the favorite).

Michigan St or Tennessee Will (Likely) Be the Team Left Off the 1 Line

Note: The following post was compiled before the SEC and Big 10 championship games had been played

Due to a couple of results from the past week, the four #1 seeds in this year's tournament are far from certain. Virginia and Dook are in (and one of them will be #1 overall), but there are conceivably 4 teams for the last 2 spots. Will the ACC get three #1 seeds, something a conference has done only once before? Will Gonzaga remain on the top line even after losing handily to a bid stealer? Or will the SEC and Big 10 get one or both?

I'm using the Bracket Matrix to try to answer this question, which is a compilation of 51 publicly available brackets, all trying to predict what the committee will do in a few hours. This compilation currently has North Carolina barely hanging on to the last #1 seed and Gonzaga solidly at #3 overall. But mine is a bigger question: who is getting boxed out of the top line?

I'm assuming that Kentucky has no shot; "Only twice in the past nine years has a 1-seed been given to a team that didn't win either its regular-season or conference tournament title." So that leaves the other 4 described above, Gonzaga/North Carolina/Tennessee/Michigan St. I then looked at every #1 seed combination on the Bracket Matrix:

Top Line	Count
Virginia,Duke,Gonzaga,North Carolina	24
Virginia,Duke,Gonzaga,Tennessee	12
Virginia,Duke,North Carolina,Tennessee	7
Virginia,Duke,Gonzaga,Michigan State	3
Virginia,Duke,Tennessee,Michigan State	2
Virginia,Duke,North Carolina,Michigan State	1
Virginia,Gonzaga,North Carolina,Tennessee	1
Virginia,Duke,North Carolina,Kentucky	1
Total	51

We can really ignore the last 2, which were last updated before Dook won and Kentucky lost yesterday. Of the rest, each team was left out:

Team	# Times Left Out
Michigan State	31
Tennessee	25
North Carolina	17
Gonzaga	8

The ideological differences in the brackets are interesting. It looks like it comes down to Gonzaga vs Tennessee, as 31 of the 49 predictions I considered only contain one of these two schools, and only 12 leave off North Carolina in favor of BOTH Gonzaga and Tennessee. And none of these combined 43 have Michigan St. 

We'll see tonight if the committee follows the majority of forecasters here (31/49) and chooses one of Gonzaga or Tennessee, or if they go contrarian (12/49) and leave off North Carolina.

2019 ACC Bracket Math

It's March! And the ACC tournament being moved forward a day has thrown me off again (thanks John Swofford!)

Here are the tournament ratings and probabilities anyway, using a composite of the Massey Composite and Kenpom:

Seed	Team	Rating
1	Virginia	0.919
2	North Carolina	0.874
3	Duke	0.892
4	Florida St.	0.826
5	Virginia Tech	0.844
6	Syracuse	0.781
7	Louisville	0.817
8	North Carolina St.	0.788
9	Clemson	0.795
10	Georgia Tech	0.684
11	Boston College	0.677
12	Miami FL	0.720
13	Wake Forest	0.616
14	Pittsburgh	0.685
15	Notre Dame	0.698

Seed	Team	2nd Round	Quarters	Semis	Final	Champion
1	Virginia	100.00%	100.00%	75.00%	53.07%	33.67%
8	North Carolina St.	100.00%	48.99%	12.06%	5.36%	1.98%
9	Clemson	100.00%	51.01%	12.94%	5.88%	2.22%
4	Florida St.	100.00%	100.00%	52.77%	18.91%	8.02%
5	Virginia Tech	100.00%	71.39%	38.05%	14.75%	6.72%
12	Miami FL	61.56%	19.82%	6.96%	1.66%	0.48%
13	Wake Forest	38.44%	8.79%	2.22%	0.37%	0.08%
2	North Carolina	100.00%	100.00%	65.85%	34.24%	16.57%
7	Louisville	100.00%	66.56%	26.00%	10.79%	4.11%
10	Georgia Tech	48.31%	15.78%	3.74%	0.98%	0.23%
15	Notre Dame	51.69%	17.66%	4.41%	1.21%	0.30%
3	Duke	100.00%	100.00%	73.38%	43.28%	22.67%
6	Syracuse	100.00%	62.57%	18.91%	7.35%	2.45%
11	Boston College	49.09%	18.16%	3.68%	1.01%	0.23%
14	Pittsburgh	50.91%	19.27%	4.02%	1.13%	0.27%

Note that I'm not using any kind of adjustment to categorize Charlotte (this year's site) as a "semi-home" for Dook or Carolina. Even so, Virginia is not as large a favorite as last year since both of those powerhouses are also so good this year (three 1 seeds??). Those 3 teams combine to win this tournament about 3/4 of the time.

Kia Soul Fuel Efficiency on ECO Mode

My 2015 Kia Soul has an "eco mode", which supposedly "helps the models to achieve a higher level of fuel economy by adjusting the engine and transaxle operating parameters". I usually have left it on since I drive quite a bit, with a 47-mile one way commute (94 miles round trip daily). Thing is, I have had no idea whether it actually does anything. It certainly makes changing gears slower, which makes it way harder to accelerate and sometimes feels like I'm driving a golf cart. Which certainly isn't ideal when I'm predominately driving on highways.

So over the past 3 months, I've started tracking splits of my mileage, gas fill ups, etc based on whether I have the "eco" button ON or OFF. Over a full timetable of 7,685 miles driven over 20 fill ups since 9/17/18, I've experienced the following performance per fill up:

Eco	Miles Driven	Gal	MPG	Count
ON	348.0	12.31	28.28	10
OFF	351.1	12.65	27.77	10
Total	349.6	12.48	28.02	20

So the eco mode actually does have an effect! My fuel efficiency is about 0.51 miles per gallon better when I have eco mode turned on. 

The car also gives an "estimated" range every time I fill it up, and these "estimates" certainly don't reflect what my tracking has shown me, skewing high in both cases and also a much smaller predicated delta between ON/OFF (0.18 miles per gallon):

Eco	Est Range	Gal	Est MPG	Count
ON	354.1	12.31	28.77	10
OFF	361.6	12.65	28.59	10
Total	357.8	12.48	28.68	20

So how much am I actually saving? Is it worth feeling like I need to start pedaling like Fred Flintstone in order to squeeze out another 0.51 miles per gallon? The current average gas price in Miami is around $2.35 per gallon, but over the course of my tracking I've been spending closer to $2.64 per gallon. So my savings would be:

0.51 miles per gallon * $2.64 per gallon * 1.56 savings per week = $2.10 per week

Is it worth ~$2 a week, or ~$104 a year, for a worse driving experience? Considering that I'm driving almost 100 miles round trip each day, 5 days a week, I think I'll leave eco mode OFF going forward.