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Shortly after 8 tonight, a large human in a fine suit will walk across the Radio City Music Hall stage, clasp hands with NFL Commissioner Roger Goodell and bask in the feverish adulation that comes with being the first pick of the draft.

With each ensuing name that’s announced, excitement gradually will wane. Only draft diehards and folks who fall asleep with their televisions on stick around through Saturday afternoon’s seventh round.

When the theater clears and the draftniks formulate their grades on each team’s class – even though the prospects haven’t been issued helmets yet – don’t forget an often-overlooked but critical component of draft weekend.

Teams will scramble Saturday to sign dozens of players who didn’t get drafted. Many of them will make opening-day rosters. Some will become superstars while top draft picks fizzle into oblivion.

The Buffalo Bills likely will depend on undrafted rookies in 2013.

They went 6-10 and have lost more starters than they’ve signed since the season ended. The Bills have serious needs: quarterback, receiver, tight end, guard, linebacker, cornerback and safety among them. The Bills have only six draft picks.

“It’s an important phase to drafting for every team, whether you’re Buffalo or San Francisco,” former Atlanta Falcons, Tampa Bay Buccaneers and Oakland Raiders personnel executive Ken Herock said.

“Everybody wants that one guy they can find as a free agent and make it big. Every year, somebody makes the team as a free agent. They’re a big part of the draft, and you better be prepared to find and sign them.”

Players who don’t get picked are vital to any organization. They’re necessary for managing the salary cap, covering up draft mistakes and providing inspirational leadership.

Fringe prospects get passed over because they’re too small, too slow or played against suspect opposition.

“There are players that don’t quite fit the mold and get stereotyped,” former St. Louis Rams personnel chief Charley Armey said. “You have to be able to find the people without giving up on two things: production and competitiveness.

“They’re out there if you do your homework and put aside some stereotypes.”

When an undrafted rookie makes a roster, coaches often will hold him up as an example for the rest of the team.

Of the Bills’ six opening-day captains last season, four of them weren’t drafted: running back Fred Jackson, fullback Corey McIntyre, safety George Wilson and punter Brian Moorman.

Bills coach Doug Marrone said last week he and his staff are always, “pulling for that underdog, pulling for someone that might have been overlooked.”

“I think it’s much more difficult in this day and age, with all of the film that’s out there and all the stuff we get, to go ahead and find that diamond in the rough,” Marrone said. “You have to look for those intangibles or those strong points in those players that might not have been developed yet.

“And then I really think when you get those types of players in that can play with a role and make your football team, you become a better football team.”

Three of Buffalo’s most productive offensive players in recent years – Jackson and receivers David Nelson and Donald Jones – weren’t drafted. Other discoveries over the past decade include tackle Jason Peters, safety Jim Leonhard, cornerback Jabari Greer and punter Shawn Powell.

Warren Moon, Marion Motley, Dick “Night Train” Lane, Emlen Tunnell and St. Bonaventure grad Jack Butler are among 15 Pro Football Hall of Famers who weren’t drafted.

Also undrafted were current stars Tony Romo, Arian Foster, Wes Welker, Victor Cruz, Antonio Gates, James Harrison and Cameron Wake.

There’s a reason movies get made about overachievers.

“These guys have something to prove,” said film producer Mark Ciardi. “There’s enough of these stories where these guys just survive and climb over players teams have a lot of money invested in. It’s just a different thing when you’ve got to prove people wrong.”

Ciardi, a 15th-round draft choice of the Milwaukee Brewers in 1983, reached the majors four years later. He almost flamed out within weeks of turning pro, but got his break when teammate Jim Morris got hurt. Ciardi pitched a shutout in his spot start.

In 2002, Ciardi produced “The Rookie,” starring Dennis Quaid as Morris, who got sidetracked by life and finally made his major-league debut at 35 years old. Ciardi also produced “Invincible,” starring Mark Wahlberg as Philadelphia Eagles walk-on Vince Papale, “Miracle” and “Secretariat.”

“Underdogs are great stories,” Ciardi said. “They’re more easily identified with than the superstar first-round pick.

“It’s fear. If you have the attitude that ‘This opportunity might go away,’ then you have that set of inspirational motivation that other guys don’t have. I was scared the dream would pop.”

Armey was lucky enough to find for the Rams two of the NFL’s best undrafted gems of a generation. Quarterback Kurt Warner, named the greatest undrafted player by NFL Films in 2011, should go into the Hall of Fame some day.

But Armey’s favorite discovery was a squatty linebacker from Division III John Carroll named London Fletcher, who won a Super Bowl with the Rams and later played for the Bills.

“The ones that you drafted and missed on don’t hurt as bad,” Armey said of finding a player nobody else thought to draft.

Armey called discovering undrafted contributors “lucky,” but Herock refused that word. Herock was more pragmatic – and self-critical.

“It wasn’t any great satisfaction to get that late-round player or rookie free agent,” Herock said with a laugh, “because if I thought he was so damn good, I should have drafted him.”

email: tgraham@buffnews.com