Adam Dunn of the White Sox reacts after striking out during a spring training game against Los Angeles on March 20. Dunn, a notorious slow starter every year, leads all of baseball with 22 spring strikeouts. (Nam Y. Huh/Associated Press)

He stared at the bat in his hands like it was some sort of mysterious, futuristic tool. He rotated it, 360 degrees, staring into the grain. What is this thing? What is its purpose? And then Adam Dunn shrugged, stuck the bat back in his locker and ran a meaty hand through his mop of hair.

“I can’t hit water if I fell out of a boat. I feel terrible at the plate. And it’s almost game time” for the regular season, Dunn said. “So perfect — I’m right where I need to be!”

Though he’s in a new uniform (that of the Chicago White Sox), a new league (American) and a new exhibition circuit (the Cactus League), Dunn is enduring his annual spring training slump — the kind that also marked his two springs with the Washington Nationals — where the homers come in a trickle, if they come at all, and the strikeouts pile up in bunches.

And being Adam Dunn, the affable “Big Donkey,” a fan and clubhouse favorite during his two seasons in Washington, he is handling it with his typical humor and grace.

“I’m not asking for much,” he said. “Just have a normal spring. Just hit .250 or something, hit a few bombs and feel like you’re ready for the season to start. Is that asking too much?”

The numbers? Yeah, they’re ugly. Entering Wednesday, Dunn was leading the majors this spring in strikeouts, with 22 in only 53 at-bats. He was hitting .208 with a .311 on-base average and a .358 slugging percentage, with one measly home run.

But to know Dunn is to understand those numbers matter not in the slightest. A year ago, the burly slugger limped north to Washington sporting a .208/.321/.250 slash line and not a single home run in 48 at-bats. And then, the bell rang for the start of the regular season, and he cruised to a 38-homer, 103-RBI season that pretty much fell in line with his career norms. The year before (no homers, no RBI all spring) was the same story.

Besides, there are extenuating circumstances this spring that might explain his troubles at the plate. After 10 years in the National League — where he split his time between left field and first base, relishing in the two-way nature of the game even as critics were sneering that his natural position was designated hitter — Dunn is trying to adjust to life as a full-time DH, a one-way player divested of his stake in half the game.

Though Dunn has seen some action at first base, and will do so as well during the regular season, the White Sox consider veteran Paul Konerko their regular first baseman and Dunn their DH.

“It’s fine,” he said when asked how he is taking to the role. “I knew that’s what I was going to do, and that’s what I’m doing.”

But it’s not going fine. The key to becoming comfortable with the DH role, as Dunn has learned from conversations with Konerko — himself a veteran of 183 career games as a DH — is finding a suitable between-at-bats routine and sticking with it. And that is virtually impossible to do during spring training, where most stadiums don’t have indoor batting cages behind the dugouts, the way the big stadiums do up north. Here, Dunn has little choice but to sit on the bench between his at-bats, biding his time until his next turn.

“It’s almost like you’re pinch-hitting four times a game,” he said. “You just sit there, and when it’s your time to hit you have to hit the gas. I don’t even know what my routine will be. Trial and error, I suppose. I’ll probably spend a lot of time in the cage, but I haven’t been able to work through that down here.”

As Konerko said, “It’s harder [being a DH] here than it will be anywhere else this year, because he doesn’t have anywhere to warm up. Nobody here is worried about Adam Dunn.”

Dunn’s departure from Washington has been well-dissected: How the Nationals made an offer late in the season, for three years and $35 million, that they probably knew had zero chance of being accepted. How the team never made another offer. How the White Sox beat out a handful of additional suitors, all of them AL teams, to secure Dunn’s services with a four-year $56 million contract.

How the Nationals held firm to their vision of going with defense first, signing the slick-gloved Adam LaRoche to replace Dunn.

For the mellow, easy-going Dunn, not even the Nationals’ industry-rocking signing of right fielder Jayson Werth to a $126 million contract — less than a week after Dunn’s signing with the White Sox — caused an ounce of consternation. Another player might have felt slighted that an organization that seemed so frugal when it came to his own contract situation would spend so lavishly on someone with whom it was infinitely less familiar. Not Dunn.

“I don’t care about all that stuff, dude,” Dunn said with typical nonchalance. “Good for them. Good for Jayson. I couldn’t care less. I’m where I want to be. I’ve got a chance to win a ring.”

Having spent only seven weeks, out of a 10-year career, on a winning team — 44 games with the 82-win Arizona Diamondbacks in 2008 — Dunn values the White Sox’s contender status above all else.

“I feel great about this team — how could you not?” he said as he walked away, bat in hand. “I just hope I don’t screw it up.”