I don't know how real odds makers do the calculations, but here's what I did:

1. Looked at Sagarin ratings for each team (e.g. App State = 65.77, Lafayette = 47.49).
2. Added 2.56 to the home team's rating, as per Sagarin
3. Calculated the difference in ratings
4. Calculated the odds of each team winning each game (no difference in ratings = 50%, each 1 point of difference = 2-3% additional chance of winning, e.g. a 7 point difference is about a 64% chance)
5. Calculated the likelihood of each potential second round matchup and made assumptions as to who would host (e.g. Montana @ Texas State, SIU @ App State, etc.)
6. Repeated steps 2-5 for rounds 2, 3, 4

From this, I estimated the likelihood of winning the whole thing as (percentages and odds are rounded, so they may look a bit wacky):

App State - 24.8% (4 to 1)
UNH - 14.2% (7 to 1)
Texas State - 10.0% (10 to 1)
Montana - 7.0% (14 to 1)
EWU - 6.2% (16 to 1)
SIU - 6.0% (17 to 1)
Nicholls State - 5.5% (18 to 1)
Cal Poly - 5.0% (20 to 1)
UNI - 4.5% (22 to 1)
Furman - 4.4% (23 to 1)
Hampton - 3.9% (25 to 1)
Ga. Southern - 3.8% (26 to 1)
Richmond - 3.6% (28 to 1)
EIU - 1.1% (95 to 1)
Lafayette 0.1% (981 to 1)
Colgate 0.1% (1,028 to 1)

Odds of reaching finals:
App State 44.9% (2 to 1)
UNH 27.3% (4 to 1)
Texas State 18.6% (5 to 1)
Montana 13.7% (7 to 1)
SIU 12.3% (8 to 1)
EWU 12.2% (8 to 1)
Nicholls State 11.3% (9 to 1)
Cal Poly 10.0% (10 to 1)
Furman 10.0% (10 to 1)
No. Iowa 9.9% (10 to 1)
Hampton 9.6% (10 to 1)
Richmond 8.0% (12 to 1)
Ga. Southern 7.9% (13 to 1)
EIU 3.4% (29 to 1)
Lafayette 0.5% (194 to 1)
Colgate 0.4% (238 to 1)