The Kansas student section gets wild before tipoff against Oklahoma State on Tuesday, Jan. 30, 2024 at Allen Fieldhouse. Photo by Nick Krug

The level of consistent success that Kansas men’s basketball has experienced in its 20-plus years led by Bill Self yields a lot of bafflingly lopsided win-loss statistics.

Right up there among the most perplexing of all is this: During Self’s tenure, KU is 13-0 when it faces a higher-ranked, top-five opponent at Allen Fieldhouse.

That streak began with a victory over then-No. 3 Michigan State in Self’s second game on Nov. 25, 2003, and continued all the way through this past December, when KU beat then-No. 4 UConn 69-65 thanks to a clutch string of late-game 3-pointers by Kevin McCullar Jr. (As it happens, UConn is now the No. 1 team in the country.)

The Jayhawks have a chance to beat another No. 4 and defend the Phog on Saturday when Houston comes to town.

“The thing about UConn is, it was the first of December,” Self said Thursday. “And that feels like a season ago. This is getting into the dog days.”

And it’s not certain yet if they’ll have McCullar, who is dealing with a bone bruise — Self said Thursday, “I’m anticipating him being able to go, but I don’t know to (what) extent, or how much it’ll bother him, or anything like that.”

The game will have significant implications for the muddled Big 12 Conference race as it approaches its halfway point. Houston is currently in sole possession of first place with a half-game lead over Iowa State and Texas Tech and a one-game lead over KU and TCU.

It will also represent a clash between the Big 12’s old guard and its hotshot newcomer — two of the best teams in college basketball overall over the last several years. The Cougars, fresh out of the American Athletic Conference, haven’t been perfect by any means this season, as they lost back-to-back road games at Iowa State and TCU early in Big 12 play. But they have weathered the storm to put together a five-game winning streak and most recently won in overtime at Texas on Monday.

They field a stunningly stingy defense that allows the fewest points per game, at 52.9, of anyone in the country by a wide margin. KU handled the No. 6 scoring defense, Iowa State, fairly well last Saturday (albeit in a loss) but will face another increase in degree of difficulty against the Cougars.

“They’re connected,” Self said. “They fly around. They load up, they’re a very good ball-screen defensive team, and they trap a lot, they pressure out of it and they pressure and steal.”

Three players average at least a block per game (Ja’Vier Francis, Joseph Tugler and J’Wan Roberts) and standout point guard Jamal Shead makes 2.2 steals on average.

Their offensive is sharp as well and makes every possession count. The Cougars are No. 7 in the country in offensive rebounds per game at 14.86, even though no individual player grabs more than 2.75, and commit the eighth-fewest turnovers per game (9.1) in the nation.

Scoring-wise, UH relies on the shooting of Baylor transfer LJ Cryer, the main addition to a core composed primarily of players who were on last year’s No. 1-seeded squad. Cryer is averaging 15.1 points per game and is 62-for-164 (37.8%) from deep on the year.

Shead and Emanuel Sharp are also double-digit scorers and Shead contributes 5.8 assists along the way.

Between Shead and Cryer, Self said, “It would be hard to say, as far as two-way players, if there’s a better set of guards in America.” Center Hunter Dickinson made sure to shout out Sharp as well, who he said doesn’t get talked about enough.

“I think those three guards are really dynamic and they do a really good job being able to create for themselves and others,” he said.

This is the first of two KU-UH games that could serve as inflection points in the Jayhawks’ season. “You’d have to really pull a rabbit out of your hat” to win the conference if you don’t win Saturday’s game, Self said.

On the other hand: “If we are successful against them, you know, having beat Houston, Tennessee, Kentucky and UConn, I don’t know if there’s a school out there that would have four better wins than that,” Dickinson said.

The teams play again in a return matchup in Houston on March 9, the final game of Big 12 play.

No. 8 Kansas Jayhawks (17-4, 5-3 Big 12) vs. No. 4 Houston Cougars (19-2, 6-2 Big 12)

• Allen Fieldhouse, Lawrence, 3 p.m.

• Broadcast: ESPN

• Radio: Jayhawk Radio Network (in Lawrence, KLWN AM 1320 / K269GB FM 101.7 / KKSW FM 105.9)

Keep an eye out

Heavy rotation: In the last top-10 matchup, against UConn, Self really only rotated six players, as his remaining three scholarship options combined to play four minutes and 31 seconds. Will Saturday look similar (except with Elmarko Jackson and Johnny Furphy’s roles reversed from that December clash), or will he open things up somewhat? The KU bench played encouragingly well against Oklahoma State, but on the other hand the fact that they played more minutes also means the starters are better rested and could be equipped to go the distance against UH.

Possible momentum: In either circumstance, Jackson will need to deliver for the second game in a row. He has not played especially well in consecutive games this season and in fact his three double-digit scoring performances have been at least three weeks apart. He’ll need to demonstrate the same confidence and poise he did against OSU Tuesday when facing a substantially tighter defense Saturday. Dickinson said that for Jackson it’s about “just continuing to stay confident in his talent and in what he does. I think obviously making shots definitely helps that and definitely will improve any confidence for sure.”

By the wayside: Around the same time Jackson’s offensive improvement was last a key talking point, so was KJ Adams’ defensive rebounding. Beginning Dec. 30 against Wichita State, Adams had double-digit rebounds in three of four games after never having done so previously in any game in his career. That was driven primarily by his improvement on the defensive glass. Since that stretch, Adams has pulled down just 18 rebounds total in the last five games. He continues to excel more generally, though, and Houston coach Kelvin Sampson called him “the most underrated player in America” on Thursday. He shot 100% on Tuesday, after all. But the rebounding facet of his game in particular will need to improve against a team that is so threatening on the offensive glass.

“He hasn’t gone after the ball the same way he did those particular games, but he will soon, he will moving forward,” Self said. “We’re asking him to do a lot, play a lot of minutes and all that stuff, but that’s the one area I think that he can help our team win more than any area for him, is to improve in that area, and certainly he’s going to need to be big in that area Saturday.”

Off-kilter observation

Houston assistant coach K.C. Beard spent his lone season as a video intern for the Utah Jazz the same year that former KU star Brandon Rush played one year for the team.