I pulled some miscellaneous data today about the odds in the Sweet 16 round and on some of the historical trends for each team. Here are the highlights:
South Region
Here are the odds for the eventual Regional Final matchup:

In the South, the odds are just over 50% to see an Auburn/MSU final. Tom Izzo is 10-5 in Sweet 16 games, with the only upset loss coming in 2012 when No. 1 MSU lost to Rick Pitino and No. 4 Louisville. No. 2 seeds are 26-11 (70%) all time vs. No. 6 seeds and 21-3 since 1993. Tom Izzo is also 3-0 all-time versus No. 6 seeds and 11-3 as a No. 2 seed.
Auburn is 2-3 all time in the Sweet 16, but in their only game as the favorite, No. 1 Auburn lost to No. 4 Ohio State in 1999. Michigan is 8-4 in the Sweet 16 including three upset wins over a No. 1 or No. 2 seed in 1992, 1989, and 2013.
Ole Miss has only one previous Sweet 16 appearance. In 2001, No. 3 Ole Miss lost to No. 2 Arizona by 10 points. Ole Miss only has two upset wins in Tournament history, both in the first round (in 1999 and 2013).
East Region

In the East, the odds are over 55% to a see a Duke/Bama regional final. Bama has been a No. 2 seed three times but never made it past the Sweet 16. Bama is 1-1 all-time versus No. 6 seed. Duke is 9-5 as a No. 1 seed in the Sweet 16, but 4 of the losses came against No. 5 seed.
This is BYU's third trip to the Sweet 16 in the modern era (since 1979). In 1981, No. 6 BYU beat No. 3 Notre Dame but lost to Virginia in the next round. Arizona is 2-0 all-time as a No. 4 or No. 5 seed in the S16 with wins over No. 1 Duke (2011) and No. 1 Kansas (1997).
Midwest Region

The odds in the Midwest are just over 50% that Houston and Tennessee will both advance. Houston's last 2 runs both ended with losses to a No. 4 and No. 5 seed in the Sweet 16. Tenn. is 2-7 all time in the Sweet 16, but the No. 2 Vols did get by No. 3 Crighton last year.
Purdue is 5-8 all time in the Sweet 16 and 0-8 all time against No. 1 seeds.UK is 19-6 all time in the Sweet 16, including a 4-2 record with three upset wins when seeded No. 3 or lower.
West Region

The odds in the West also favor the two highest seeds to advance. UF is 9-2 in the Sweet 16 and 10-1 as a No. 1 seed with the only loss in the 2014 Final Four to UConn. This is just the 6th Sweet 16 appearance for Texas Tech but TTU is 3-2 as a No. 3 seed vs. a No. 2 seed.
Maryland is just 2-9 all time in the Sweet 16 with no upset wins. The Terps are 2-5 all time against No. 1 seeds. Arkansas is 7-5 all time in the Sweet 16, but only one of those wins was as the underdog (in 2022 over Gonzaga).
South Region
Here are the odds for the eventual Regional Final matchup:

In the South, the odds are just over 50% to see an Auburn/MSU final. Tom Izzo is 10-5 in Sweet 16 games, with the only upset loss coming in 2012 when No. 1 MSU lost to Rick Pitino and No. 4 Louisville. No. 2 seeds are 26-11 (70%) all time vs. No. 6 seeds and 21-3 since 1993. Tom Izzo is also 3-0 all-time versus No. 6 seeds and 11-3 as a No. 2 seed.
Auburn is 2-3 all time in the Sweet 16, but in their only game as the favorite, No. 1 Auburn lost to No. 4 Ohio State in 1999. Michigan is 8-4 in the Sweet 16 including three upset wins over a No. 1 or No. 2 seed in 1992, 1989, and 2013.
Ole Miss has only one previous Sweet 16 appearance. In 2001, No. 3 Ole Miss lost to No. 2 Arizona by 10 points. Ole Miss only has two upset wins in Tournament history, both in the first round (in 1999 and 2013).
East Region

In the East, the odds are over 55% to a see a Duke/Bama regional final. Bama has been a No. 2 seed three times but never made it past the Sweet 16. Bama is 1-1 all-time versus No. 6 seed. Duke is 9-5 as a No. 1 seed in the Sweet 16, but 4 of the losses came against No. 5 seed.
This is BYU's third trip to the Sweet 16 in the modern era (since 1979). In 1981, No. 6 BYU beat No. 3 Notre Dame but lost to Virginia in the next round. Arizona is 2-0 all-time as a No. 4 or No. 5 seed in the S16 with wins over No. 1 Duke (2011) and No. 1 Kansas (1997).
Midwest Region

The odds in the Midwest are just over 50% that Houston and Tennessee will both advance. Houston's last 2 runs both ended with losses to a No. 4 and No. 5 seed in the Sweet 16. Tenn. is 2-7 all time in the Sweet 16, but the No. 2 Vols did get by No. 3 Crighton last year.
Purdue is 5-8 all time in the Sweet 16 and 0-8 all time against No. 1 seeds.UK is 19-6 all time in the Sweet 16, including a 4-2 record with three upset wins when seeded No. 3 or lower.
West Region

The odds in the West also favor the two highest seeds to advance. UF is 9-2 in the Sweet 16 and 10-1 as a No. 1 seed with the only loss in the 2014 Final Four to UConn. This is just the 6th Sweet 16 appearance for Texas Tech but TTU is 3-2 as a No. 3 seed vs. a No. 2 seed.
Maryland is just 2-9 all time in the Sweet 16 with no upset wins. The Terps are 2-5 all time against No. 1 seeds. Arkansas is 7-5 all time in the Sweet 16, but only one of those wins was as the underdog (in 2022 over Gonzaga).