Effect of Multiple Byes on Number of Games Played

Yesterday I investigated the impact having multiple byes has on winning conference tournaments, aiming to quantify the "benefit" of gaining/losing an additional bye. However, you could also argue there are other ways to measure a "benefit", such as the number of games you're expected to play (similar to the short-term effects of seeding). More games means more game experience, more practice time, more fan engagement, etc.

Recapping my findings: relative to chances of winning the whole thing, the current format:

1. Benefits the top seeds, who have to play 1 less game (except for Virginia)
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%

But what about games played? It seems fairly straight forward that the teams with more byes will have less games under the current format, and the teams with no byes will have more games (since they play weaker teams at the start and have a greater chance to move on).

		E[Games Played]
		Current	No Byes	Dif
1	Virginia	2.04	2.05	-0.01
2	Duke	1.52	2.38	-0.86
3	Miami FL	0.49	0.97	-0.48
4	Clemson	0.69	1.29	-0.61
5	North Carolina St.	0.92	0.93	-0.01
6	North Carolina	1.41	1.40	0.01
7	Virginia Tech	0.76	0.71	0.05
8	Florida St.	0.63	0.63	0.00
9	Louisville	0.64	0.64	0.00
10	Notre Dame	1.32	0.74	0.58
11	Syracuse	0.88	0.55	0.33
12	Boston College	0.90	0.64	0.27
13	Georgia Tech	0.78	0.43	0.35
14	Wake Forest	0.67	0.54	0.13
15	Pittsburgh	0.34	0.11	0.24

This follows the above hypothesis as expected. As before, Virginia is the sole outlier, which is because they have a first round bye no matter how the bracket is constructed.