There is a reason teams care so much about character. And no, we’re not talking about public relations.

Just look at the first game of the regular-season schedule, where the Patriots (minus Tom Brady) will host the Steelers (sans Le’Veon Bell) in a matchup that will remind everyone of the many black-eyes the league has recently endured in the court of public opinion.

However, there is a silver-lining to bringing in players with character concerns, and that silver line can be found on the bottom line. Because for some teams — we’re looking at you, Cowboys — a red flag on a scouting report means the same thing as a blue light at Kmart.

This conversation has to begin in Dallas, where the Cowboys revamped their pass rush with the additions of Greg Hardy and Randy Gregory. Hardy, who would have commanded over $30 million in guaranteed money if not for last year’s domestic abuse case, settled for a one-year, $11.3 million deal that is structured on a pay-per-game basis. Gregory, who would have been a top-10 pick if he wasn’t a pothead with no self control, fell to Dallas at the bottom of the second round.

Then there’s OT La’El Collins, who would have been a first-round pick this year until news broke of his pregnant ex-girlfriend’s murder. The Cowboys were so anxious to cash in on Collins’ free-fall that they signed him as an undrafted free agent even before the murder investigation was completed.

“I couldn’t be in a greater place,” Collins said after signing his contract.  “I just want to thank Mr. [Jerry] Jones, his family this organization and everybody that is standing behind me because I guarantee you this: I’m going to give this organization everything I have and more. This is going to be the best offensive line in NFL history. Mark my words.”

Here’s the catch with some of the discount deals: they keep a player’s cap figure in check for a long time. Collins signed a three-year deal, while Gregory gets a four-year contract. That’s some high-quality, low-cost labor that will help keep Dallas’ salary cap deceptively healthy through 2017.

The Cowboys aren’t done making deals on the cheap, either. Dez Bryant, whose rights were retained via the franchise tag, is going to be hard pressed to get a market-value deal because of concerns about his character. While he doesn’t have any major missteps of the Ray Rice variety, Bryant has a famously short temper and a few too many police run-ins on his record, including one that stemmed from a fight with his mom in 2012.

Dallas is happy to bring Bryant’s missteps into the light. In November, a news company partially owned by Cowboys owner Jerry Jones ran a story claiming police had been called to Bryant’s home in DeSoto, Texas, six times. Further investigation revealed emergency personnel only came out five times; all of the instances were minor; and Bryant was not mentioned in any of them.

Was that simply gamesmanship by Jones trying to drive down Bryant’s asking price?

And while it’s fun to pick on the Cowboys, Dallas is certainly not the only team eager to take advantage of a player whose character issues dropped his price tag. The Broncos traded up in the first round of this year’s draft to select Missouri pass rusher Shane Ray with the No. 23 overall pick. Like Gregory, Ray would have likely been a top-10 pick if not for his inability to put football ahead of marijuana.

One year after going on a spending spree that netted Emmanuel Sanders, Aqib Talin, DeMarcus Ware and T.J. Ward, the cap-strapped Broncos endured a tough offseason that saw several key players leave in free agency, including Julius Thomas, Terrance Knighton, Orlando Franklin and Rahim Moore. Looking to replenish his talent level without cap space or a high draft pick, VP John Elway capitalized on Ray’s poor judgement to land the impact player his roster badly needed.

“I think he slid because of that,” said Elway or Ray’s marijuana citation. “But we were excited sitting at 28 where we had an opportunity to move up and get a football player like Shane that we had rated high on our board. So to have that opportunity, we thought it was the best opportunity so we moved up and took Shane.

“We’ve done extensive work with Shane and talked to him after the incident. He’s owned up to it. I think he’s learned from that, so we don’t anticipate having any more problems like that.”

The Bears also got in on the discount shopping, signing DE Ray McDonald in free agency. McDonald was released by the 49ers last offseason after being investigated for domestic violence and sexual assault, although he was not charged in either case. He must not had made too bad an impression in the Bay Area, though, as defensive coordinator Vic Fangio opted to bring McDonald with him to the Windy City.

McDonald signed a one-year deal with a total payout of just over $1 million.

Saif Fangio: “I know who he is. Even you guys, it’s been well reported about the process that we went through here in deciding whether to sign him or to pursue signing him. At that point where it was said we weren’t going to pursue it, at that point I called two other teams in the league to recommend that they sign Ray. And I called Ray’s agent to tell him, hey, if you need any character reference, anybody wants to talk to me about Ray, that they might be interested in signing him, have them feel free to call me. I think that tells you what I feel about him.”

That’s the catch-22 regarding life in the NFL. Teams want to come across as an ethical collection of community role models, but more than that, they want to win on Sundays. When those two desires prove mutually exclusive, it is clear to see which which way most franchises lean. And if general managers can land a player who is a bad person but a great value, that deal usually proves too good to pass up.

After all, every owner in the league would rather have New England’s collection of tarnished Super Bowl trophies than Minnesota’s morally-mandated empty cupboard.