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My basic stats model shows our chances are ~ 40%. by Irishbuzz

I found this result surprising. I figured ND would have a much lower chance, but essentially we need 3 of 5 groups of teams ahead of us to lose:
- Bama (25% win out)
- Oregon (50% win out)
- Big10 (tOSU, MSU, Mich) (65% 1 team wins out)
- Big12 (OU, OkSt) (38% 1 team wins out)
- Cinci (38% win out)

Result Probabilities:
63% At least 3 groups lose
40% At least 3 groups lose and ND wins out
15% Cinci wins out and at least 3 other groups lose (both Cinci and ND make playoffs)

Assumptions:
I assumed probabilities for each team to win their remaining games. You may debate these, but small moves (10% adjustments) don't have much effect on the overall results.
Georgia is in the playoff even with a loss to Alabama and would not lose prior to the SEC championship game.
ND would not be ranked ahead of any grouping above that wins out.
ND would be ranked higher than any 2 loss team including Bama.
ND would be ranked higher than Cincinnati if they lost a game.

Personally, I don't think it's fair for ND to make the playoffs over Cincinnati if they lost one of their remaining games. Head to head winner with same number of losses deserves higher ranking.

Feel free to look at the spreadsheet plug in your own numbers.