Nate Silver, fresh off his 50 for 50 performance in forecasting the 2012 presidential election, is in his third year of publishing NCAA tournament probabilities. Likewise, we're in our third year of using those to calculate the probabilities of interesting results starting with the Sweet 16.
47.8% probability of a #1 seed winning the championship
19 champs have been #1 seeds - most since seeding began in 1979
6.7% probability of three #1 seeds in the Final Four
Three or more #1 seeds have made it four times since seeding began
14.5% probability of no #1 seeds in the Final Four
A #1-free Final Four has happened three times since seeding began (last in 2011)
19.9% probability of a Louisville vs. Florida final
The most likely championship game pairing
15.2% probability of #2 seed winning the championship
Six champs have been #2 seeds - second most since seeding began
25.3% probability of #3 seed winning the championship
The 2011 champion (UConn) was a #3 seed. Florida (21.3%) accounts for most of this chance.
6.8% probability of a #12 seed or lower in the Final Four
The lowest team to make a Final Four is an #11 seed (George Mason 2006, VCU 2011).
3.6% probability of a first time national champion
Miami, Wichita State, and Florida Gulf Coast are the only schools left wihtout a championship. The other 13 schools have a combined 25 championships.
7.1% probability of all-B1G Final Four championship game matchup (Corrected)
One Big Ten team has won the national championship in the last 23 seasons (2000 Michigan State)
3.6% probability of both remaining ACC teams making the Final Four
More likely, there is an 65.7% chance neither will
0.4% probability of all-B1G Final Four
The 1985 Final Four saw three teams from the Big East.
5.7% probability of a rematch of the 2007 Florida/Ohio State championship game
100% probability of a Sweet 16 rematch of the 1987 Indiana/Syracuse championship game (just making sure you're paying attention)