How fitting that the 24-year-old would share blood with someone nicknamed "Machine Gun," as Kelly sports a cannon for a right arm and regularly dials up his fastball to the mid-90s. That power arm earned Kelly a nickname of his own -- "Kid Dynamite" -- this season in Triple-A.
But when asked about his gangster heritage, Kelly doesn't attempt to hide a smile. Truth is, as far as Kelly knows, there is no history of Prohibition Era bootlegging or bank robberies in his family's past. Kelly made the fact up.
"I've told multiple people that's not true," Kelly said. "But it just stays."
While there may be no truth to Kelly's famous family connection, the right-hander's ability and confidence on the mound, as well as his value to the Cardinals, are the real deal.
Since his Major League debut on June 10 -- when he allowed one earned run over five innings against Cleveland, one day after his 24th birthday -- Kelly has proven to be a reliable No. 5 starter for St. Louis.
"He's got a confidence about him that is well deserved and well-justified," starter Jake Westbrook said. "I think he's handled himself a lot better than you'd expect a young kid to handle himself. It's been fun to watch."
Kelly was called up from Memphis to fill a void when Jaime Garcia went on the disabled list with a shoulder strain. Since joining the rotation, Kelly has posted a 2.75 ERA in seven outings. He has turned in five straight quality starts.
"I don't think we're losing a whole lot with Joe out there," said starter Adam Wainwright. "He deserves a chance, because he's a competitor and goes out there with great stuff."
Kelly said he has managed to discard the butterflies and put his nervous energy behind him, beginning with his second outing. And since letting go of the awe of being in the big leagues, Kelly has soaked in knowledge from the rest of the Cardinals' starters.
"He's kept his mouth shut and done a lot of listening," manager Mike Matheny said. "He's gone about it the right way, as a young pitcher should do, especially on a staff like this. He's listening and taking in all he can, and he's working his butt off between starts.
"I've been impressed with how he's gone about it, and his stuff speaks for itself."
Kelly's stuff starts with his sinking fastball, which, when located down in the zone, makes him a ground-ball machine. Before his promotion, Kelly was leading the Pacific Coast League with 12 double plays induced.
It's difficult to pinpoint where the velocity on Kelly's fastball comes from. Listed at 6-foot-1, 185 pounds, Kelly has a lean frame that doesn't scream power pitcher. He said he tries to use "every ounce of [his] body" in his delivery and suggests his flexibility might also be an asset.
"I think he's just a natural, God-given athlete," said Memphis catcher Bryan Anderson. "I don't know where it comes from, but he's got it."
However, along with rave reviews about his fastball and athleticism, Kelly's scouting report also notes concern about command and ability to locate secondary pitches. It's something Kelly is aware of, but neither of those issues have done much to stall his climb.
Kelly, a third-round pick in the 2009 First-Year Player Draft, never spent more than a full season at any Minor League level. This year, when the Cardinals' need for a starter arose, Kelly was leading the PCL with a 2.86 ERA.
He had also just thrown seven straight quality starts.
"I went to Triple-A with a chip on my shoulder, and wanted to show everybody what I had," said Kelly, who posted a 5.01 ERA in 11 Double-A starts to end the 2011 season. "[I wanted to] just try to go out there, have quality starts and be the best I could be."
Kelly has yet to pitch past the sixth since arriving in the Majors, though he is already creeping up on the career-high innings count of 132 that he established last year. As a result, the Cardinals will keep an eye on Kelly's workload as the season progresses.
Kelly worked almost exclusively as a reliever in college, setting a school record with 24 career saves. It wasn't until 2010 that Kelly transitioned into a starter.
"Relievers, once they become starters, tend to want to try and pace themselves throughout the course of the whole game, as opposed to coming out and giving everything they've got," Cardinals pitching coach Derek Lilliquist said. "He hasn't been that way. He's gotten after every pitch. At the end of the day, you look up and it's six innings."
Kelly's immediate future remains uncertain, despite his success. The Cardinals' front office has expressed interest in adding a starter before the July 31 non-waiver Trade Deadline.
Garcia could replace Kelly in August when he comes off the DL, and the Cardinals may want to have someone more experienced than Kelly in the rotation for a postseason run. That means Kelly could end up back in the Minors, or he could find a fit in St. Louis' bullpen.
For now, though, Kelly's intent is to focus solely on what he can control.
"I felt like I've gotten better at every level, and I feel like I'm still getting better and learning every day." Kelly said. "I just want to go out there and pitch my game."