Even Jeter, though, did not make an All-Star team until his third full season, 1998, when he was on his way to a second championship. Judge is seeking his first postseason appearance, his legacy still in its infancy. But his legend is growing.

“When you walk up to him, he’s way bigger than you think he is,” said Boston’s Mookie Betts, the starting center fielder for the American League. “He looks like he belongs in the N.B.A. Obviously, his ability’s gotten him to where he is, but that part’s not the amazing part. It’s just that he’s so big. For a human to get like that is pretty amazing to me.”

Brad Mills, the Cleveland Indians bench coach who is managing the A.L. as Terry Francona recovers from a heart procedure, put Judge in the No. 3 spot in the lineup. The reason, he said, is that Judge has been such a big story this season, and Mills wanted him to bat in the top of the first inning.

“I’ve seen it from afar, the year he’s had — obviously been the best hitter in the American League,” said Washington’s Max Scherzer, the N.L.’s starting pitcher. “I think they will all agree with that. I enjoy facing the best.”

Judge has earned such praise, but he was careful to acknowledge that Giancarlo Stanton, the slugger for the host Marlins who will start at designated hitter for the N.L., was the favorite in the Home Run Derby. Stanton, who is 6-6 and 245 pounds, was an inspiration to Judge in the minors.

“He was the big guy that was having success in the big leagues,” said Judge, who studied video of Stanton then. “I was like, ‘What’s this guy doing that I can incorporate in my swing?’ He uses his legs well, his barrel stays through the zone for a long time, so he’s able to barrel up a lot of balls, and his room for error is real large. Just his swing — and he’s an athlete out there, too.”

Stanton, who won the Home Run Derby in San Diego last July, agreed with the clear similarities but quickly grew weary of questions about Judge before batting practice.