Effect of Multiple Byes on Win Probability + ACC Bracket Math

In the past I've always put out win probabilities for my MDS Model for the top 5 conference tournaments. Thanks to the Big 10 moving everything up a week to play in Madison Square Garden, I completely missed it this year. So here's the bracket math for the ACC and only the ACC:

Seed	Team	2nd Round	Quarters	Semis	Final	Champion
1	Virginia	100.00%	100.00%	84.04%	70.36%	49.35%
8	Florida St.	100.00%	49.58%	7.86%	3.93%	1.31%
9	Louisville	100.00%	50.42%	8.11%	4.09%	1.37%
4	Clemson	100.00%	100.00%	50.51%	12.96%	5.05%
5	North Carolina St.	100.00%	60.17%	25.27%	5.18%	1.67%
12	Boston College	56.39%	23.97%	8.36%	1.37%	0.36%
13	Georgia Tech	43.61%	15.86%	15.86%	2.12%	0.47%
2	Duke	100.00%	100.00%	72.32%	52.98%	26.62%
7	Virginia Tech	100.00%	55.27%	12.90%	5.98%	1.58%
10	Notre Dame	77.36%	39.45%	9.49%	4.49%	1.21%
15	Pittsburgh	22.64%	5.28%	5.28%	1.13%	0.12%
3	Miami FL	100.00%	100.00%	35.31%	11.00%	2.81%
6	North Carolina	100.00%	70.14%	44.93%	19.40%	7.03%
11	Syracuse	57.68%	18.78%	8.69%	2.46%	0.57%
14	Wake Forest	42.32%	11.07%	11.07%	2.55%	0.48%

Virginia is a cut above in the model, with Duke the only other serious threat. Nothing surprising there.

But this spawns a bigger question: which teams/seeds benefit from the double bye/single bye tournament format? All major conferences (including the ACC) use some iteration of this multiple bye system where the best teams get two byes (playing at most 3 games), the middle tier get one bye (playing up to 4 games), and the worst teams have to play 5 straight games (in 5 days) to win the conference title.

I've written on the short-term effect of seeding in the past, and so there needs to be a definition of what "benefits" a team. For my purposes here, I'm only looking at each team's chance of winning the tournament.

I reran the win probabilities with a standard 16-team bracket (where only the 1-seed gets a bye) and then compared this output to the current format:

Seed	Team	Quarters	Semis	Final	Champion
1	Virginia	100.00%	84.04%	70.70%	49.82%
8	Florida St.	49.58%	7.86%	3.98%	1.34%
9	Louisville	50.42%	8.11%	4.14%	1.40%
4	Clemson	70.72%	43.16%	11.07%	4.35%
13	Georgia Tech	29.28%	11.55%	1.54%	0.34%
5	North Carolina St.	57.50%	27.79%	5.69%	1.85%
12	Boston College	42.50%	17.50%	2.86%	0.76%
2	Duke	91.52%	69.82%	51.27%	25.76%
15	Pittsburgh	8.48%	1.95%	0.42%	0.05%
7	Virginia Tech	49.01%	13.66%	6.37%	1.68%
10	Notre Dame	50.99%	14.57%	6.94%	1.88%
3	Miami FL	61.30%	25.59%	7.90%	2.02%
14	Wake Forest	38.70%	12.16%	2.75%	0.51%
6	North Carolina	67.43%	45.74%	19.73%	7.16%
11	Syracuse	32.57%	16.50%	4.62%	1.07%

As expected, the current format:

1. Benefits the top seeds, who have to play 1 less game (except for Virginia, which we'll get to)
2. Is about the same for the middle seeds, who have to play the same number of games, but have a slightly higher chance of playing a worse team in their first game
3. Damages the chances of the higher ranked worst seeds, who have to play an additional game

		Champion
		Current	No Byes	Dif
1	Virginia	49.35%	49.82%	-0.46%
2	Duke	26.62%	25.76%	0.86%
3	Miami FL	2.81%	2.02%	0.79%
4	Clemson	5.05%	4.35%	0.70%
5	North Carolina St.	1.67%	1.85%	-0.18%
6	North Carolina	7.03%	7.16%	-0.13%
7	Virginia Tech	1.58%	1.68%	-0.11%
8	Florida St.	1.31%	1.34%	-0.03%
9	Louisville	1.37%	1.40%	-0.03%
10	Notre Dame	1.21%	1.88%	-0.67%
11	Syracuse	0.57%	1.07%	-0.50%
12	Boston College	0.36%	0.76%	-0.40%
13	Georgia Tech	0.47%	0.34%	0.12%
14	Wake Forest	0.48%	0.51%	-0.04%
15	Pittsburgh	0.12%	0.05%	0.08%

The outlier is Virginia, which has the same number of games in each setup, yet has a worse chance of winning it all. Their first (bye) and second (Florida St/Louisville) matchups remain the same, but Duke's chances of making the final are greatly increased (which specifically hurts Virginia).

Overall, playing a different number of games has the greatest effect on the odds of winning the tournament, but matchups do also matter. This is why the very worst seeds are helped slightly and the best (Virginia) is hurt, even though they have to play 1 more and 1 less game, respectively.