Among those not surprised is his father, David, who over the years has come to understand his son's goals exceed simply becoming a Major Leaguer.
"The guys will always ask, 'Is your goal to be in the big leagues?'" the elder Schafer said. "He's always said, 'No, my goal is to be in Cooperstown, not the big leagues.'"
Nobody is currently reserving space for Schafer in the Hall of Fame, and the Braves aren't even guaranteeing he'll be making his Major League debut at any point this season. But having had the chance to see him on a daily basis this spring, they are even more confident that he would be ready if needed this year.
"He's impressed me with everything that he's done both offensively and defensively," Braves hitting coach Terry Pendleton said. "He knows how to play to the game. If anything happens to any of the guys up here and we need to bring a guy up, I think he'd probably be ready."
Entering the split-squad game he played against the Astros at Osceola County Stadium on Saturday afternoon, Schafer was hitting .321 (9-for-28) with three doubles, four walks and six strikeouts.
Not bad for young player in his first Major League camp, and even more impressive considering that he's never played above the Class A at the Minor League level.
"I'm just trying to soak up as much as I can and get better every day," Schafer said. "That's really what it's all about."
While respectful, Schafer has never seemingly been in awe of sharing a locker room with the likes of Chipper Jones, Tom Glavine and John Smoltz. His stroll suggests cockiness, but his demeanor has provided an indication that he's simply filled with a sense of confidence that his father says has existed for more than 10 years.
Schafer's first introduction to a superstar came back in 1994, when Michael Jordan's disappointing one-year tour of the Minors visited his hometown of Winter Haven, Fla.
Just 7 years old at the time, Schafer made a sign that read, "Hey Michael, It's Not So Fan-tastic." Upon seeing the creative play on one of the NBA's popular slogans, the basketball superstar laughed.
A few years later, while serving as a bat boy for the Royals at their Boardwalk and Baseball Spring Training complex, Schafer was asked if he wanted to get any of the players' autographs.
As David remembers, his son responded with, "No, because I'm going to be here someday."
"He's never been intimidated by these surroundings at all," said the elder Schafer, whose observation was once again confirmed back on March 3 when his son took one of Mets closer Billy Wagner's fastballs to the opposite field for a single.
Schafer's surroundings have certainly changed over the course of the past year. At this time last year, he was preparing for a second consecutive season at Class A Rome amid little fanfare. He'd hit just .240 with eight homers while admittedly struggling with his plate approach during the 2006 season.
"I never doubted myself," Schafer said. "I just new I had a bunch of stuff to learn."
Instead of sulking about having to repeat at Rome, Schafer instead accepted the challenge. Just 30 games later, after he'd hit .372 with a five homers and 15 doubles, he earned a promotion to High Class A Myrtle Beach, where he'd hit .294 with 10 homers in 106 games.
"He didn't hang his head and he didn't act like he was being left behind [in Rome]," said Braves director of player development Kurt Kemp. "He went in there and said, 'I'm going to show you that I'm going to advance to the next level.'"
After Schafer hit .324 with 34 hits and 16 RBIs during the 26 games he played in the Arizona Fall League, he was considered by many to be the top prospect in the Braves organization.
Before acquiring Mark Kotsay from the A's in January, the Braves flirted with the possibility of filling Andruw Jones' vacated void in center field with the young Schafer.
If Kotsay's back proves to be a problem and sidelines him for an extended period this year, Schafer will patiently await the opportunity to prove why he's always believed he's destined to be a Major Leaguer.
When his father used to take him out of school to watch Indians Spring Training games in Winter Haven, Schafer never considered Kenny Lofton or Manny Ramirez to be his idols. He was too busy chasing batting practice homers with the rest of the kids and holding the belief that he would one day prove worthy enough to walk the same career path.
"Jordan has never been in awe here, even playing in big league games," the elder Schafer said before seeing his son play in Winter Haven earlier this month. "He doesn't think like that, because he doesn't just want to be in the big leagues. He wants to be really good in the big leagues."
Mark Bowman is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.