For as often as J.R. Graham hears the term “Rule 5,” you would think he had broken it.

“You get labeled, and that’s a pretty big label. I’m not ‘J.R. Graham’ anymore, I’m ‘Rule 5 pick J.R. Graham,’ ” the Twins rookie reliever said. “But that’s OK, I just embrace it. It’s what gave me this opportunity, so I’ll wear it proudly.”

Twins draftees probably wear it more proudly than most, given the team’s above average — and in one case, spectacularly successful — results with these midwinter pickups. Current reliever Ryan Pressly was a Rule 5 draftee. So was Scott Diamond, who won 12 games for the Twins in 2012, the year after he was selected. Outfielder Shane Mack helped the Twins win a World Series in his second year after being selected from the Padres’ system.

And then there’s the time the Twins hit the Rule 5 jackpot: Convincing the Marlins in 1999 to draft an Astros farmhand named Johan Santana and trade him to Minnesota. That transaction produced perhaps the best pitcher in Twins history, a two-time Cy Young Award winner. “You can’t expect to find a Johan Santana,” Twins General Manager Terry Ryan said, “but that was a pretty good deal.”

The draft is the baseball equivalent of panning for gold; teams hope to discover future big leaguers who may have just developed more slowly than others. Rule 5 says that any player who has been in the minor leagues for four or five seasons (depending on age at signing) and is not on a major league roster may be drafted by any other team at the winter meetings in December.

The catch: That player has to remain on his new team’s 25-man roster (or disabled list) for the entire next season, or be offered back to his original team. It’s a direct ticket to the majors.

That’s not an easy commitment for most teams, and it’s clearly easier if the player is a pitcher or catcher. But it can be worth it.

“We really struggled with [keeping] Santana,” Ryan said of the lefthander, who pitched only 86 innings and posted a 6.49 ERA while fulfilling that roster requirement in 2000 — and learning the changeup that would eventually make him a star. “We had to battle that.”

Now Graham is part of that battle, a former top Atlanta prospect whose career was derailed by shoulder injuries in 2013. He has never pitched above Class AA (nor had Pressly when the Twins took him), and the Twins understand that he must be brought along slowly. But it has to be in the major leagues.

“When you take a Rule 5 guy, I don’t think you should anticipate he’s going to be a regular guy. ‘Let’s go get him in the seventh inning’ — probably not,” Ryan said. “I thought we’d have to be very careful. He threw hard, you could see that, but we all know it’s a little different animal up here. But he’s holding his own.”

He is, even if the Twins aren’t yet certain what they have. Graham might be the hardest thrower on the team, with a fastball that he promises will reach 97 miles per hour before the summer is gone. But his command can be shaky; he has walked six batters in 11⅔ innings, given up nine hits, and broke Royals outfielder Alex Rios’ hand with a pitch during the Twins’ home opener.

Manager Paul Molitor is still trying to figure out how to use the inexperienced righthander, who does possess a 1.54 ERA. At the moment, he is limited to blowout games — Graham’s past six appearances all have come with the Twins leading or trailing by at least six runs.

“For various reasons early in the year, I got him in situations that were a little bit more stressful, in terms of potentially influencing the outcome of a game,” said Molitor, who admits he was impressed enough in spring training to imagine Graham handling some late innings. “After it started, I just had to re-evaluate. … But we’re inching that way. Little by little, he’ll find himself getting in more situations of significance.”

Graham says he doesn’t care when he pitches; the experience he’s receiving this year is “the best learning experience any young player can go through. It’s the best players, the best coaching staff, so I’m learning so much, from every direction, every day.”

That’s the plan, Molitor said. Before long, the manager wants people to forget the Rule 5 label. “We all believe this guy’s makeup is going to allow him to develop quickly,” Molitor said. “I imagine his role getting gradually bigger this season.”