HOUSTON -- For an NFL team that's looking for an up-and-coming playcaller to be its next head coach, the 500-point offense is the gold standard.

Those offenses are coveted, celebrated and chronicled. Those teams are framed as groundbreaking and ahead of the curve, as the ones that have cracked the code.

And then they almost never win the Super Bowl.

The 2016 Atlanta Falcons were the 19th team in the Super Bowl era to finish a season with 500-plus points on offense. Yet with their historic, confounding collapse in Super Bowl LI on Sunday, the Falcons became the 15th team to score 500 points in a season yet not win the Super Bowl.

Even as the league continues to tip the rulebook toward offense, most of the highest-scoring teams in league history continue to conclude their seasons devoid of the Lombardi trophy. In fact, seven of the teams that finished a season with at least 500 points didn't even make it to the league's title game. The 1994 San Francisco 49ers, 1998 Denver Broncos, 1999 St. Louis Rams and 2009 New Orleans Saints are the only teams to score 500 points in a season and go on to win the Super Bowl.

Stunned by the loss to the Patriots, Matt Ryan said: "We always play aggressive and play to win, and we had opportunities as players. We had opportunities, and we made some mistakes on the field that, at the end of the day, ended up costing us." Eric Seals/USA TODAY Sports

The Falcons led the NFL in scoring this past season with 540 points, and after they failed to hold a 25-point lead over the New England Patriots and lost 34-28 in overtime, disconsolate, befuddled QB Matt Ryan was left with "no words" to describe what happened.

"I thought we played the way that we play," Ryan said. "We always play aggressive and play to win, and we had opportunities as players. We had opportunities, and we made some mistakes on the field that, at the end of the day, ended up costing us."

Ryan, the newly minted league MVP, has plenty of high-profile company. Tom Brady and Peyton Manning lead the way on the quarterbacks-of-offenses-that-didn't-get-it-done list. Drew Brees and Aaron Rodgers are on there, along with Hall of Famers Kurt Warner and Dan Marino.

In 2013, Manning set a single-season record for passing yards (5,477) and touchdowns (55), and the Broncos became the only 600-point team in league history. The Broncos lost the Super Bowl by 35 points to the Seattle Seahawks.

Brady was behind center for the Patriots in 2007, when the team finished the regular season 16-0 and scored 589 points. The Patriots were upset 17-14 by the New York Giants in Super Bowl XLII.

Brady's Patriots also scored at least 500 points in the 2010, 2011 and 2012 seasons but did not win the Super Bowl. In 2011, three teams topped the 500-point threshold -- the Patriots, Saints and Green Bay Packers -- and none of the three won the Super Bowl.

Ask coaches and personnel people around the league, and theories about this phenomenon abound, but three rise to the surface.

First, the highest-scoring teams that included a solid running game have won the title. The 1999 Rams scored 32.9 points per game as the Greatest Show on Turf, and they were fifth in the league in rushing (128.7 yards/game). The 2009 Saints were sixth in the league in rushing (131.6 yards per game). The 1994 49ers were sixth in the league in rushing (118.6 yards/game). The 1998 Broncos, with Hall of Famers John Elway and Terrell Davis, were second in the league in rushing (154.3 yards/game).

The only team in the 500-point club that had a top-six rushing attack but didn't at least play in the Super Bowl was the 2011 Saints.

Second, the adage that "defense travels" is never more true than in the title game. Rhythm and timing are keys to an offense, and with the Super Bowl's extended buildup, pregame warm-ups on a field crowded with people and extended halftime, it's difficult to keep your routine.

But No. 1-ranked defenses? In the past four seasons alone, three No. 1 defenses have prevailed in the Super Bowl. The Seahawks stifled the Broncos' 606-point offense, the Broncos overpowered the Carolina Panthers' 500-point offense, and the Patriots recovered just in time to finish the Falcons.

Third, with so much emphasis on the pass in most 500-point offenses, sometimes those offenses reach when the simplest of plays will do.

On Sunday, the Patriots had momentum in the fourth quarter, but the Falcons still had a 28-20 lead and the ball at the New England 22-yard line with 4 minutes, 40 seconds to play. Three nondescript running plays and a field goal likely would have preserved the win for the Falcons.

Instead, after a 1-yard loss by RB Devonta Freeman on a first-down run, the Falcons went to the passing game. Ryan was sacked for a 12-yard loss on second down, and then Jake Matthews was flagged for holding on the next play -- a pass play.

The Falcons were pushed back to the New England 45-yard line, out of field goal range. They punted, and New England scored to tie the game and went on to win in overtime.

"Well, we thought we'd have a good look based on the personnel that was in the game for them," Falcons coach Dan Quinn said. "We trust our guys, so we thought that was the opportunity to let it rip. When it doesn't go that way, then it's easy to question it."

"I think everybody across the board would have liked to have done things differently because at the end of the day, we didn't get the job done," Ryan said.