WEST PALM BEACH, Fla. — Adam Eaton has worn the same gray Mighty Mouse T-shirt in the Washington Nationals’ clubhouse at The Ballpark of the Palm Beaches every day for the past week. His wife bought it for him at Nordstrom Rack because Mighty Mouse, a cartoon with a bodybuilder’s physique popular in the 1940s and ’50s, was the 5-foot-8 Eaton’s nickname in college. Eaton mistakenly believed Mighty Mouse was Mickey’s younger brother — there’s no relation — but that’s beside the point.

“I’ve tried to just embrace the Mighty Mouse character,” Eaton said.

Eaton, by his own admission, has a little Napoleon in him, too. He’s needed the complex to smash glass ceilings: First, to play Division I baseball at Miami University of Ohio; then to get drafted in the 19th round; then to reach the majors; then to become the best big leaguer nobody had heard of with the Chicago White Sox over the past three seasons. Eaton was remarkably consistent in those three years — his on-base percentages were .362, .361, and .362 — and he posted the 15th-highest Wins Above Replacement in baseball during the period, according to Baseball Reference. Each of the 14 players ahead of him except one — Tampa Bay Rays defensive wizard Kevin Kiermaier — made at least one all-star team.

That cloak of anonymity was removed during winter meetings in December, when the Nationals sent three top pitching prospects to the White Sox for Eaton. The Nationals were drawn to the 28-year-old Eaton’s gritty style and relatively cheap contract, which places him under team control for the next five seasons for $38.4 million. But the price was steep — industry consensus was perhaps too steep — for what turned out to be the splashiest acquisition of the Nationals’ quiet offseason.

“It’s not my job to try to put weight on my shoulders or try to see what they’ve given up for me,” the gregarious Eaton said. “I’ve been doubted my whole life, my whole career, and it doesn’t change when you come over to a new team.”

Eaton was acquired to play center field every day between the 6-5 Jayson Werth in left and the 6-3 Bryce Harper in right, an opportunity to reestablish himself at the position following an involuntary hiatus. In 2014, Eaton was one of the best center fielders in baseball. He finished fifth in defensive runs saved and was named one of the three finalists for the American League Gold Glove. But he was a completely different center fielder the next year as he dealt with a shoulder injury and compiled a defensive-runs-saved rating of minus-14 in 2015. As a result, the White Sox bumped him to right field last season. He made 110 of his 153 starts there and reclaimed his status as an elite defender, compiling 22 defensive runs saved, which ranked second in the majors.

“It doesn’t matter,” Eaton said of his move back to center. “I actually had a meeting with Dusty [Baker] and I told him to put me wherever he wants to put me. Just don’t put me behind the plate.”

Eaton’s spot in the Nationals manager’s batting order remains less clear. He’s hit leadoff at every level — he was there in every one of his 123 starts 2014, in all of his 151 in 2015, and in 119 last season — but Trea Turner wreaked havoc atop the Nationals’ order the entire second half last season and has also led off the bulk of his baseball career. On Saturday, Baker hinted that Turner will be the leadoff hitter and Eaton could bat second or further down if the club decides against having three left-handed batters — Eaton, Harper and Daniel Murphy — in a row.

“Wherever he has me is where I’m going to hit,” said Eaton, who has also spoken with Baker about the batting order. “He’s the manager and his say is final. He fills up the lineup card. I hope that my play can help him with his decision, wherever it may be.”

Baker said he sees former White Sox manager Robin Ventura during his annual offseason vacation in Hawaii. This year, Baker said Ventura sought him out to tell him about Eaton, who played under Ventura for his entire tenure in Chicago. Baker didn’t divulge all the conversation’s details, but said he came away encouraged.

“Robin said he comes to play,” Baker said. “And I think that’s the No. 1 thing that we’re getting paid for. You come to play. That’s a good sign and it’s a very good reputation to have, that he’s a ballplayer.”

Eaton, for once, isn’t the smallest ballplayer in a big league clubhouse. That distinction at Nationals spring training belongs to Tim Collins, a 5-foot-7 reliever rehabbing from his second Tommy John surgery. Eaton joked the two, both bearded, are twins. But only one wears a Mighty Mouse T-shirt every day.

“It’s my only one,” Eaton said. “I need my wife to buy me more.”