The double life of Taysom Hill begins every Wednesday at 6:30 a.m., two and a half hours before the New Orleans Saints’ first team meeting of the week. Hill studies film and reviews new plays in the Saints’ quarterback room. When Drew Brees and Teddy Bridgewater head to install plays after the team meeting, Hill splits for the special teams meeting room, a place foreign to pretty much every other quarterback. But then, pretty much every other quarterback cannot sprint 40 yards in 4.4 seconds or lift weights like a linebacker.

All day, Hill bounces between football worlds. He walks through plays with the offense, then skips quarterback-center exchange sessions to practice blocking punts or covering kicks. He steals spare time to learn new calls for the kick return team. He stays late to learn plays at different offensive positions and watch more film as a quarterback. He leaves at 7 p.m.

Hill has learned it takes a lot of time to live out one dream while keeping another alive.

“I am exhausted,” he said.

Hill, a second-year reserve quarterback, offensive chameleon and special teams ace, might be the NFL’s most fascinating player. Hill has played 17.4 percent of New Orleans’ offensive snaps, lining up as a wildcat quarterback, tight end, running back and wide receiver. Monday night, he picked up a crucial third down with a 16-yard burst and was the lead blocker on an Alvin Kamara run that nearly sealed the game. He has played a team-high 79.4 percent of Saints special teams plays, doing everything from returning kicks to blocking punts. Hill’s role began late last season as an experiment. It has bloomed this year and made him a crucial part of the NFL’s best team.

Hill’s role is a triumph of rare individual willingness and refreshing organizational imagination. He has helped the Saints thrive in an NFL season that has rewarded creative thinking. The Chicago Bears have made Tarik Cohen, a 5-foot-6 running back from North Carolina A&T the focal point of a division-winning offense. Patrick Mahomes has become an MVP front-runner while slinging no-look passes blessed by Coach Andy Reid. The Ravens have salvaged their season using rookie Lamar Jackson as a borderline single-wing quarterback. And the Saints have turned a quarterback nobody wanted into the league’s most valuable Swiss Army knife.

The Saints claimed Hill only after every team passed on him in the draft and one team found no use for him after one training camp, and they have maximized his impact because they embraced his unique athleticism. Rather than worry he’d be typecast and lose the chance to play NFL quarterback, Hill welcomed the chance to contribute on a unit typically comprised of linebackers and tight ends.

“If you give him a helmet and put a ball out there and say, ‘ready, go,’ he’s happy,” said Virginia Coach Bronco Mendenhall, who coached Hill at BYU. “If you make him sit in the pocket, that actually takes away the fun for him. He wants to do everything possible.”

If injury struck, Hill would replace Saints long snapper Zach Wood “without any problem whatsoever,” special teams coach Mike Westhoff said. He’s not New Orleans’s emergency kicker or punter, “but I did tell them I could do it,” Hill said. At Highland High in Pocatello, Idaho, Hill punted to a 44-yard average, blasted most of his kickoffs to the end zone and booted a 47-yard field goal to win a playoff game his sophomore year. Highland Coach Gino Mariani instructed Hill not to cover the infrequent kickoffs that didn’t result in touchbacks, for fear he’d take unnecessary hits.

“Of course, that’s not him,” Mariani said. “He’d get in the play.”

Hill has always possessed freakish athleticism. At his BYU pro day, Hill ran a 4.44-second 40-yard sprint. If he had been invited to the NFL combine, it would have been the fastest time by a quarterback other than Robert Griffin III since at least 2000, according to Pro Football Reference. He has a quarterback’s right arm attached to a 6-foot-2, 221-pound hunk of muscle.

“He was the strongest player on our team, the fastest player on our team and the best athlete at any position on our team,” Mendenhall said. “And it wasn’t close.”

In college, coaches christened him “Thor-terback” for his powerful running style. Against Texas as a sophomore, he bashed through tacklers and ran for 259 yards. On the sidelines, he grinned as he described his exploits with Australian-tinged accent, a souvenir from his Mormon mission trip.

“He was like a mix between a superhero and Crocodile Dundee,” Mendenhall said.

Hill entered the 2017 NFL draft as a complicated case. He suffered four season-ending injuries in college. (“It was almost like he was too strong for his own body,” Mariani said.) His mission trip made him old for his class — he’d be 27 when he played his first NFL game.

After Hill’s career ended, NFL teams asked Mendenhall if he believed Hill could play at a variety of individual positions — quarterback, running back, wide receiver, H-back, safety. The inquiries reflected what Hill was capable of, but also the rigidity of NFL thinking. Scouts and executives needed to categorize Hill to understand his potential, which Mendenhall viewed as a mistaken approach.

