The 1984 campaign did not mark the Dolphins’ first Super Bowl appearance. From the 1971 season through ’73, Miami advanced to three straight title games, winning twice. The ’72 squad remains the only team in NFL history to finish a season undefeated, and they famously pop champagne every time the last no-loss NFL team falls in any given season.

TIME CAPSULE January 1985 JANUARY 1 MTV Networks launches Video Hits One (now known as VH1), a soft-rock spin-off aimed at the older set. Its first video is Marvin Gaye’s rendition of “The Star-Spangled Banner.” PEOPLE magazine’s review described the new network thusly: “They say it’s a channel for people who like music but who are no longer on the cutting edge of rock’n’roll. That’s just a delicate way of saying it’s music for those of us who are future full-figured women, and for men who’ll soon be searching for their receding hairlines.”

In 1982, the Dolphins returned to the NFL’s final game for the first time in a decade. They met the Redskins in Super Bowl XVII on Jan. 30, 1983. They took a 17-10 lead into halftime at the Rose Bowl, behind a 98-yard kickoff return by Fulton Walker, only to fall, 27-17. Their quarterback, David Woodley, finished with four completions in 14 attempts for 97 yards, a touchdown and an interception—a quarterback line among the worst in title game history, the kind that does not encourage a replacement so much as it begs for one.

The seeds for 1984 were actually sown then. “That was probably the pinnacle of our defensive core,” says Doug Betters, a Dolphins defensive end from 1978 to ’87. “The Killer B’s. We were playing at the top of our game, but our offense was lagging behind. If we had Dan in that Super Bowl, we could have beaten the Redskins.”

All season, Betters says, the Dolphins’ defensive coaches told them not to worry about the offense, to shut down teams and seize games on their own. But this was before defenses regularly substituted. The cumulative impact was a defense worn down by the time it reached the Super Bowl. “We felt like we had been a quarterback or a player away from winning it all,” says Nat Moore, a Miami receiver from 1974-86.

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The Dolphins needed a quarterback, and—blessed by good fortune, or, in hindsight, doomed one year too late—the 1983 NFL Draft was filled with more elite signal callers than any edition in league history, before or since. That group included Marino, who tossed 37 touchdowns as a junior at Pittsburgh but returned to a team that struggled his senior year, when he had only 17 TD throws. To explain the drop off, rumors of drug use by the Panthers ran rampant in the lead up to the draft, with Marino no exception. (He has denied them.)

The draft was full not only of quarterbacks but of elite talent. Six future Hall of Fame players went in the first round. Don Shula, the Miami coach, didn’t expect Marino to be available when the Dolphins picked 27th. But he did meet Marino at the NFL Combine and came away impressed that the quarterback did not make excuses for how poorly his senior season went. Shula filed that nugget away.

As the draft approached, Shula targeted a defensive lineman from Syracuse named Mike Charles. (He got him anyway, in the second round. Charles played nine seasons with three franchises, including 1984 with the Dolphins.)

When the draft started, John Elway went first overall to the Colts, who traded him to the Broncos. The Chiefs took Todd Blackledge seventh, the Bills took Jim Kelly 14th, the Patriots took Tony Eason 15th and the Jets took Ken O’Brien 24th. Suddenly, Shula had to make an unexpected decision that wasn’t a difficult choice at all. Marino was the Dolphins’ pick, one of four members of his quarterback class to lead a team into the Super Bowl and one of three, along with Elway and Kelly, now enshrined in the Pro Football Hall of Fame.

The Dolphins teams that seized Super Bowls in the 1970s did so behind running backs. Miami had more than seemed fair, with Mercury Morris, Larry Csonka and Jim Kiick all patrolling the same backfield. Then Marino arrived. “They were nobody’s idea of an exciting team,” says Greg Cote, a longtime writer for the Miami Herald. “Marino was the opposite. He was a sexy, curly-headed kid with a lot of bravado about him.”

In his first practices, Marino impressed Shula. He was better than expected: stronger arm, quicker release, faster at making decisions. He also had an innate sense of when the pass rush was closing in and a nifty slide step to avoid pressure. That bought him extra time to throw farther down the field.

JANUARY 13 Edmonton Oilers star Wayne Gretzky, 23, becomes the youngest player in NHL history to score 400 goals. Bruce Bennett/Getty Images

Teammates noticed, too, the way the ball whistled when it left Marino’s hands. Receivers told Betters they worried that a particularly hard throw would break a finger in practice. “He had a reputation from college as being very confident,” says Jim Lampley, the broadcaster and television personality who did pre- and post-game work at the Super Bowl in 1985. “But it was what he did on the field that was amazing. He’s the first guy I remember who could make the back-shoulder throw. He had a unique arm. Unbelievable velocity.”

Marino didn’t open the 1983 season as the starter, though, a decision that Shula later admitted was a mistake. Marino first played in Week 3, against the Raiders, and again in Week 5, against the Saints. His started for the first time against Buffalo in Week 6, and he threw for 322 yards and three touchdowns, although he was intercepted twice. The Dolphins lost all three of those games but still managed a 12-4 season that culminated in a playoff berth.

The Dolphins and their rookie signal caller hosted Seattle in the divisional round on Dec. 31, 1983. Marino threw two touchdowns and two interceptions and his rookie campaign ended. “We didn’t know how good we could be,” says Tony Nathan, a Dolphins running back from 1979-87.