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Obviously in order to reach the Final Four, let alone a national championship, every team has to beat some top-shelf opponents, but relative to their strengths, Kansas actually has a pretty manageable draw to look forward to.
As a two seed, Kansas will face Horizon League champion Detroit. Detroit (22-13) had an impressive win over a favored Valparaiso ball club, but are no match for a major college program like the Kansas Jayhawks. Guard Ray McCallum has had an excellent year, but the improved defense of Tyshawn Taylor means he'll likely have a rough night and the Detroit Titans simply don't have the talent to hang with Kansas for long.
From there they would face the winner of St. Mary's (27-5) and Purdue (21-12). Both teams had very respectable years, and St. Mary's ranks 14th in the nation in assists with 15.9 per game. Point guard Matthew Dellavedova is an excellent shooter and St. Mary's could be a challenge, but certainly a task Kansas will be up to.
Purdue's team had a solid season, considering the loss of seniors JaJuan Johnson and E'Twaun Moore to the NBA, but senior forward Robbie Hummel's 16 points and seven rebounds per game has helped the Boilermakers back to the NCAA tournament. Still, the combination of Robinson and Withey should bother Hummel, making a tilt with Purdue an easy win.
The Jayhawks would likely take on Georgetown (23-8) in the Sweet 16, a team they handled earlier in the season at the Maui Invitational. Georgetown has the talent and size with players like Henry Sims, Jason Clarke and Otto Porter to bother Kansas, but if Kansas' frontcourt can handle Sims the Jayhawks have a great chance to pull out that game. As the team's leader in assists at 3.5, a huge portion of the Hoyas' offense is Sims, and if he can be taken out of the game, their team is much worse.
Barring an upset at the hands of Temple (24-7) or a resurgent Michigan (24-9) team, the North Carolina Tar Heels (29-5) would face Kansas in a phenomenal Elite Eight matchup. This is a game in particular where I think the maturity of Kansas would significantly help them. UNC may have more talent, but if Elijah Johnson and Travis Releford can bother Harrison Barnes, Kansas' overall poise and versatility could lead them to a tremendous win.
A lot could happen in the East Region before Kansas meets any of those teams, but they would likely play either Florida State (24-9), Ohio State (27-7) or Syracuse (31-2), the region's top three seeds. Florida State has an elite defense, but if Kansas can run them off the three-point line, they are certainly a beatable team.
Syracuse's lack of size means Withey and Robinson could have a field day on the glass and hammer them relentlessly on the inside, and after beating Ohio State once, Kansas could strive to take Sullinger out of the game and make the Buckeyes win it from the perimeter.
I actually think the Orange are an ideal match for Kansas despite their stellar season because of their lack of size and paint presence.
Now, if they can accomplish this they would face a stiff test likely with a Kentucky team they lost to earlier in the season, or possibly Michigan State, Missouri or Duke. There's no way to predict how these games would go, but I think anything to avoid Kentucky would be ideal for the Jayhawks.
Ultimately, Kansas can't be too upset with their bracket in this year's tournament as it gives them a great chance to win it all this season.