The first Hail Mary in pro football was nothing like the choreographed desperation we see today. It was Dec. 28, 1975. The Dallas Cowboys were trailing the Minnesota Vikings 14-10 in the final seconds of a divisional-round playoff game. Dallas quarterback Roger Staubach gave his best receiver simple instructions as the Cowboys lined up at the 50-yard line: make a move and go deep.

The pass was a few yards short of the end zone, but receiver Drew Pearson outmuscled the only defender contesting him for the ball and trotted in for the winning score.

Staubach joked afterward that he had closed his eyes and said a Hail Mary prayer with the ball in the air. "A Catholic kid from Cincinnati," as he told NFL Films in a documentary on the play.

In the ensuing years, NFL teams have synthesized the desperate heaves into a science that no longer needs intervention from the mother of Jesus. Hail Marys have succeeded roughly once in every 12 attempts over the past decade, boosted by unique protection schemes, enhanced quarterback fundamentals, counterintuitive defensive techniques and a debate on whether to blitz or play coverage.

There have been 193 Hail Mary attempts since the start of the 2009 season, according to ESPN Stats & Information tracking, including the regular season and playoffs. They have produced 16 touchdowns, including three from the arm of Green Bay Packers quarterback Aaron Rodgers. (The Cincinnati Bengals' Andy Dalton is the only other quarterback with more than one during that span, having twice hit receiver A.J. Green on such plays.)

Rodgers honed his approach during his three years as a backup to Brett Favre. In what turned out to be a gift, coaches typically pulled Favre from that portion of practice to protect his arm and gave the snaps to Rodgers.

"You get good at it by practicing them," Rodgers said over the summer. "I was always doing the Hail Mary reps in those years, and I got used to throwing it outside the pocket, or finding a spot to throw it inside the pocket, and kind of got used to what the throw felt like, height and distance wise. And I've always been a little nerdy about that -- watching the ball, where it would land, feeling and remembering what that throw felt like. Was it all out? Was it 80 percent? Was it 90 percent because of the wind? And just kind of locking those things away."

As Rodgers, one of the best to ever do it, illustrates, a lot more goes into Hail Mary throws than simply dropping back, sending receivers sprinting downfield and uncorking a deep ball. We explored every facet of the biggest of football's big-play attempts, speaking with multiple quarterbacks, receivers, defensive backs and coaches, and going inside what they are trying to do in those moments.

The search for a launch point

By nature, the Hail Mary play starts far from the end zone. The average Hail Mary pass since 2009 has traveled 44.7 yards past the line of scrimmage, according to ESPN Stats & Information research.

The successful attempts, however, aren't usually wild throws but instead the result of a carefully planned series of movements. Much of the dirty work occurs even before the ball leaves the quarterback's hands. "Finding your launch point," Rodgers said, is the first stress point of the play.

Quarterbacks differ in their preferences. Some want to find a spot where they can have a long run-up to the throw, maximizing distance. Others just want to find a clean area -- inside or outside the pocket -- that allows them to step into the pass and follow through.

"The big thing for me is to buy time," says Vikings quarterback Kirk Cousins, who has a pair of Hail Mary touchdowns on his résumé. In 2011, Cousins, then a college quarterback at Michigan State, launched a 44-yard pass against Wisconsin that receiver Keith Nichol snagged out of the air and pushed over the goal line for the winning score. And in 2018, he hit Vikings tight end Kyle Rudolph in the end zone for a 44-yard scoring play on the final snap of the first half against the Detroit Lions.

"Can you find time in the pocket, or can you escape the pocket and put yourself in position to step up?" Cousins said. "By the time you run around a little bit, the receiver is in the end zone and that's where you want them. To throw the ball while they're still running, I think there is going to be a lower percentage chance of a completion. It helps if you can buy as much time as possible, let the receivers get their feet underneath them and be underneath the ball as it comes down."

The average time before a Hail Mary throw over the past decade is 4.75 seconds per ESPN tracking, almost twice as long as a normal play. In his three most recent Hail Mary attempts, veteran quarterback Alex Smith has averaged 7.42 seconds before throwing. Rodgers, meanwhile, has averaged 5.51 seconds before his 10 such attempts.

In some cases, the Packers have implemented distinctive pass-protection schemes to give him enough time to find the launch point he wants, most notably pulling a guard toward the sideline to give Rodgers what Cousins calls "a predetermined ability to roll out." In a 2015 play against the Lions, Rodgers escaped pressure inside the pocket by sprinting toward the right sideline, where he found enough open space to set his feet and throw a pass that traveled 61 yards in the air to tight end Richard Rodgers for the winning touchdown.

Aaron Rodgers used a "crow-hop" technique to get himself into balance just before the release.

