When you think of great underdogs enjoying unlikely success, the New Orleans Saints offense doesn’t exactly come to mind. When Drew Brees & Co. are playing at the highest level, they often seem several steps ahead of the opposition, with Brees alternating between easy outlets for first downs and surgical strikes downfield for touchdowns in the service of head coach Sean Payton. At their best, they’re as good as anybody in football.

Before they all arrived in New Orleans, they were a hodgepodge of players and coaches nobody wanted or valued appropriately. More than any other team in football, the Saints under Payton have found ways to extract value out of players who don’t fit into traditional boxes or perceptions of what football players should be shaped like. In fact, the Saints have often been disappointed when they’ve gone out of their way to acquire traditional players at the top of the draft. New Orleans has cut its teeth with unlikely superstars, and that starts with the guy who begins the whole thing.

The Architect

Nowadays, Payton is widely considered one of the most valuable coaches in football. Like many players, it took absence to reveal his true impact: During his suspension last year as a result of the Bountygate scandal, the Saints notably fell from 13-3 to 7-9, but with Payton returning this season, they’re one of the five undefeated teams left in football. Payton has a Super Bowl ring, earned by upsetting the mighty Peyton Manning with a hyperaggressive game plan that was virtually unprecedented in the Super Bowl, famously attempting an unexpected onside kick to start the second half. He’s one of the game’s brightest offensive minds and most creative tinkerers.

This is the same Sean Payton who, in 2002, was being emasculated on the Giants sideline by head coach Jim Fassel. Payton, who had been calling the plays in New York for two-plus seasons, was scapegoated in the New York media as the reason why an offense with the megawatt power of Kerry Collins, Ron Dayne, and Ike Hilliard couldn’t score points. By Halloween, Fassel agreed and took back the play-calling duties he had given Payton before the 2000 season, worrying that the offense was too complicated. A Giants attack that had been averaging just 12.7 points per game that season rocketed all the way up to 25.7 points per contest, and for weeks, every time the Giants scored, the cameras would cut to a shot of Payton dutifully looking at a clipboard or wrangling some linemen for an extra point with the same implied message: “This guy is a dummy, right?”

Payton moved on after the season to Dallas, where he served as the team’s quarterbacks coach before eventually becoming assistant head coach and taking over as offensive playcaller from Bill Parcells. In 2004, the Raiders were so close to hiring Payton to take over as head coach that staffmate Maurice Carthon actually told the media Payton was taking the gig; Jerry Jones came back and doubled Payton’s salary to $1 million to make him stay.

Two years later, Payton would leave Dallas for good. He interviewed with the Packers before they turned to Mike McCarthy, and then offered his name for what was likely the least inviting head coaching job in the league at the time. The Saints had just endured a 3-13 season in the aftermath of Hurricane Katrina, which had decimated both the city of New Orleans and the Superdome, forcing the Saints to play home games in Baton Rouge, San Antonio, and the Meadowlands. Even independent of the storm, the team was bereft of talent after years of questionable drafts; any new head coach in New Orleans would have to decide whether the immortal Aaron Brooks would be the long-term quarterback in town. Payton won a search that included Donnie Henderson, Carthon, Mike Sherman, and Mike Martz, none of whom would go on to get a head coaching job in the NFL.

Ironically, Payton’s star pupil in Dallas didn’t burst onto the scene until Payton had already left for New Orleans. Tony Romo was an undrafted free agent out of I-AA Eastern Illinois who spent three years on the Dallas practice squad behind the likes of Drew Henson and Vinny Testaverde, but Payton (himself a former Eastern Illinois quarterback) spent years molding Romo into a viable NFL player. During Payton’s first year in New Orleans, the Cowboys finally gave up on the statuesque Drew Bledsoe and brought in Romo, who immediately became one of the league’s most compelling quarterbacks. The quarterback with whom Payton would instead be forever linked was also unwanted, but for entirely different reasons.

