I used Massey Composite Ratings for win probabilities. One significant limitation is that I my simulations currently don't have the capability to recalculate win probabilities partway through the season. For example, if we are 11-0 when we play Houston, our win probability in that game should be significantly higher than if we are 6-5, but I currently can't account for that. For you stats nerds, I assumed that the winner of each game is a random variable that is independent from the winner of every other game, even though I know that is not true. In the future I hope to improve this.

Results are below.

BYU Records:
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12-0: 4.0%
11-1: 18.0%
10-2: 31.6%
9-3: 28.8%
8-4: 13.8%
7-5: 3.1%
6-6: 0.2%
mean: 9.59-2.41

BYU B12 Regular Season Rankings:
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This is our probability of finishing the regular season ranked so high in the conference based only on conference record (no tiebreakers). If three teams are tied for first place and then BYU is tied for second place with three other teams, that is recorded here as rank 4.
1: 26.1%
2: 24.7%
3: 18.8%
4: 12.0%
5: 7.3%
6: 5.2%
7: 2.3%
8: 1.2%
9: 1.0%
10: 0.5%
11: 0.1%
12: 0.1%
13: 0.1%
mean: 2.95391

BYU B12 Rankings Detailed:
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This breaks out the odds of being ranked in each place by looking at whether we won that spot outright or were tied with various numbers of other teams. For example, T2(4) means we were in a 4-way tie for 2nd place. Results with probability < 0.1% are omitted.
1 outright: 12.5%
T1(2): 10.1%
T1(3): 2.9%
T1(4): 0.4%
2 outright: 10.1%
T2(2): 9.2%
T2(3): 3.7%
T2(4): 1.2%
T2(5): 0.3%
3 outright: 5.5%
T3(2): 6.5%
T3(3): 4.6%
T3(4): 1.7%
T3(5): 0.3%
4 outright: 3.0%
T4(2): 4.5%
T4(3): 2.5%
T4(4): 1.0%
T4(5): 0.5%
T4(6): 0.2%
5 outright: 1.2%
T5(2): 1.7%
T5(3): 1.7%
T5(4): 1.6%
T5(5): 0.7%
T5(6): 0.1%
6 outright: 0.5%
T6(2): 1.4%
T6(3): 1.9%
T6(4): 1.0%
T6(5): 0.2%
7 outright: 0.4%
T7(2): 0.8%
T7(3): 0.5%
T7(4): 0.2%
T7(5): 0.1%
8 outright: 0.1%
T8(2): 0.1%
T8(3): 0.2%
T8(4): 0.3%
T8(5): 0.2%
T9(2): 0.2%
T9(3): 0.4%
T9(4): 0.2%
T9(5): 0.1%
T10(2): 0.2%
T10(3): 0.1%

Probability of Making CCG:
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Arizona: 0.2%
Arizona St: 2.3%
BYU: 40.5%
Baylor: 0.0%
Cincinnati: 3.6%
Colorado: 1.7%
Houston: 0.0%
Iowa St: 63.9%
Kansas: 0.0%
Kansas St: 45.1%
Oklahoma St: 0.1%
TCU: 1.1%
Texas Tech: 22.0%
UCF: 0.5%
Utah: 8.3%
West Virginia: 9.8%

B12 CCG participants:
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I only listed the combinations with greater than a 0.1% chance of happening.

Iowa St v Kansas St: 20.7%
BYU v Iowa St: 20.1%
BYU v Kansas St: 12.4%
Iowa St v Texas Tech: 10.0%
Kansas St v Texas Tech: 5.6%
Iowa St v West Virginia: 5.3%
BYU v Texas Tech: 3.9%
Iowa St v Utah: 3.3%
Kansas St v Utah: 2.5%
BYU v West Virginia: 1.6%
Cincinnati v Iowa St: 1.4%
Kansas St v West Virginia: 1.4%
Arizona St v Iowa St: 1.0%
BYU v Utah: 1.0%
Texas Tech v Utah: 0.8%
Colorado v Iowa St: 0.8%
Cincinnati v Kansas St: 0.7%
BYU v Cincinnati: 0.6%
Texas Tech v West Virginia: 0.5%
Iowa St v TCU: 0.5%
Arizona St v Kansas St: 0.4%
Cincinnati v Texas Tech: 0.4%
Colorado v Kansas St: 0.4%
Utah v West Virginia: 0.3%
Kansas St v TCU: 0.3%
Arizona St v Texas Tech: 0.3%
BYU v Colorado: 0.2%
Arizona St v BYU: 0.2%
Iowa St v UCF: 0.2%
Kansas St v UCF: 0.2%
BYU v TCU: 0.1%
Cincinnati v Utah: 0.1%
Cincinnati v West Virginia: 0.1%
Arizona St v Utah: 0.1%
Arizona v Iowa St: 0.1%
Arizona St v West Virginia: 0.1%
Colorado v Texas Tech: 0.1%

Probability of Winning Conference:
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Arizona: 0.0%
Arizona St: 0.6%
BYU: 15.9%
Baylor: 0.0%
Cincinnati: 1.1%
Colorado: 0.4%
Houston: 0.0%
Iowa St: 39.3%
Kansas: 0.0%
Kansas St: 25.9%
Oklahoma St: 0.0%
TCU: 0.4%
Texas Tech: 8.2%
UCF: 0.1%
Utah: 3.5%
West Virginia: 3.8%

BYU Regular Season Record when Made CCG:
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9-3: 3.0%
10-2: 43.9%
11-1: 43.2%
12-0: 9.9%
mean: 10.60-1.40

BYU Probability of Making CCG Given Record:
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9-3: 4.4%
10-2: 56.2%
11-1: 96.4%
12-0: 100.0%