“Once you try to label him, his value goes down,” Mendenhall said. “If you take the labels off, how could you not value him? Because you’re basically getting the equivalent of four players. I could sense teams trying to put him in a box. Then you add the missionary age to it. It started to make me wonder if anyone was going to be brave enough or forward-thinking enough to draft him. And they weren’t.”

The Green Bay Packers signed Hill as an undrafted free agent but decided they didn’t want to carry a third quarterback and instead trusted 2015 draftee Brett Hundley to back up Aaron Rodgers. While scouting a wideout on the fringe of the Packers’ roster, Saints Coach Sean Payton noticed Hill and told General Manager Jeff Ireland to claim him. When Green Bay cut Hill, the Saints scooped him up.

At the start of the 2017 season, Hill served as an emergency quarterback and became a spectator for the first time in his life. He was the youngest of four siblings in a ultracompetitive family, a state champion in high school and a four-year starter in college. He desperately missed the field.

In mid-November that year, Payton lured Westhoff out of retirement, a rare in-season hire. Westhoff didn’t know anyone on the team, but on one of his first days he walked through the locker room and saw Hill walk past with a towel wrapped around him. “Who’s that?” Westhoff thought. When he inquired, Payton informed Westhoff of Hill’s background.

“Let me have one day with him,” Westhoff requested.

After one practice, Westhoff ran Hill through basic special teams drills.

“The simple things we were asking him to do, you could tell,” Westhoff said. “He’s so powerful with it. This guy coming off the edge on a punt return is a problem.”

With Westhoff’s insistence, Saints coaches determined Hill was one of their best 46 football players, regardless of position, and he should be on the field. When they told him they planned to use him covering kicks, Hill was surprised first, then excited — he would no longer be a spectator.

“I would also say that there was some moments, too, where I was like, ‘Ah, man, what does this mean for my career? Is this them telling me they don’t see me as a quarterback?’ ” Hill said. But Saints coaches “made it very clear that in no way is this dictating what my future is going to be like here. They still felt like I had the potential to be a starter in this league. They addressed that early so I never had to.”

Westhoff kept Hill’s responsibilities simple at first, but after he made two tackles in his first game, Westhoff continued to expand his role and teach him techniques, like how to shed open-field blocks.

Hill isn’t the first quarterback to play special teams for Westhoff. Brad Smith, a part-time wide receiver as well, returned kicks for him with the Jets. Tim Tebow played as the personal protector on punt teams. A lot of people ask Westhoff to compare Tebow to Hill, both of them stellar, muscled college quarterbacks. Westhoff says there is no comparison.

“Tim Tebow was never going to run downfield on a kickoff,” Westhoff said. “Please. He’d have a heart attack. He’s not in the same league as Taysom Hill as a special-teams player.”

Hill brings a quarterback’s mentality to special teams. He understands not only his role, but also what the other team is trying to accomplish and how best to attack it. “He’s learning, he’s inquisitive,” Westhoff said. “He always wants to find a better way to do it. A lot of that comes from [being around] Drew and Sean all the time.”

The mind-set led to Hill’s biggest play yet. Two weeks ago, before they played Tampa Bay, Hill and Alex Okafor devised their own punt block scheme, called “TE Game.” Okafor would line up over the end, and Hill lined up across from the tackle. Okafor drove straight upfield, creating space for Hill to bolt around Okafor’s back and lose his blocker in the scrum. From there, Hill sprinted toward the punter and swatted the ball coming off his foot. The blocked punt keyed a second-half comeback, and Hill won NFC Special Teams Player of the Week.

Even for a player used to scoring touchdowns, the feeling of blocking a punt, Hill said, was special — like a shot of adrenaline.

Hill wants to throw more touchdowns in his future. He stills sees himself as a quarterback, and learning from Brees, he believes, gives him his best opportunity to become an NFL starter. In the meantime, the Saints have incorporated him into their offense in creative ways, frequently playing Brees and Hill together at the same time.

Where can Hill be most valuable? Mendenhall coached Brian Urlacher in college as New Mexico’s defensive coordinator. He sees the same athletic traits in Hill. “We already know with Urlacher, he made the Hall of Fame,” Mendenhall said. “If used appropriately and correctly, I think Taysom would do the same.”

For now, Hill will maintain his exhausting schedule. The defining trait, for a player who defies simple definition, is how much he loves football. He came back from four devastating injuries in college, and he accepted a job hurtling his body full-speed at ball carriers without blinking.

“Let’s go make the most of this opportunity,” Hill said. “You’re still going to have an opportunity to play quarterback here or somewhere else. Let’s go help the team win.”

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