The Engineer

Almost exactly one year after Payton was stripped of the play-calling duties in New York, Drew Brees lost his grip on the starting job in San Diego. On November 10, 2003, Marty Schottenheimer officially benched Brees, who had thrown 12 interceptions against seven touchdowns and had a passer rating of just 63.3, for 41-year-old Doug Flutie. Brees would get his job back at the end of the year for evaluative purposes, but after a rough finish in Week 17 saw Schottenheimer bench him again, the offseason was rife with rumors that the Chargers would use the first overall pick in the upcoming draft on a quarterback, likely Eli Manning. The team did select Manning before trading him on draft day to the Giants in a deal that netted them Philip Rivers, Shawne Merriman, Roman Oben and Nate Kaeding.

Brees, in the third year of his rookie deal, was now the bridge to the future. He was never the obvious choice as San Diego’s long-term starter; after the Chargers took him with the first pick of the second round in the 2001 draft, there was plenty of speculation that Brees couldn’t cut it at the pro level. He had played in a spread offense at Purdue, back when spread was a dirty word, and he was generously listed at 6 feet. And when he failed to impress after those first three years, well, the book was closed on Brees. He was Colt McCoy or Chad Henne or, at his best, Andy Dalton: a guy who could be a competent fill-in and nothing more. The Chargers were already booking their future without him.

Of course, Brees came back in 2004 a changed man. He beat out Flutie and Rivers for the starting job, completed 65.5 percent of his passes during a breakout season, and made it to the Pro Bowl. The team franchised Brees in 2005, but after nearly completing a second consecutive excellent season, Brees famously suffered a torn labrum in his throwing shoulder in the second quarter of the Week 17 game against the Broncos, leading Chargers GM A.J. Smith to pass on retaining Brees, either with another season on the franchise tag or on a viable long-term deal. Brees hit the market and ended up with two real suitors: New Orleans, which had Payton and an open spot at quarterback, and Miami, which had Nick Saban and a promise to try to compete immediately with a veteran roster. After Brees refused to come off his demands for a six-year, $60 million deal, the Dolphins eventually abandoned their pursuit and traded for Daunte Culpepper, giving up a second-round pick for a player coming off a traumatic knee injury. It was the second — and last — time an NFL team would fail to identify Brees appropriately as the best quarterback available to them. Ironically, of course, Culpepper would spend most of his time in Miami injured or playing through pain, while Brees hasn’t missed a meaningful game since he arrived in New Orleans, where that six-year, $60 million deal he received became one of the biggest bargains in the history of free agency.

Now, the coach who had been run out for Fassel and the too-short quarterback who had been benched and passed on twice were together. It was time to fill in the rest of the pieces.

The Supporting Cast

Just two of the 11 offensive starters who took the bulk of the snaps for the 2005 Saints would remain in the starting lineup for the 2006 team: veteran wideout Joe Horn and 2005 first-round pick Jammal Brown, who moved from right tackle to left tackle and made the All-Pro team. Fullback Mike Karney and young wideout Devery Henderson would also play important roles on the 2006 team, but the vast majority of the starters from the 3-13 team left town. Brooks was cut. Antowain Smith, filling in for an injured Deuce McAllister, never played in the NFL again. Donte’ Stallworth was traded at the end of camp to the Eagles. The left side of the line departed, and center LeCharles Bentley, the team’s best player and only Pro Bowler in 2005, signed a $36 million deal to join the Browns. Payton had Brees and a lot of holes left to fill. It’s hard to imagine a team finding more during one offseason than the Saints did; the players found by general manager Mickey Loomis and developed by Payton over the next several springs would become cornerstone pieces for one of the league’s greatest offenses.

The Running Game

Ironically, the one player the Saints expected to become a franchise player from that year’s haul failed to live up to expectations. The Saints drafted Reggie Bush with the second overall pick in the 2006 draft after the Texans famously failed to come to terms with Bush on a pre-draft contract and quickly negotiated a deal with defensive end Mario Williams. With Bush falling into their laps, Payton quickly went to work building a role that capitalized on Bush’s rare variety of skills. While Bush was a useful receiver his rookie year, catching 88 passes, he was a very inconsistent runner, producing just 3.6 yards per carry. His five seasons with New Orleans would end up being pockmarked by inconsistency and injuries; Bush never played a full season in town after his rookie year, and his role with the offense declined each season. By the time he left town after the 2010 season, he was seen as a bust; only in Miami did Bush revitalize his career, which has led to a brilliant start in Detroit this season.

