The thing is, his fastball has lit up radar guns at a blinding speed that batters want to declare illegal.
Ned Yost, now the Royals' skipper, was managing the Milwaukee Brewers when they made the right-handed Jeffress a first-round Draft choice in 2006.
"When I saw him before, he had very raw stuff, coming at you with a 101, 102 mph fastball," Yost said. "Decent breaking ball, command was an issue for him, like it is for all young pitchers. But he's definitely refined his command to the point where he throws a lot more strikes with that really good stuff. He's impressive so far."
What about this "exploding" stuff?
"It jumps on you. There's a difference," Yost said. "There are guys that throw hard, but you can see it the whole way. When it comes out of his hand, it just like gets there and goes 'shhhhhhhhhhmp!' You think you see it, but you don't see it."
That's the hope anyhow and, if enough batters don't see it, Jeffress is likely to be part of the Royals' bullpen this year.
He came as part of the four-player package that the Brewers gave up to acquire pitcher Zack Greinke and shortstop Yuniesky Betancourt.
And the fastball isn't his only weapon.
"He's got a hard, tight curveball," Yost said. "It's not your slow, little lollipoppin' breaking ball. It's got some life and some break to it. ... When you've got a good curveball like that, it makes your 100 mph fastball look like 110."
Of course, the trick will be to throw these searing pitches where they're supposed to go, never an easy task.
Jeffress is not a real big guy -- 6 feet and something over 200 pounds -- but he's always been able to throw hard.
"I was blessed with the talent just to throw it," he said. "When I was younger, I was able to throw it that hard as well."
Jeffress, 23 and part of the baby boom in camp, developed that talent in the small town of South Boston, Va., where his father, Fred, is a computer technician and his mother, Yolanda, is a school secretary. The youngest of four children, he played baseball and basketball at Halifax County High School. He was considering Clemson or Longwood universities when the baseball Draft and a reported $1.55 million bonus intervened.
His progression up the Brewers' system was twice interrupted by suspensions for violating the Minor League Drug Treatment and Prevention Program, which Jeffress acknowledged was for use of marijuana. His second offense in 2007 cost him 50 games; his third offense in 2009 cost him 100 games.
If there's a next time under the Minor League program, he'd receive a lifetime ban. The Major Leagues have a different set of rules and players are not tested for marijuana.
"Yeah, it'd be lifetime," Jeffress said. "It's always in the back of my mind. It's a bump in the road that I will have to deal with. You can't really dwell on that, you can't dwell on the past. You can't focus on the bad things, you've got to focus on the positives and the work ethic that you'll be able to provide for your team and yourself."
Coming off the latest suspension last June, Jeffress worked his way through two Class A teams and Double-A Huntsville and got his first Major League shot in September.
His debut came when the Brewers were in Cincinnati and he pitched a scoreless inning of relief.
"It was, No. 1, the greatest experience in my life," Jeffress said. "It was actually a blessing that came from above. It was just the best thing of my life, a dream come true.
"It felt wonderful. I kind of felt like I went through a lot. I came from the bottom. The only place I could go was to the top."
Jeffress was so excited, he can't remember what Reds batters he faced that night. Let the record show that Miguel Cairo singled, but Paul Janish bounced into a double play and Ryan Hanigan grounded out.
The fastball must have been exploding.