Ray Rice, right, has remained unsigned since being reinstated late last year. (AP Photo/Gail Burton)

NFL training camps are under way for some teams and about to start for others. But running back Ray Rice remains on the outside of the sport looking in, having gone unsigned since his suspension by the NFL was overturned by a former judge in November.

The cases of Rice, Adrian Peterson and Greg Hardy put the NFL under intense scrutiny and produced unyielding criticism last year, both for the conduct of the players and for the league’s handling of disciplinary measures. But while Peterson and Hardy are back in the league, Rice’s chances of resuming his NFL career remain uncertain.

Some within the sport attribute that not only to Rice’s high-profile domestic violence case but also, to a lesser degree, to his diminished on-field production in his final season with the Baltimore Ravens. Any team that might weigh signing Rice, they say, must consider whether he will be enough of an asset as a player to offset the off-field implications of bringing him in.

“We all know that talent-versus-character equation,” said a front office executive with an AFC team who, like others interviewed in recent days about Rice’s job prospects, spoke on the condition of anonymity because of the sensitivity of the topic. “Time has passed since that incident. Some people may be willing to give him another chance. But he didn’t have a very good year in ’13. There’s more than one thing working against him.”

Rice, 28, averaged a career-low 3.1 yards per carry for the Ravens in the 2013 season. He had not averaged below 4.0 yards per carry in any of his first five NFL seasons, all with Baltimore.

Rice said during the 2014 NFL preseason that he’d “added a little bit of extra weight” during the 2013 season. But he was lighter and at a “comfortable” weight last summer, he said then.

The AFC executive said he could envision Rice possibly being signed by a team during training camp if that team becomes shorthanded at running back because of injuries. The executive said Rice’s play over the course of his entire NFL tenure would warrant an opportunity minus off-field considerations.

“I think he’d be in a camp based off his career’s work,” the executive said. “But the last time he played, the arrow was going down. There was talk about his weight. You can look at the production, and it wasn’t very good.”

A personnel executive with an NFC team said: “From a football perspective, he’s definitely a sign-able player. He’s definitely a good enough player. But with all that’s happened, it’s gonna be tough.”

The NFC executive said he could foresee Rice being signed by a team with a coach and front office with established reputations that would enable that organization to withstand any backlash from fans over the move.

Rice’s indefinite suspension by the NFL was overturned on appeal in November by Barbara S. Jones, the former federal judge appointed by Commissioner Roger Goodell to hear and resolve the appeal. The indefinite suspension was imposed by the league last September after video of Rice striking Janay Palmer, then his fiancée and now his wife, in a hotel elevator in Atlantic City earlier last year became public. The Ravens released Rice on the same day. The NFL previously had suspended Rice for only two games, which Goodell later called a mistake.

Rice’s representatives did not respond to messages seeking comment about his prospects for being signed. ESPN reported last week that Rice has been working out in Connecticut and that his supporters, including Greg Schiano, have been contacting teams in an intensified effort to try get him signed. Schiano coached Rice in college at Rutgers and later coached the Tampa Bay Buccaneers.

New England Patriots owner Robert Kraft predicted in a televised interview last September, just after the video of the elevator incident was released, that Rice never would play again in the NFL.

“I don’t think he’ll play another NFL game,” Kraft told CBS then. “I’ll be shocked if some team would pick him up.”