The NCAA Tournament is off to a good start for the Virginia Cavaliers for two big reasons. The first one is obvious: Virginia didn't get upset by 16th-seeded Hampton, then beat Butler to advance to the Sweet 16.
But, also importantly, UVA's odds of making a Final Four and winning it all in Houston have increased because of the carnage in the Midwest region, where #10 Syracuse and #11 Gonzaga will play for a berth in the Elite Eight. (Purdue, who computers rank as marginally better than Iowa State, falling in the first round helps UVA's probability as well.)
While the team is focused only on their matchup with a really good Iowa State team, we fans who aren't actually playing or participating in the on-court action could look at things more broadly and probabilistically. Here's what a few computer projections say about UVA's chances.
BPI, where UVA is ranked #2 in the nation behind UNC, is bullish on Virginia. Their model gives UVA a 67% chance of beating Iowa State, then a 79% chance of winning its Elite Eight matchup, for an overall 53% chance of making the Final Four, best of any team remaining.
The team's 21% chance of a National Title are also the highest remaining - UVA's odds almost doubled last weekend.
Sweet 16 matchups are now set in the South, East and Midwest regions— ESPN Stats & Info (@ESPNStatsInfo) March 21, 2016
The latest BPI projections: pic.twitter.com/PVkQ2TVohU
FiveThirtyEight's model isn't quite as high on Virginia's chances.
It has Iowa State as a slightly tougher matchup, giving UVA a 65% chance of a win, then a similar 66% chance of winning its next game against Cuse or Gonzaga, which is much smaller than BPI's projections, for a 43% chance at a Final Four berth. Once there, UVA has a 13% chance of winning it all. Kansas's 21% probability leads the way, followed by UNC at 19%.
KenPom hasn't updated his log5 projections from before the tournament. Those had UVA as the second-most likely champion (13.2% odds of a title), and gave UVA a 34% chance at a Final Four. If he re-ran his projection, we could assume that those Final Four odds have increased somewhat, to what I would estimate as about 50% (71% chance of UVA beating Iowa State, then about a 75% chance of winning the team's next round matchup).
Per Bovada, UVA has the third best odds to win the National Championship at 23/4 (behind Kansas's 7/2 and UNC's 17/4). That implies a 15% probability. UVA also 10/11 odds to win the Midwest region, which translates to about 52%. Discounting by about 7% for the vig, we'd have odds more like 48% to advance to the Final Four and 13% to win the title.
To summarize, overall, the Hoos have a two-thirds chance of beating ISU Friday, and a 50-50 shot at making the Final Four. UVA's chances of winning it all are somewhere in the ballpark of 15%.