The Saints instead produced a running game that relied upon no-names. Bush and a returning McAllister would split the load in 2006, but Bush struggled with the aforementioned woes, while McAllister was hurt again in 2007 and out of football after 2008. That created a space for Pierre Thomas, whom the team signed as an undrafted free agent out of Illinois following the 2007 draft. Since Thomas entered the league, just five players who have carried the ball as frequently have produced more yards per carry than Thomas. He would be joined by Broncos castoff Mike Bell and later Tiffin University product Chris Ivory, both undrafted free agents. Of course, the one player who would eventually fail as a Saints back was the most conventional runner the team could acquire, 2011 first-round pick Mark Ingram, who has averaged just 3.9 yards per carry while showing little aptitude as a blocker or receiver.

The model that Payton began to build for Bush was perfected when the Saints acquired Darren Sproles in free agency. While Bush had the size to approximate the workload of a full-time back, Sproles was a 5-foot-6 scatback with a broken leg on his résumé whose best work had come as a return man. Where other teams saw limitations, the Saints saw opportunities. Sproles had always been a good receiver out of the backfield, but he didn’t really have the skill set to be a between-the-tackles runner. Payton took away many of Sproles’s duties as a traditional running back and amped up his usage as a receiver by moving him around the formation; he does his best work now as a slot receiver running Wes Welkerian option routes past overmatched linebackers, notably excelling in the red zone. Again, the Saints got the most out of a player whose size didn’t match up with the league’s idea of what a player at a given position should look like. That would keep happening up and down the offensive roster.

Those running backs needed a new offensive line, which came into focus shockingly quickly. Brown moved to left tackle and excelled, while the team replaced Bentley with the player whom Bentley supplanted in Cleveland, Jeff Faine. Jon Stinchcomb, a 2003 second-rounder, emerged after injuries and obscurity to take over at right tackle, and former backup Jamar Nesbit filled in at left guard for the short term.

The notable arrival that offseason was fourth-round pick Jahri Evans. A left tackle at tiny Bloomsburg University of Pennsylvania, Evans moved to right guard in camp and started from Week 1 on. As in, Evans started the next 114 regular-season games before finally succumbing to an injury that kept him out of the Saints-Cardinals game two weeks ago. Then, in 2008, the Saints would use their fifth-round pick on another left tackle, taking Nebraska product Carl Nicks, who had a tumultuous final season in school that saw him banned from the university’s Pro Day. Nicks was pushed inside to left guard and also started from Week 1 on; by the time Nicks finished his four-year career with the Saints, he and Evans were the best one-two punch of guards in football by a significant margin.

The Saints didn’t even skip a beat when Brown went down with a hip injury before the 2009 season; they stuck in another fourth-rounder, Jermon Bushrod, and saw him make it to two Pro Bowls before leaving for Chicago this past offseason. Most teams dream about turning three guards taken with triple-digit picks into Pro Bowlers; a lot of the credit for that has to go to offensive line coach Aaron Kromer, who followed Bushrod to Chicago this offseason.

The Receivers

Of course, the Payton offense is predicated on a heavy dose of passing, and Brees needed receivers to hit with his throws. He had one season of Horn before the veteran left for Atlanta on an ill-fated four-year, $19 million contract. Henderson stuck around as an occasional deep threat, and I already mentioned the impact that Bush (and eventually Sproles) would have as pass-catching backs.

The real star of the New Orleans passing attack, of course, was a seventh-rounder from a school that doesn’t even have a football program anymore. Marques Colston was drafted out of Hofstra University with the 252nd pick during that 2006 draft, just three selections before Mr. Irrelevant came off the board. At 6-foot-4 and 225 pounds, Colston’s 4.55 40-yard dash made him too slow to be a wide receiver, but he lacked the blocking ability of a tight end, which caused him to be slapped with a description no draft prospect wants to hear: tweener. His scouting report noted that he struggled to move the chains and could possibly develop into a no. 2 receiver, even though Sports Illustrated expected him to go undrafted.

