Cruise Brothers

So it is that on New Year's Eve the two boys and their 21-year-old sister, Julie (a day student at nearby Cal State-Fullerton, where Jeremy played for the 1995 national champions), drove to Las Vegas to usher in the new millennium. "Our parents would have gone, too," says Jason, "except that our dad had to stay close to home for the Y2K thing." Their father, John, is the president of a small chain of banks.

You may have a pretty clear idea of the social opportunities awaiting major league players. Now picture the two boys going to Disneyland with the rest of the Giambi family over Christmas. Or imagine them sitting around the dinner table and one of them getting an idea to go to a movie, and the whole bunch trooping off to see Any Given Sunday.

This normalcy is impossible to explain. It's true that John, a Mickey Mantle fan and former junior college ballplayer, placed terry-cloth bats and balls in the boys' cribs soon after they were born, but neither he nor Jeanne was a Little League monster. They were supportive, in that exaggerated suburban way in which parents chauffeur the kids to about 20 activities each week. Kids who jump off roofs and run through sewers can be inclined toward more organized sports as well. At South Hills High in West Covina, both boys played football and basketball in addition to baseball.

It was a typical Southern California upbringing, with the bonus that dad liked to throw BP. Even so, there was never a sense that the kids were being groomed to be pro athletes. Jason, however, had an inkling of his destiny. Throughout grade school, while taking career-day surveys, he would raise his hand and ask his teachers where the box was for baseball player. A lot of kids probably wondered that, but not many of them would grow up to be 6'3" and 235 pounds. "A good thing I made it," he says. "I didn't consider a fallback position."

Jason was the pioneer, going where nobody in his family had gone before, hitting .397 during his career at Long Beach State and then advancing through the A's system slowly but surely. He wasn't a power hitter until he got into pro baseball. But once he started wielding a wooden bat, he noticed that those checked swings that had resulted in opposite-field singles at Long Beach and on the 1992 U.S. Olympic team were producing dribblers and leaving him with splinters in his hands. "So I started pulling the ball," he says—all the way over the fence.

Jason has a knack for acquiring mentors. Oddly, among the strongest influences on him was Michael Jordan, whom he met at the Olympics and with whom he renewed acquaintances when the two were in the Double A Southern League, Jason with the Huntsville Stars and Jordan with the Birmingham Barons. "I remember standing on third, and here comes Michael sliding into me," Jason says. "He says out of the blue, 'Hey, G.' " They became frequent dining partners, and their relationship intensified when each played in the 1994 Arizona Fall League.

While Jordan taught Jason a lot about handling fame, Mark McGwire, a star on the A's when Jason arrived in Oakland in 1995, taught him to sit on a pitch. "He took me under his wing," Jason says. "That really flattened the learning curve." Jason's at the point now, says Tampa Bay Devil Rays manager Larry Rothschild, where "he doesn't get cheated in his at bats. He's going to find a way to beat you, and it doesn't matter what pitcher he hits against."

This is the gospel, book of Mark. "He's a freak of nature, no question," says Jason of McGwire, "but he's also the toughest guy I know. He taught me a lot about baseball, when to let it loose, for example. My confidence has grown to the point where I want to be that guy, the one at the plate when it counts. Mark helped with that."

But if he and McGwire were best buddies when they were together in Oakland—and remain very close—it was despite some noticeable differences in taste. Jason has gravitated toward an outlaw look, with longish hair and, on his left arm, a bizarre tattoo (the face of a skull with a sun around it, and a tribal band around the biceps). He has become such an avid professional wrestling fan that clubhouse boys have to tape the extravaganzas for him, and he has cultivated some wrestlers as friends. "I've gotten to know Goldberg," he says, in the manner of somebody who feels a bit defensive about such flamboyant name-dropping. "Good guy."

Jason has also acquired a pair of custom-built motorcycles (neither of which he is permitted to ride, by contract, but both of which he rides) of such fearsome design that to see one in your rearview mirror would cause you to immediately pull onto the shoulder and allow certain death to pass you by. "Here, look at this one," he says, pointing to the fuel tank, which depicts the skeletal form of himself swinging the bat. "Oh, I'm a bad boy." Really? "I've got some issues."