Sportswriting so often succumbs to the mawkish that it can be hard to recognize a truly extraordinary story when it comes along. But seriously, these Broncos qualify. If Kevin Costner wrote this script — for himself, naturally — you’d roll your eyes.

Two and a half years ago, Peyton Manning didn’t know if he would play again. Two and a half months ago, John Fox didn’t know if he would coach — or do anything else — again.

In between Manning’s cervical fusion surgery and Fox’s open heart surgery, the Broncos lost a host of front-line players — cornerback Champ Bailey, left tackle Ryan Clady, pass rushers Elvis Dumervil and Von Miller. The Dumervil episode — which turned on a fax machine and communication snafu worthy of the Marx Bros. — gives the tale its comic relief.

But the Manning story trumps them all. He was understandably reticent to talk about his physical difficulties when he first arrived in Colorado. He had lived for 14 years in a professional world in which you divulged nothing about your physical vulnerabilities lest the information be used against you in your next game.

Over time, details have emerged. The first throw after multiple neck surgeries, to old pal Todd Helton in the Rockies’ indoor batting cage, was so feeble Helton thought it was a joke. Early on, he was unable to lean on his right arm or feel his right hand. They told him the nerve regeneration would take time.

“Unbelievable” is the most overused word in sports, but the fact that Manning is going to the Super Bowl for the third time at age 37 is still hard to believe, even after one of the best seasons we’ve ever seen. The fact that the Colts cut him after 14 seasons, 13 of them fabulous, was hard to believe. The fact that he found a new home in Denver, where he immediately produced consecutive 13-3 seasons, is hard to believe. Even, maybe, to him. Somebody asked if he expected this.

“I can’t say that for sure,” he said after Sunday’s 26-16 victory over the New England Patriots in the AFC Championship Game at Mile High. “I was truly taking things slowly, kind of phase by phase. Nobody could give me a real timetable or prediction as far as physical recovery.

“I had never switched teams before. I had no idea how long it would take to form some chemistry offensively, to get comfortable with the culture. I talked to some other players that had changed teams and I think it depends on the individual — how you mesh with your new teammates, how comfortable you are in your new surroundings. So the folks here in Denver, the city and the organization, made me feel welcome. That has certainly been very helpful. I have put a lot of hard work in. A lot of people — teammates, coaches, trainers — have helped me along the way.”

Sunday’s game was like a gift from his new home. In the middle of January, Denver delivered a September day, sun-splashed with temperatures in the 60s and a slight breeze. You might remember what Manning did last September. Fifty-two points in one game. Forty-nine in another.

The Broncos didn’t score that much against the Patriots, settling for field goals more than usual, but Manning was basically the same guy, completing 32 of 43 passes for 400 yards, two touchdowns, no interceptions and a passer rating of 118.4. Among all the other records he set or challenged this year, the fact that he became just the third quarterback to throw for 400 yards in an AFC championship game seemed barely a footnote. The Broncos’ 507 yards of offense was the most a Bill Belichick-coached Patriots team has ever surrendered.

You had a feeling it might be Manning’s day early when he bobbled a shotgun snap, then bobbled it again — that close to an early fumble, twice — and not only regained control but hit Eric Decker for a first down.

“New England does a great job disguising coverages and you do want to get a post-snap read on their coverages,” Manning explained. “Your job is to look the ball in, and I’m not sure I looked it in all the way. I was trying to get a read on (safety Devin) McCourty or (safety Steve) Gregory and I thought I had it, then I bobbled it again. I was glad to finally get a hold of the grip and get the laces. I know my quarterbacks coach (Greg Knapp) will be proud of me that I was still able to go through my progression on that play and find an open receiver.”

This is the sort of thing that still gives Manning pleasure, pleasing a position coach by attending to the smallest details.

His counterpart, Tom Brady, to whom he is often compared unfavorably owing to Brady’s 3-1 edge in Super Bowl championships, was also good, completing 24 of 38 for 277, one touchdown and a rating of 93.9. But he missed some available big plays down the field, one to Julian Edelman early and another to Austin Collie later.

“I just overthrew them,” Brady said.

The storyline coming in was the magnificent performance of Patriots running back LeGarrette Blount the previous week. All anybody could talk about was whether the Broncos could stop New England’s power running game. After rushing 24 times for 166 yards and four touchdowns against Manning’s former team the previous week, Blount carried five times for six yards against the Broncos.

“They didn’t play the Broncos last week,” said Bailey, who returned to his left cornerback position after a long absence and will play it in his first trip to the Super Bowl after a 15-year career that has included 12 Pro Bowl selections. “They are a good running football team, but we got some guys up front that don’t like that, and they’re going to do whatever it takes to stop that run. That’s really what it’s all about, the guys up front.”

After rushing for 234 yards as a team against the Colts, the Patriots managed but 64 against the Broncos. As they did the previous week against San Diego, the Broncos deployed their base defense on more snaps than usual, moving Bailey into the spot vacated by Chris Harris, who tore an ACL last week. Bailey and Dominique Rodgers-Cromartie made a formidable tandem in pass defense and Tony Carter, called on to replace Bailey as the nickel back, held his own.