"When you're outside the pocket, if you can come to a balance, it will allow me to put the ball where I want it," Rodgers said. "When you're throwing to the right on the run, and obviously you have to account for the ball tailing a little bit to the right because you're moving, but as I got to set up, into the crow-hop, I could put it exactly where I wanted to."

The perfect throw

The mechanics of throwing a Hail Mary pass extend well beyond buying time and launching. Quarterbacks must drop the ball into a relatively tiny window where as many as a dozen players could be gathered. The throw must be high enough to allow receivers to track it adequately. It must be far enough to reach or nearly reach the end zone but short enough not to risk traveling out of the back.

To compensate, quarterbacks adjust their technique. Rodgers said he typically takes "a bit of a bigger draw" before releasing, pulling his arm farther back than normal. Cousins makes sure his front shoulder is tilted up, and his back shoulder is down.

"That will put the arc on it," Cousins said. "You want the ball coming down at the receivers. You don't want a driven ball. As quarterbacks, we talk about how there are different types of throws. You have a driven ball. Then you have a ball with arc and also pace. And then you have a ball that truly is a moonshot. You want more of a moonshot, where the ball is truly coming down at the receivers in the end zone."

The force needed to make some of these throws can appear violent and stressful on the arm. But Rodgers compares them to smacking a baseball on the label or hitting the middle of a golf ball.

"You're torquing your body and laying it out there," he said. "But [when the mechanics are right], you don't feel it when it comes off your hand. You're getting so much rotation into it, and loading up on your back leg. It's actually a throw I've always enjoyed."

That force and violence must be tempered, however, the closer the line of scrimmage is to the end zone. Another part of the equation is avoiding the back of the end zone. It's not always the how-far-can-you-throw-it type of play that it's commonly thought to be.

"You want to err on the shorter side rather than the longer," Rodgers said. "Once you get inside the 40-yard line or so, that's where you really have got to start thinking about the exact spot and missing shorter or deeper in the end zone. The last thing you want on the last play of the game is to throw the ball out of the back of the end zone."

The window for a successful throw, Cousins said, is sometimes less than 5 yards long.

"Say you're throwing it from midfield," he said. "That could be a 50- or 55-yard throw, and you have to be accurate. You could say the end zone is 10 yards deep, but really it has to be a 5-yard window. You've got that back line you can't contend with, or it goes out of bounds, and then you have a front line that you can't contend with. You can't have the ball tipped forward too much and hope that someone can catch it and run it in. You really want it to land in the middle of the end zone, and you could argue that's a 4- or 5-yard window."

On Cousins' 2018 Hail Mary strike to Rudolph, the pass landed perfectly 5 yards deep in the end zone.

The scrum

Rudolph has played football at some level for the better part of two decades. Over that time, he estimates he has been part of Hail Mary attempts perhaps 10 times. Only one -- that pass from Cousins -- even came close.

"The crazy thing is that it's a play we rarely practice full speed," he said. "We rarely practice it against a defense. We walk through it every Saturday morning. Here, at least, we don't even throw the ball. It's just a walk-through situation. But it can obviously make a difference in the outcome of a game."

At nearly 6-foot-7, Rudolph is a prime Hail Mary target. More often than not, however, he has found himself situated as what he called a "middle guy" -- an initial target who has a chance to tip the ball to a teammate in front of him if he can't catch it himself. "You probably see a completion of a Hail Mary tip as much as a straight catch," he said.

That's why defenders say their top priority is to subordinate the instinct for an interception and simply swat the ball to the ground at all costs. Of the 193 total Hail Mary attempts since 2009, 50 have been intercepted -- including four by receivers (Julio Jones and Keenan Allen) or tight ends (Tony Scheffler and Coby Fleener) who have been used on defense to maximize their ball skills. A total of 19 have been caught, either for a touchdown or short of it, meaning that about two-thirds have been tipped or otherwise fallen to the ground.

Arguably the most famous consequence of a failure to knock down the ball came in 2012, when Packers safety M.D. Jennings jumped above the scrum in an attempt to intercept Seattle Seahawks quarterback Russell Wilson's pass. Jennings appeared to have the ball initially, but Seahawks receiver Golden Tate got one arm around it as they fell to the ground, and the game's replacement officials -- the NFL was in the middle of a lockout of its regular officials -- awarded the catch and winning score to Tate.

"You're thinking, 'Make sure everyone stays in front of you and then just high-point the ball and smack it down,'" Pittsburgh Steelers cornerback Joe Haden said. "Your instincts are to want to get that pick, but coaches are always telling us not to tip it in the air, and that's what can happen if you somehow don't get the interception."

Even that technique can be fraught with risk, however. On the final play of a 2010 game in Jacksonville, Houston Texans, safety Glover Quin tried to knock down a David Garrard pass intended for Mike Sims-Walker. Instead of the ball deflecting down, however, it traveled horizontally into the hands of Jaguars receiver Mike Thomas, who overcame his shock to secure the catch at the 1-yard line and step into the end zone for the winning score.

