Duke’s Shane Battier, acknowledged as the nation’s No. 1 defensive player, decided to go on a scoring spree on Tuesday night. And when he decided to score, he didn’t mess around. The junior forward piled up a career-high 31 points as 10th-ranked Duke won its eighth straight game by destroying Davidson 109-65.

It may have been the most efficient 31-point night in basketball history. Playing only 24 minutes, Battier shot 8-for-9 from the field, 12-for-12 from the line and sank three 3-pointers. He was so hot that he twice scooped up loose balls and fired 3s through the hoop. Perhaps the only surprise was that he actually missed a shot — a 3-point try that took an unfriendly roll.

Battier scored 20 points in the game’s first eight minutes, pushing the Blue Devils to a secure 40-23 lead against the 3-4 visitors from the Southern Conference.

Battier had a similar night last season against Maryland when Terps coach Gary Williams decided to surround now-departed Blue Devil stars Elton Brand and Trajan Langdon and let Battier roam free. Battier responded with 27 points, proving he could indeed shoot the ball when he’s in the mood.

Still, Tuesday’s outburst was as unexpected as Carl Torbush’s revival, especially after Battier let fly just once in the first half of a lackluster effort against North Carolina A&T on Sunday.

“I wasn’t aggressive in that game,” said Battier, who boosted his scoring average to 16.2 ppg. “My teammates got on me and the coaches were on me. They said for us to become a great team, I have to assert myself.”

“It was a point of emphasis tonight,” said Duke coachMike Krzyzewski. “Shane wasn’t hunting his shot. He was sitting in the high post or the low post and he wasn’t moving around. He was making himself very easy to defend.”

But there was no defense against Battier last night. He scored 16 of Duke’s first 26 points and never cooled.

Battier had plenty of help as Duke shot 61.4 percent from the field for the game and 68 percent in the second half. Freshman center Carlos Boozer didn’t score in the first 16 minutes but finished with 21 points. He poured in 11 straight Blue Devil points early in the second half.

Freshman guard Jason Williams looked like he still had his mind on exams. He missed two layups and was jerked once by Krzyzewski after back-to-back awful decisions on fastbreaks. Still, Williams is so talented that he produced 20 points in 27 minutes on a bad night. Chris Carrawell added 13 points and grabbed eight rebounds. The senior dished out seven assists, while making only one turnover.

With veteran Nate James ailing with tendinitis in his knees, Duke started three freshmen and often played four. Still, it looked like a different team than the one that snoozed along two days earlier.

“We played more together, played harder and played more intelligently,” said Krzyzewski.

Duke played so well that it led 58-37 at halftime and reached 100 points with over six minutes remaining.

After doing a pretty fair impression of Scrooge on Sunday, Coach K was back in good spirits after the 550th win of his career.

“That many wins just means I’m getting old,” he said. “It means I’ve had some good players and some good teams.”

Davidson coach Bob McKillop is pretty sure that this Duke team, despite its overwhelming youth, can become one of Krzyzewski’s better ones.

“They controlled everything,” said McKillop. “They force you to dribble when they tell you and pass when they tell you. You shoot when they want you to shoot. Their ability to control you is what sets Mike’s teams apart from every other team in the country.”

McKillop appeared irate with the officiating (Duke had two fouls in the first 11 minutes of the second half) during the game, but was calm afterward.

“Duke anticipates well and is quick,” he said. “We do not anticipate well and we are not quick. We were a step slow

Battier, on the other hand, stepped forward.

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