FOXBOROUGH, Mass. – Draft day can be exhilarating for those players whose name is called. But far more players never hear Mel Kiper talk about their prospects of playing in the NFL.

That doesn’t mean they’re any less important.

Their chance comes after the draft, when teams start the process of filling their rosters with undrafted free agents. Phone calls are made, offers are extended.

For 19 such players, their chance to make the New England Patriots began Friday with the opening of the team’s rookie minicamp.

They joined the seven players drafted by the Patriots, plus a group of four players in on tryouts, in attempting, as young Brandon Jones said, “to find my role on this team.”

Jones was one such undrafted free agent. A cornerback from Rutgers — where else? — his name went uncalled in the draft, even as he saw the Patriots select three of his defensive teammates: cornerback Logan Ryan, safety Duron Harmon and linebacker Steve Beauharnais.

But even before the draft ended, he was getting calls from teams indicating they might be interested in him. When the Patriots called, he jumped at the chance.

“It’s a very prestigious organization,” he said. “It was a no-brainer for me. As soon as I got that call it was, ‘Let’s go.’ “

Asked if he has anything extra to prove, that he should have been drafted, Jones shook his head.

“I think every rookie has something to prove,” he said. “These guys have been here and played football here, some for a long time. You’ve got to come here and try to insert yourself and try to find a role on this team.

“That’s what I’m trying to do in this rookie camp and hopefully through training camp, try to find my role with this great group of guys.”

Jones said it wasn’t hard to watch the draft and go unannounced. He was just grateful for his friends. Besides, he said, he got the call and is joining them with a chance to play for the Patriots.

Every undrafted free agent knows the score. They all talk the same game: Just glad to have this opportunity to play football a little longer.

Ben Bartholomew, a fullback from Tennessee, is a long shot. At 6-foot-2, 252 pounds, he had only two career carries in college. He is a blocker, a human bowling ball to clear the way for faster backs. That position is almost non-existent in the NFL these days.

But he is glad to be at Gillette Stadium because that means he’s still playing.

“If I wasn’t playing football? I don’t know what I’d be doing,” he said. “Football is the only thing on my mind at this time.”

You look at punter Ryan Allen. He came here knowing that Zoltan Mesko, a fifth-round pick in 2010, is returning after another good season.

But this is where he wants to be. “When you step out to the next level of competition, coming from college to the NFL, there’s a high level of expectation and high level of play, he said. “Just to be able to be part of that and compete, that’s an honor.”

He got the call from New England minutes after the draft. After talking with his agent, they decided “this is what we thought was the best fit: to go out and compete and be part of a winning program.”

These players come here to continue to play the game they love, to challenge themselves and because they know of the Patriots’ history of giving undrafted free agents a shot.

New England’s roster includes nine players who were signed as undrafted free agents.

Armond Armstead, who signed with New England after playing a year with the Toronto Argonauts after going undrafted in 2012 out of USC, said that is all the incentive any of these players need.

“It just shows you that they don’t care where you came from,” he said. “It’s what you do when you get here. I have the opportunity, have the chance to show what I can do now.”

Allen, who is following in the Patriots’ tradition of left-footed punters (Mesko, Ken Walker, Josh Miller to name some), knows that every NFL roster includes players not drafted out of college who “go on to have outstanding careers over a long period of time.”

Punting at Lousiana Tech, he won the Ray Guy award, given to the nation’s outstanding punter, in 2011 and 2012 — the first player to win that award in back-to-back years.

But he also knows that doesn’t mean a thing any more.

“In a sense, once you step to next level, that’s all out the door,” he said. “When you step to the next level, the expectations of play at this level is what you have to focus on. It’s all about looking forward now.”

And getting one more chance to play.

Mike Lowe can be contacted at 791-6422 or at:

mlowe@pressherald.com

Twitter: MikeLowePPH