Although the Frank Erwin Center isn't a place Kansas has had much success, there (statistically, at least) isn't much reason to believe that Kansas will be upset on Saturday.
According to KenPom, Kansas has a 69% chance of winning the game tomorrow, and here's why:
For starters, the Longhorn defense has been abysmal lately. They're 38th in adjusted defense this season, but in Big 12 play they are allowing 1.03 points per possession, which is sixth in the league. But before you get too confident, a lot of that is due to the Longhorns allowing teams to shoot 42% from three. Kansas has gotten better from beyond the arc in Big 12 play, but they're still at just 35.5% for the season.
Texas's two point defense is a semi-different, and very interesting, story. For the season as a whole they rank 11th, allowing teams to shoot just 41.3% from two, but in Big 12 play they are allowing teams to shoot over 49%, which is 7th in just the conference. THe Horns haven't played the world's greatest offenses in Big 12 play (other than Missouri), so it could be that they boosted their numbers based on a poor non-conference schedule, or that the defensive swoon they went through at the end of last year is starting early this season.
offense (values are for conference play only)
The Longhorns leading scorer is J'Covan Brown, who is also leading the conference in scoring at 19.222 points per game. He's also second in the league (to Thomas Robinson, of course) in points per 40 at 22.9. He's doing it reasonably efficiently as well, shooting 47.5% from two and 38% from three. He's also drawing almost 5 fouls per 40, which is an ability shared by multiple Longhorns, chief of whom is Freshman guard Myck Kabongo.
Kabongo is part of the Canada to Texas pipeline (I would think that someone from outside the US would want to play college basketball in a state that doesn't hate immigrants, but what do I know) and although there has been a bit of an adjustment period, he has proven to be a valuable commodity in Austin. He's not a great shooter yet, with an eFG of just 47% (he also shoots just 30% from three, but unlike Elijah Johnson has quit taking so many and has learned how to contribute in other ways), but Kabongo has an impressive 36.8% assist rate and draws 6.4 fouls per 40 minutes. His FT rate of 91.5 is tops in the country as well, and could be a major problem for Kansas if Robinson or Withey gets in foul trouble early.
Other than Kabongo and Brown though, I don't think much can hurt Kansas. Texas shoots just 33.6% from three on the year, and are at just 44% from two in Big 12 play. Stranger things have happened than a team making a few more threes than they "should" in a home game in one of the biggest games on their slate, but I would be surprised if they made enough to matter.
Texas will probably be in desperation mode, as they need a big win for their NCAA tournament profile (yes, it's that time of year already) but I don't think it will be enough. KenPom has Kansas winning by five, and while Kansas seemingly has a history in gagging the game after a big win I think they double that margin of victory fairly easily.
Your discussion question of the day is this: with Missouri leaving the Big 12, who is our new rival? The obvious answer is seemingly Kansas State, but I'm picking Texas, who is the last team to win in Allen Fieldhouse and has been the opponent in some great games recently. They've also been consistently the second best team in the league, so it makes sense that they'd be our main rival.