Freshman forward Brook Lopez’s recent play has excited the kind of speculation that ends in wild projections about guaranteed NBA millions and future celebrity. In Lopez’s case, those predictions might not be too far off. Conventional wisdom holds that he will end up as a lottery pick in the draft, whenever he decides to enter it.

But Lopez — who has scored over 20 points in each of the Cardinal’s last four games, revealing a glimpse of his tantalizing potential — had other things on his mind when he strolled into Monday’s press conference, wearing a Spider Man T-shirt, and slumped his 7-foot frame into a folding chair.

“I’m a little tired,” he said. “I’ve been up all night writing a paper.”

First-round bonus baby or no, Lopez is still a freshman, a fact that his coach has stressed all season. And though he often shows off his jumping ability on the court (just ask Southern California, against whom he recorded 12 blocks in one game earlier this season), he is doing all he can to keep his feet on the ground otherwise.

“What I really like about Brook is that he trusts in his teammates, in the school, in the people around him,” head coach Trent Johnson said. “He scores 20 points a few games in a row and suddenly everyone and their mother is coming to the games. What you lose sight of is that he’s only 18. The real questions to me are — Is he having fun? How’s he doing socially? Those are the important things.”

But Johnson and the rest of the team have also come to rely heavily on Lopez’s presence in the starting lineup. Abstract expectations are one thing, but he has increasingly been asked to shoulder more of the burden on both the offensive and defensive ends of the floor.

In his last 10 games, beginning with the block party against USC, Lopez has averaged 17.5 points and 7.3 rebounds. At the beginning of the season, Johnson said that it would be unreasonable to expect Lopez to average 15 points and 10 rebounds, but the coach’s star freshman has come pretty close of late.

“He’s taking better shots each game,” Johnson said. “His talent leads him to take a few bad ones every so often. Sometimes he shoots a fade-away or a three-pointer, as opposed to playing big.”

Lopez’s offensive surge has been, in large part, a product of necessity. He has averaged 23 points in the four games since sophomore Anthony Goods, the Cardinal’s second-leading scorer, went down with an ankle sprain at Washington. And while Lopez has failed to compensate for Goods’ three-point shooting — he’s made one of eight over that span — he has kept Stanford’s offense afloat.

“That’s probably it; I’ve gotten more shots with Anthony out,” said Lopez, trying to explain his recent scoring. “But I’ve also been more confident in practice and in full-court training with the team. It’s repetitive, but it really helps me just to go through the post moves in practice.”

Lopez is peaking at the right time on offense. He credits an early-season back injury, which caused him to miss the season’s first five games, for keeping him fresh down the stretch run. His brother, Robin, meanwhile, has faded on offense since Brook’s surge and has not scored in double-digits in any of the last 10 games.

Though his offensive game has blossomed, Brook has expressed a good deal of self-criticism over his performance on the defensive end over the last three weeks, with Stanford losses to Washington and the Los Angeles schools. He senses, like many NBA scouts must, that he still has plenty of room for improvement.

“I think our defensive intensity has been lacking,” Lopez said. “I didn’t feel like we wanted to go after guys; something was missing. That carried into rebounding, especially mine. We weren’t looking to get on the floor, get to the lost ball. We were just watching it and expecting someone else to get it.”

Lopez attributed it to mental focus rather than physical shape; but his coach said that, if anything, Brook was trying too hard.

“It’s funny that he said he felt like he wasn’t playing hard enough [on defense against UCLA] because he’s usually very smooth,” Johnson said. “The game comes naturally to him. And after watching the tape, I thought he was exerting a lot of energy.”

Despite Lopez’s self-criticism, Johnson said that he has been impressed by his freshman forward’s ability to keep his head up during games. That is a challenge for any young player, especially on a team that relies as heavily as Stanford does on freshmen and sophomores.

“I think he’s doing a lot better with the double-team,” said Johnson. “He’s keeping his composure.”

“Earlier in the year, he would get down on himself and tell me, ‘I look like you,’” Johnson continued, pausing to demonstrate a hang-dog expression, curling his mouth into an angry frown. “That’s an ugly sight. It means that there’s a lot of anger and frustration there. I told him I don’t want him to look like me.”

Johnson hopes he doesn’t see that expression this weekend in games against Arizona State and Arizona — games which could determine whether the Cardinal receives a bid to the NCAA tournament. He does, however, hope to see Lopez in a Stanford jersey for at least another year or two, before the pull of the NBA drags Lopez into its current. Johnson said that players leaving the Farm early has contributed to a decline in the Stanford basketball tradition over the past few years.

Lopez is playing the cards close to his vest when it comes to the draft, maintaining that he will make that decision with input from his family and coach when the time comes. For now, though, he’s enjoying his freshman year. And, of course, preparing for tonight’s game against Arizona State.

“I was watching their game against Arizona with one of my friends on the hall, who’s a big Arizona fan,” Lopez said, referring to ASU’s 61-58 loss last weekend. “I told him, ‘Watch out for ASU, they’re dangerous.’ Sure enough, they made a big comeback in the second half.”

“I wouldn’t say that I’m worried,” Lopez said, “but I’m cautious.”

Which is probably the way Johnson feels about the chances that his talented freshman will stick around long enough to rebuild the Stanford tradition.