That coaching point carries an implicit understanding that players on both sides are essentially immune from pass-interference penalties. There hasn't been a single such flag on a Hail Mary pass since at least 2009, largely because the NFL does not want a game decided on a penalty. Most Hail Mary plays turn into a mosh pit of pushing, pulling, boxing out and bracketing receivers on all sides.

"You at least are trying to make them catch it through your body," Steelers safety Terrell Edmunds said. "You don't want them to have a clean catch, because a lot of time [receivers] are taller than you. You want to force as much contact as you can with them to disrupt the pass and disrupt the catch.

"You know that a flag is going to be rare. It's the last play of the game usually, and people do everything. You have to stand your ground. That's a man's time right there."

For that reason, most successful Hail Marys can be traced in part to a defensive breakdown. Perhaps the most famous of all Hail Marys, the 1984 pass from Boston College's Doug Flutie to receiver Gerard Phelan, worked in part because University of Miami defenders let Phelan get behind them.

In Detroit last season, Rudolph ran to his usual spot in the middle of the end zone. One defender hung on his back, but teammate Aldrick Robinson stood in front of him to effectively, if inadvertently, shield him from any other defenders. Rudolph calmly reached up and snagged the ball out of the air.

"Usually it just turns into a giant scrum," Rudolph said. "The one we executed in Detroit was thrown so perfectly that their guys didn't have time. I ran down into the end zone, I turned and all of a sudden it was there."

Rodgers acknowledged that two of his three Hail Mary touchdowns -- against the Lions in 2015 and during the playoffs in the 2016 season against the New York Giants -- were "both misread by the defense." The Lions kept Richard Rodgers in front of them but had no one in place to obstruct his path to the ball. The Giants, meanwhile, allowed receiver Randall Cobb to get behind them and catch the ball inches from the back line.

The third? Aaron Rodgers beat the rarest of defensive strategies against the Hail Mary: a blitz.

Sending the house

In a 2015 playoff game, Arizona Cardinals coach Bruce Arians decided to send seven pass-rushers as Rodgers set up at the 41-yard line with five seconds left in regulation, later telling reporters that he overruled defensive coordinator James Bettcher because "most teams play the prevent" in such situations. Indeed, Rodgers was flushed from the pocket and forced to make an awkward, off-balance throw before receiver Jeff Janis reached the end zone. That the ball settled into Janis' hands for a score seemed more a result of Rodgers' elite arm than the Cardinals' defensive scheme.

It was the only time Rodgers has been blitzed on a Hail Mary throw -- although the Kansas City Chiefs also sent a six-man rush at the end of the first half Sunday night and sacked Rodgers before he could get off a likely Hail Mary pass. Coaches have sent more than four pass-rushers on only 15 of the 193 Hail Mary throws (7.8%). On the other hand, they have sent three or fewer rushers on 109 of them (56.5%), accounting for nine touchdowns against.

Earlier this season, the New Orleans Saints sent five pass-rushers on a final-play Hail Mary against the Cowboys. Dallas quarterback Dak Prescott threw under duress after only 2.54 seconds, and his pass was intercepted 10 yards short of the goal line.

"When you get one of these last-play situations, you have two choices," Saints defensive coordinator Dennis Allen said. "You have a choice of taking your chances in three-man rushing, which a lot of teams do, and putting more defenders back there to defend the ball when it gets down the field. You've got more back there than they've got to catch it.

"The other thought is take your chances up on the line of scrimmage and not let the quarterback get the ball down the field. That's been a little bit of a philosophy of ours. We're going to try to do what we can to affect the quarterback and not let those guys run 40 yards down the field and let the quarterback launch the ball down the field to have a chance down there. We'd rather take our chances on the line of scrimmage."

As with standard plays, the blitz is most effective as a changeup. But the debate on whether to use it on a Hail Mary is a symbol of sorts, a sign that the play has caught the attention of those who think most deeply about the game.

Sunday night in Kansas City, for example, the Packers overtly manipulated themselves into position for one. They called a timeout as the Chiefs were getting into position for a field goal attempt with 1:15 left in the half, and then once getting the ball back, Rodgers took the unusual step of cutting inside on a scramble to pick up 5 extra yards as the clock ticked down, rather than going out of bounds. He jumped off the ground, called a timeout with three seconds left to set up for the big throw.

On this occasion, of course, the Chiefs' defense was ready.

The Hail Mary is no longer a matter of closing your eyes and uttering a prayer when all else is lost. It doesn't catch anyone by surprise. It's serious business, meant to manipulate and exploit the NFL's incentivization of the passing game. More than hope, it's about strategy. In the age of big-armed mobile quarterbacks and super-tall pass targets, it's another hammer in the collective offensive toolbox.

ESPN's Mike Triplett contributed to this report.