Kevin Williams greets Benjamin Watson the same way every morning.

Williams is four months older than Watson, who turns 35 in a month. By merely reaching that milestone in a young man’s NFL, a player commands respect, a sort of instant entry into a fraternity that offers its members an opportunity to playfully remind each other how far they’ve come.

“How you doing, old man?” Williams always asks Watson. “I beat him to it. It’s crazy the shape he’s in.”

Dismissed by most as merely a blocker for most of the offseason, Watson was essentially an afterthought as pundits both local and national tried to figure out how the Saints could replace tight end Jimmy Graham without adding a high-profile name to the position.

But the Saints have been keeping a secret: Watson, who caught just 39 passes in his first two seasons in New Orleans, this year ranks among the top five tight ends in the NFL with 38 catches for 472 yards and three touchdowns, numbers that put him on pace to challenge his career highs in every category.

With Graham gone, the afterthought has become a focal point. It was a transition the Saints saw coming.

“I’ve always felt like he was just a phenomenal athlete and could do everything,” quarterback Drew Brees said. “I don’t know if there is a more complete tight end in the league, in regards to what he brings to the run game, pass game, not only catching but blocking, what he means to us in the locker room. The way that he practices, his approach, his demeanor, his leadership ability, his character, just all those things. He’s the total package.”

The old man has had a season like this in him all along.

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All Watson needed was an opportunity.

For most of the past two seasons, that path remained blocked by Graham. With Graham making headlines and dominating the highlights, Watson handled blocking duties.

Watson, who had a great relationship with Graham and admired the younger player’s freakish abilities, handled the role without any problem. Nine years spent in all sorts of situations — from occupying a key role in New England to trying to find chemistry with the revolving door of quarterbacks that came through the offense in three years with Cleveland — taught Watson to take a big-picture approach to his role in the offense.

Earlier in his career, the complementary role Watson has played in New Orleans might have quietly left him yearning for more.

“Mentally, I probably was in a different state, just trying to attain and attain and attain,” he said. “I was never a player that was like, ‘I want you to give it to me,’ to vocally say, ‘Give me the ball.’ But there were things that I obviously wanted. I think now I realize the importance of every single play and every position on the field.”

The Saints remained quietly confident that Watson could handle a featured role if needed. When the Saints decided to trade Graham, the organization proved it by refusing to add a high-profile player in either the draft or free agency, and Watson responded by dominating offseason practices over the summer and into training camp.

“We have seen tight ends play well into their 30s, because they understand leverage and they are smart and have great hands and have real good change of direction,” coach Sean Payton said. “Ben is one of those players who is smart and has very good football instincts, and I think there is that rapport, or that trust, that Drew has when he’s locating him in the progression or potentially throwing the ball to him off a flush pocket.”

Now, with Graham in Seattle, Watson is getting to reap the rewards of all that patience. Used as a featured weapon against Atlanta and the New York Giants, Watson twice has broken his career-high for single-game yardage as he torments linebackers and safeties over the middle.

“As an offensive player, you want the football. All of us do,” he said. “You love that chance to get your hands on the ball, to make plays in the passing game.”

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Watson’s breakout season remains an anomaly. Few NFL players turn in the best statistical performance of their careers at 34. Fewer still find themselves handling an increased role.

Even a player like Williams, who has five All-Pro honors on his résumé, is on a snap count designed to keep him fresh and healthy for the entire season. New Orleans is also regularly giving Williams, receiver Marques Colston and guard Jahri Evans the luxury of veteran off days, a Wednesday spent out of practice to help them recover, a common practice around the NFL.

Despite a workload that has included 86.2 percent of the Saints’ snaps so far — the highest for any skill-position player on the offense not named Brees — Watson hasn’t taken a day off yet. He hasn’t even been offered the opportunity.

“He’s in too good of shape,” Payton said.

Watson is still a physical freak, a chiseled player who looks like he could make a run at the next superhero role Marvel needs to fill out its ever-expanding franchise. At his age, a lot of players remain in great shape by going above and beyond in offseason workouts, putting themselves through hell to get their beat-up bodies another shot.

But rest is the key to Watson’s physique.

“I’ve had to cut back,” Watson said. “There was a time early in my career when, a few weeks after the season, I would start lifting weights again and start running. Now, after the season, I take a much longer break.”

Watson didn’t pick up a weight for two months last offseason. He spent that time doing yoga and pilates, increasing flexibility and guarding his muscles against the kinds of strains and pulls that often derail the offseasons of much younger players.

The minimalist approach remains when Watson begins training in earnest. A lot of NFL players travel to other states to train under the watchful eye of experts at specialized institutes, but Watson stays with his family in New Orleans. Instead of paying thousands of dollars to have somebody take a close look at his every move, Watson relies on the Saints’ program and his own knowledge to get ready.

“I know what I need to do. I’m pretty motivated,” he said. “I don’t need anybody to tell me what to do, so I just stay with my family instead of going somewhere else.”

Once the season begins, Watson is smart enough to let the games push his body, rather than anything in the weight room. Watson might do big power cleans, squats and deadlifts during the offseason, but he takes those things out of his routine during the season for fear of getting injured.

The approach is working. Often injured during his time in New England, Watson has played in 108 of 112 possible games over the past seven seasons.

“You just learn what you can do and what you can’t do,” he said. “You get smarter.”

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A younger Watson used to think he had to have a season like this one to make a big impact off the field. A breakout year can give a player the kind of platform to be an influence.

A Facebook post Watson wrote last November changed that perception. Frustrated and appalled by the riots in Ferguson, Missouri, Watson wrote his thoughts on the problem, and a side of Watson that had been mostly personal suddenly opened an avenue for him. Watson found himself on national television, traveling to speak at churches and conferences in the offseason, handed an opportunity to write a book on race relations, “Under Our Skin,” that will be released next week.

“That right there just let me know that, whether you’re catching the ball or you’re a blocker or you’re on special teams, or the limelight’s on you or it’s not, God can lift you up,” Watson said. “You just need to chill out, do your job where (God) placed you and not worry about catching touchdowns — which you should want to do, but it’s not going to give you what you’re desiring.”

Watson, the son of a pastor, is a devout Christian who has always had an acute interest in the impact he can make on the world. Before the Facebook post earned so much attention last year, he’d always been an avid reader of pastors and a follower of political issues and current events.

He doesn’t want to follow in his father’s footsteps when he’s done playing football. Watson would rather get into broadcasting or writing, in part because of the schedule a pastor has to keep; the 24-hour, seven-day-a-week availability can be tough.

His father’s influence, though, can be seen all over that Facebook post, and the subsequent speaking engagements that followed.

“To be in church, to hear my father speak, to see him prepare all the time, it kind of taught me how to relay my feelings, how to speak, how to prepare, how to write,” Watson said. “How to dissect a certain issue, and not just look on the surface, but really develop those thoughts.”

Watson has never been as high-profile as he is right now, both on and off the field.

He plans on making the final years of his career count.

“Now, at this stage of my life, it’s about making an impact on the locker room and in the world,” he said. “So it’s being the best football player I can be, and if I have a chance to go speak life to somebody, encourage someone; if I have a chance to speak or write, or if I have something that could maybe help someone through a tough time, that I could put on paper, then I feel like it’s given to me. I want to leave that sort of lasting impact.”