Payton, again, turned Colston’s weaknesses into strengths. For a player who was somewhere between a wide receiver and a tight end, Payton developed a role that saw Colston make plays between the traditional locations of wide receiver and tight end. Colston became an absolute terror up the seam, destroying the then–in vogue Tampa 2 by running past overmatched middle linebackers and outjumping safeties. When Colston did line up outside, Brees used Colston’s size to create safe throwing lanes for slants and back-shoulder fades. Colston had the best rookie season ever produced by a wideout taken in the seventh round.

Colston is still a huge part of the offense to this day, as is another player who made his debut for the Saints in 2006 after spending 2005 as an undrafted free agent on their practice squad: 5-foot-9 Lance Moore. After being signed by the Browns out of Toledo following the 2005 draft and getting released, Moore caught on with New Orleans and eventually saw his role expand. He finished the 2012 season with 1,041 receiving yards, becoming one of just nine undrafted players since 2000 to produce a 1,000-yard season.

And again, the guy who failed to develop was the famous one. Robert Meachem, a 2007 first-rounder, sat out his entire rookie season and then played sparingly during his time in New Orleans, never starting more than eight games in a year. The Saints would eventually find a freak athlete capable of doing things that nobody else in their receiving corps could pull off, but even he had to take a weird path to town.

The Phenom

The Saints took Jimmy Graham in the third round of the 2010 draft with the 95th pick, two picks after the Chiefs selected Tony Moeaki and 18 picks before the Patriots and Ravens selected Aaron Hernandez and Dennis Pitta with consecutive selections. Graham, a basketball player at Miami, caught all of 17 passes for 213 yards at the college level. It seems likely that Graham could surpass that in one game if Brees keeps throwing him the ball.

After taking one year to get the lay of the land, Graham went nuts. Since the beginning of 2011, Graham has averaged 78.6 yards per game. Only six players over that time frame have averaged more yards per game than Graham, and they’re all wide receivers. His 26 receiving touchdowns in that time are topped only by Rob Gronkowski’s total. Graham’s prorated 16-game line for the past two-plus years: 96 receptions, 1,257 receiving yards, 12 touchdowns. The man is a force of nature.

Of course, it seems redundant to say this, but this doesn’t happen very often. The Chargers got great production out of Antonio Gates after he made the team, despite Gates never playing college football. Graham barely did, having pieced together college snaps over a few games, but he did run a 4.56 40-yard dash on a 265-pound frame during the combine, which should tell you a lot about how freaky his athleticism is. Even undrafted players who break out around the same time within their careers, like Victor Cruz, are successful wideouts in school.

The Saints got the most out of Graham by being aggressive in deploying him. Very few coach-quarterback dynamics in football work better than Payton with Brees, and they do a great job with motion and formations to create ideal matchups for Graham. The former Hurricane might not be able to read defenses the way that his QB and coach can, but they take care of that work for him and get him the matchup they want. If you watched him on Monday night, you saw him pick apart debuting Dolphins defensive back Jamar Taylor, who was stuck in single coverage on Graham for his third professional snap. Taylor actually did a great job running with him, and still allowed a touchdown because Graham is uncoverable. Just as Sproles lines up as a slot receiver and Colston lines up as a quasi tight end, Graham ends up split out a fair amount of the time as a wide receiver. The NFL saw all these guys who couldn’t line up in a traditional position and decided not to bother with them; Payton found homes for each of them and built an offensive scheme around their strengths.

Nobody else in football has done what the Saints have done on offense under Payton. There are other teams who specialize in buying low on players, notably New England, but the New Orleans offense is tied together by midround picks and undrafted free agents. Only one first-round pick starts regularly for the Saints on offense, and that’s guard Ben Grubbs, whom the team signed to replace Nicks when he left for Tampa. In a league where every franchise is constantly looking for a bargain, the Saints and their band of misfits and castoffs are a shining success story.