After losing defensive tackle Kevin Vickerson late in the regular season, enormous Terrance Knighton — they call him Pot Roast for a reason — repeatedly forced his way into the Patriots’ backfield and disrupted their running plays before they could get started.

But devotion to the running game was not really the Patriots’ problem. Their plan seemed to call for Brady to pass against the Broncos’ base defense and run against the nickel. He started every possession of the first quarter with a pass. All three ended in punts, two without gaining a first down. By the time Brady got into scoring position late in the second quarter, he trailed 10-0.

“We definitely had some chances on third downs and I had a chance down some lanes and I certainly wish I would’ve made that,” Brady said. “You know, it’s a tough day for our team. We fought hard and we came up short against a pretty good team.”

The Broncos settled for field goals on four of six scoring drives, a much higher percentage than usual, but they dominated the time of possession, 35:44 to 24:16.

“We were able to hold them to some field goals defensively, but our third-down defense and our third-down offense, especially in the first half, weren’t in it,” Belichick said. “We let them get too far ahead and they stayed on the field.”

The Broncos led 13-3 at intermission and emerged from the locker room with a long touchdown drive to open the third quarter. The Patriots responded by driving 51 yards in an effort to stay in the game. Rather than take a field goal on fourth-and-3 at the Broncos’ 29-yard line, Belichick elected to go for it. Brady had barely looked upfield when Knighton slipped past Patriots All-Pro guard Logan Mankins, wrapped him up and tossed him to the ground.

The Broncos responded with another drive of their own, culminating in another field goal, which gave them a 20-point lead with 12 minutes remaining. The Patriots made it interesting with a couple of fourth-quarter touchdowns, but they never got within a single score. Manning characteristically credited offensive coordinator Adam Gase for a good plan.

“They do a great job of taking away your key receiver,” Manning said. “With us, we’ve spread the ball around so well all season, it’s hard to know who really to key on. On any given play, one of five guys could get the ball. I think that puts pressure on the defense.”

Having surrendered 280 rushing yards to the Broncos in the regular-season meeting between the teams in New England, Belichick seemed as focused as Fox on stopping the run. When Knowshon Moreno and Montee Ball combined for minus one yard in the first quarter, Manning turned to his many weapons in the passing game. Demaryius Thomas caught seven passes for 134 yards and a touchdown. Tight end Julius Thomas caught eight for 85. Veteran Jacob Tamme, his teammate in Indianapolis as well, caught the first touchdown. In all, Manning spread his 32 completions among eight receivers.

It didn’t help the Patriots that their best defensive back, Aqib Talib, went out early with a knee injury after colliding with Wes Welker, but the Broncos had too many weapons for the Patriots even before that.

A year ago, the Broncos went 13-3, got the top seed in the AFC, then blew their first playoff game, much as John Elway’s Broncos did in 1996. A year later, they bounced back to make the Super Bowl, as Elway’s Broncos did in 1997.

Fox, who underwent open heart surgery on Nov. 4, will be coaching in the championship game for the first time in 10 years. His only other trip there as a head coach ended in a 32-29 defeat for his Carolina Panthers to Brady and the Patriots.

“It feels great,” Fox said. “It’s felt great for about eight weeks. Not so much before that. My medical team did great. My wife, Robin, my nurse, did even greater. A lot of good people are the reason I’m standing here.”

Manning will be back for the first time in four years, and that will be the most compelling storyline of Super Bowl 48. Amazingly, he has a chance to rewrite his biography in the twilight of his career, much as Elway did. For 14 years, Elway was the awesomely talented quarterback who could win a ton of games but never the big one. He finished by winning consecutive Super Bowls and the old tag vanished.

Manning is the awesomely talented quarterback, albeit in a different way, who won a Super Bowl following the 2006 season and lost his second following the 2009 season. That doesn’t sound so bad, but compared to Brady, who has played in five and won three, it produced a narrative that Manning hasn’t been as good a clutch player as his rival.

The bizarre part of this analysis is the assumption that Brady’s team, the Patriots, and Manning’s team, the Colts, were essentially equivalent, leaving the quarterbacks as the difference in the number of titles. This happens to be complete nonsense. The Patriots of the Brady era were superior to the Colts of the Manning era, but these tags seem to have a glue that’s impervious to logic.

Now Manning has the opportunity Elway had, at the same age. Sunday’s win gave him a 2-1 record vs. Brady in AFC championship games. A victory in New Jersey two weeks from now would be his second in three tries at the Super Bowl. And who knows? If Manning’s Broncos continue to follow the template of Elway’s Broncos, he could have yet another opportunity at 38.

But one thing at a time. Manning lost his ability to throw a football at age 35 and regained it through a long, painstaking rehabilitation. Two years later, he produced arguably the best season by a passer in NFL history at age 37. If you hadn’t seen it, you wouldn’t buy it.

“You do take a moment to realize that we’ve done something special here, and you certainly want to win one more,” Manning said.

“I just shoot him a pre-game thought,” said his older brother, Cooper. “It was, ‘Hey, you’ve come this far. Go ahead and pretend you’re a 10-year-old playing in the front yard.’ That’s what it looked like.”