Preseason games are more important to some players than others.

For the established veterans, preseason games are nothing more than a nuisance, standing in the way of the real games of the regular season. Some veterans — possibly Jets running back Le’Veon Bell and/or Giants running back Saquon Barkley as examples — might not even play a down in preseason.

For players like Jets tight end Ryan Griffin, preseason games are everything. They are their showcase, their springboard to more opportunities.

In the case of the 29-year-old Griffin, who figures to play a lot in Thursday night’s preseason game against the Falcons in Atlanta, his opportunity is a particularly cherished one, considering a big mistake he made last April that left his NFL career in potential peril.

On April 27, the Friday night of the NFL draft in Nashville, Griffin was arrested for public intoxication and vandalism. According to the police report, he was allegedly drunk and punched a window inside his hotel room. There was speculation that Griffin was incited when the Texans selected a tight end (Kahale Warring) in the third round.

Griffin was released from jail on a $1,750 bond the next morning. About three weeks later, he was released by the Texans, with whom he’d played for the previous six seasons after being drafted in the sixth round in 2013.

Despite a modestly successful NFL career, during which he produced 136 receptions for 1,491 yards and seven TDs, the former UConn star who grew up in New Hampshire sat at home, waited for the phone to ring and wondered if he was ever going to have another chance to play in the league.

“I sat at home for what felt like four months [it was actually about two],’’ Griffin told The Post. “It wasn’t fun. I know I had more ball in me, and the fact that I might have screwed that up was killing me. I feel good to have a chance to be back out here proving myself again with a fresh start.’’

The fresh start was provided by the Jets when their newly hired general manager, Joe Douglas, called Griffin in July and told him the Jets were interested.

For Griffin, that Douglas call was a lifeline thrown to him.

“When you’re in the league for long enough, you kind of know your worth, you know your game and you know what’s out on the market,’’ Griffin said. “I knew I had the talent and the film to get another job. It was just what was the best fit for me. When Joe called, I jumped at the opportunity.’’

Make no mistake: The Jets need Griffin as much as he needs them. They’ll be without their top tight end, Chris Herndon, for the first four games of the season as he serves a four-game suspension as a result of a DUI arrest.

That adds to the pot of opportunity for Griffin, who’s the best receiver among the other tight ends on the Jets roster. Eric Tomlinson, Daniel Brown, Trevon Wesco and Nick Truesdell are primarily blocking tight ends. All seven of Griffin’s career TDs have come in the red zone.

“I’m not going to try to replace Chris, because he has a totally different skill set than I do,” Griffin said. “With my body type (6-foot-6, 255), I can’t create the separation Chris does on a play-to-play basis. I just try to be that solid receiver who’s at the right place at the right time and hold down the edge on the run game. I’m just going to try to fulfill whatever Adam [Gase] needs from me.’’

Tight ends coach John Dunn said Griffin has been “a pleasant surprise,’’ calling him “the ultimate professional.’’

“I’ve been really, really impressed with how hard he works and how studious he is,’’ Dunn said. “He gets down on himself when he makes a mistake. You can tell he’s played the game. He’s got some knowledge, he’s got some recall, he’s very familiar with concepts. He’s obviously learning new terminology, but he works hard and goes about it the right way.’’

Where that takes Griffin is up to Griffin, and he knows that.

“I’m taking this opportunity as a fresh start,’’ Griffin said. “I feel like a rookie again. Any time you get released, especially with the conditions of mine, it’s always good to get a fresh start and new people and start over and kind of get rejuvenated. “