College basketball has been so chaotic, it made us wonder: Are No. 1 seeds going to be as vulnerable in the NCAA tournament as No. 1 teams were in the regular season?

Because of conference tournament upsets, the worst auto-bid teams are very weak this year. So we are about 97 percent certain the time has not yet arrived for a 16-seed to take down a 1. (You can find our analysis of first-round matchup here). But when we trained our statistical model to peer deeper into brackets, we found numerous hazards for top seeds -- including a few Giant vs. Killer matchups, where an underdog’s style of play could give a Goliath extra headaches.

And we can sum up the results of all the math involved with one word: Duck!

We studied the Path of Maximum Danger (PMD) for each No. 1 seed, asking which potential opponent would give the top team the most trouble each step along the way to the Final Four and then calculating its cumulative odds of survival. For example, our model estimates Kansas has a 99.2 percent chance of beating No. 16 Austin Peay in the first round, and then that the Jayhawks would face the gravest threats from No. 9 Connecticut (17.1 percent chance of an upset, in a GK matchup), No. 5 Maryland (28.9 percent upset chance) and No. 2 Villanova (42 percent) in subsequent rounds. That gives Kansas a 33.9 percent chance of reaching the Final Four even if everything lines up against Bill Self & Co., by far the best odds in the South Region.

North Carolina, with a PMD of No. 16 Florida-Gulf Coast-No. 9 Providence-No.4 Kentucky-No.3 West Virginia, leads the East, with a 27 percent chance of survival. WVU (15.3 percent) ranks second, despite an extremely dangerous first-round matchup against Stephen F. Austin.

In the Midwest, it’s 2-seed Michigan State (32.2 percent) that has the best odds of making it to the Final Four against its strongest foes, not 1-seed Virginia (21.5 percent). Our model likes the Spartans as a second-round Giant against Syracuse (or Dayton) more than the Cavaliers against Butler (or Texas Tech). And it simply sees Michigan State as a better team, favoring the Spartans against Virginia in a potential regional final.

But that’s downright chalky compared with the West Region. We give top-seeded Oregon a 98.1 percent chance to defeat Holy Cross, but odds of just 47.5 percent to get by 9-seed Cincinnati in the second round. If you have been following our coverage of “Wounded Lions,” you know why: The Bearcats grind opponents like glass by slowing the tempo and forcing steals, while they amass possessions by grabbing 36.8 percent of their own missed shots (ranking 20th in the NCAA). If Cincinnati knocks off Saint Joseph’s -- no lock, to be sure -- the Bearcats are perfectly suited to exploit Oregon’s weakness on the defensive boards in a classic matchup of Slow Killer vs. Generic Giant.

And from there, things would only get worse for Oregon. Our model’s basic power ratings see the Ducks as inferior to 4-seed Duke and to 2-seed Oklahoma. Overall, their PMD gives Oregon just a 7.8 percent chance to vanquish their strongest opponents and reach the Final Four. That’s far behind Oklahoma (25 percent) in the West, and lags behind Duke (16.6 percent) and Texas A&M (11.6 percent), too. Even Baylor, the region’s 5-seed, with a PMD that would require the Bears to slay Duke, Oregon and Oklahoma, isn’t far behind the Ducks (6 percent).

Since 1985 (when the tournament expanded to 64 teams), 51 of 124 of Final Four teams have been 1-seeds, for an average of 1.65 per season. With this season’s parity and bizarre seedings, one top seed, rather than two or three, will probably land in the Final Four. We can’t predict exactly who will make it, but it’s pretty clear who won’t.

Thanks to Liz Bouzarth, John Harris and Kevin Hutson of Furman University for research assistance.