ANAHEIM, Calif. - The question was hypothetical and scary, like the boogeyman.

Had Derrick Williams not played the best first half of his life Thursday against Duke - he scored 25 points and was on pace to break Ernie McCray's single-game UA scoring record of 46 - what would the halftime score have been?

"We'd probably be blown out," guard Jordin Mayes said. "For real. It's crazy what he did."

The Wildcats trailed by six points despite Williams' five first-half three-pointers. Without him?

"I don't know if we'd be even close," forward Kevin Parrom said. "He put us on his shoulders in the first half."

Brendon Lavender took a guess at the points - "15, about," he said - while Solomon Hill joked snidely that the Wildcats still would have won but by only one.

And guard MoMo Jones, never one for short sentences, finally said one.

"A lot, to a little," he said.

Williams scored the game's first basket. And then Arizona's second field goal, a three-pointer.

He made the fifth UA field goal, too, another trey, before a two-pointer.

The Wildcats trailed 14-13 and Williams had 10 points.

"With Williams, he gives you confidence," Duke coach Mike Krzyzewski said. "You always know that you have that guy on the court. Even when he's not scoring, he spreads you out.

"There's a physicality to this game. Clean, beautiful - he's a beautiful player."

The game appeared out of hand when, with UA down 31-20, Williams made two foul shots.

Then two more.

Williams sank back-to-back threes to pull the UA within four, 37-33, with 3:21 to go in the half.

"As we deal with more people that aren't familiar with us as a team, you know, if you look at the statistics, it's clearly pointed out that we have one difference-maker on our team," UA coach Sean Miller said. "Tonight, Derrick was hands-down the best player on the court.

"You always have a chance when you have a player that does what he does."

That was personified by the last shot he took in the first half.

With the Cats trailing by nine, Williams, who finished with a career-best 32, tossed up a three-pointer from the left wing over 6-foot-11-inch Duke forward Ryan Kelly. It went in as the buzzer rang through Honda Center.

"I actually just shot it up and it happened to go in," said Williams, who added 13 rebounds. "I wasn't expecting it to go in; that's probably how my reaction was.

"I knew we were down six points, so I'm not going to celebrate after a shot like that."

In the locker room, however, the Cats had reason to be confident.

While everyone not wearing No. 23 was 5 for 16 from the field, Williams was 8 for 11.

"Derrick's individual play allowed us to have a chance," Miller said. "We could have had a huge deficit at halftime, but he gave us a chance."

Williams had five three-pointers, on six attempts, while the rest of the team made one trey in the first 20 minutes.

In the first half, the Wildcats played five "wars" - Miller's term for four-minute periods between media timeouts - and won none.

"The first half Derrick did a phenomenal job," Jones said. "He did what great players do, and he put his team on his back.

"Even though we were down six we came out in the second half and played Arizona basketball.

"Like I said before, and coach Miller said before, we had to play nasty. And we came out and played as nasty as we could."

The Wildcats went out and scored 55 points against the defending national champions.

Without Williams' first-half production, UA might have scored 55 in the second half and still lost.

"I just had that zone tonight," Williams said.

The Blue Devils even tried talking to Williams, the forward said.

"They wanted to start that," he said, "and that's to their disadvantage."

It made the question about Williams - and how the Wildcats would have been in trouble at halftime without him - hypothetical.

And moot.

"We won't know," forward Kyryl Natyazhko said. "The ball went in, and we won the game."