KANSAS CITY, Mo. -- When the Chiefs take the field Sunday for the AFC Championship Game, they'll boast an MVP candidate at quarterback. Their advantages also will include the fastest receiver, the best playcaller and three of the top pass-rushers in the NFL this season. And behind the scenes, working his magic in relative anonymity, will be one of the best special-teams coaches ever.

Dave Toub just wrapped up his 13th consecutive season with a special-teams group that ranked in the top five of ESPN's efficiency metric. That consistent high-end performance -- compiled in six years with the Chiefs and seven with the Chicago Bears -- also is reflected in Football Outsiders' DVOA metric (defense-adjusted value over average).

Can you name an offensive or defensive coordinator who matches that streak? Of course not. If any one of them approached such levels, he would have been branded a schematic genius and hired as a head coach. Toub? He has been invited to a handful of interviews in recent years, but he did not get a sniff during this year's frenzy and, at 56, might have missed his window.

"I was disappointed that more special-teams coaches weren't interviewed in general," Toub said Thursday amid preparations for the Chiefs' home game against the New England Patriots (6:40 p.m. ET Sunday, CBS). "Obviously, I wouldn't have minded being able to get an interview, but that didn't happen this cycle. I think everybody knows why. The young, offensive-minded coaches were the ones that were getting most of the opportunities. That's just the way it went.

"Sooner or later, when somebody wants to hire a leader of men that's going to develop players, maybe my chance will come around."

Toub's best chance might have come and gone last year after the Indianapolis Colts fired Chuck Pagano. Colts general manager Chris Ballard, a personnel man in Chicago during eight of Toub's seasons there and two more in Kansas City, did not interview Toub for a job that first went to Patriots offensive coordinator Josh McDaniels. Nor did Ballard turn to Toub after McDaniels reneged on the agreement, hiring Frank Reich instead.

The most unbreakable convention of NFL coaching trends has been the near total refusal to consider candidates with pure special-teams backgrounds. The last head-coaching hire coming mainly from a special-teams background was John Harbaugh, chosen by the Baltimore Ravens in 2008. If someone with significant personal ties to Toub didn't hire him, what are the chances that someone else makes the leap?

Toub hasn't given up hope. He noted that the Denver Broncos last week hired longtime defensive coordinator Vic Fangio as head coach.

"He's 60," Toub said with a smile. "I'm only 56. So I've still got a shot."

If it doesn't happen, however, Toub will go down as a coach who has made a profound difference everywhere he has worked. The Chiefs' special teams ranked among the bottom third of ESPN's efficiency metric in five of the six seasons before his arrival in 2013. The Bears, meanwhile, have ranked No. 21 or lower in each of the six seasons since his departure. (The efficiency metric measures expected points per play and weighs each play for its importance.)

So, as the Arizona Cardinals move forward with a just-fired college coach and two other teams cast their line with coaching descendants of the Los Angeles Rams' Sean McVay, the Chiefs will get the distinct advantage that comes with Toub's expertise. How does an elite special-teams group impact a game?

• The Chiefs have recorded the NFL's third-best average drive start this season, while holding their opponents to the second worst.

• Their place-kicker (Harrison Butker) has missed only three of 27 field goal attempts, two of which were from 50 yards or longer.

• Dustin Colquitt, Kansas City's punter, has dropped 48.9 percent of his punts inside the 20, fourth best in the NFL in 2018, and he leads the league in expected points added (EPA) on punts.

• Tremon Smith ranks fourth in kick return average (26.9), and punt returner Tyreek Hill ranks eighth (10.7).

In 2018, the average NFL game included 5.1 kickoffs, 1.8 field goal attempts, 2.4 extra points and 4.3 punts per team. It adds up to roughly 27 plays. So against most teams, the Chiefs have an edge over their opponents on about 20 percent of the total plays in a game, before you even get into the offensive and defensive matchups that dominate public discussion.

So how does Toub master this facet of the game? He has a few secrets. Casual observers will note that he usually has been blessed with elite playmakers, from Devin Hester in Chicago to Hill in Kansas City. That has not come by accident.

"You have to get the support of the head coach in that, and we have that with Andy [Reid]," Toub said. "The bottom half of the roster has got to be good special-teams players. All of your draft picks every year, before we draft them, we'll have a meeting about them for special teams. If we have two good players that are close, we're going to take the player with the higher special-teams grade. That's how you end up getting good special-teams players."

Kickers haven't struggled much under Toub's tutelage, either. In Chicago, he helped identify and nurture Robbie Gould. (Worth noting: The Bears were eliminated from this season's playoffs because of a missed field goal by Cody Parkey.) And in Kansas City, Toub pulled Butker off the Carolina Panthers' practice squad and shepherded him into 62 conversions on 69 attempts over two seasons.

Why do kickers succeed under Toub? His selection process is simple: Identify and avoid the head cases.

"Personality is important to me there," Toub said. "It's such a head game. You see guys that have confidence in college, then all of a sudden, they get to the NFL and, boom, they lose it. You've got to try to sift through it.

"I've never been big on drafting a kicker or punter. Every kicker or punter I've had have always been free agents, guys that came up the hard way, guys that have had to fight their way, earned their way. Those are the kinds of guys I want. The so-called name guy? A couple of years ago, [Roberto Aguayo, drafted in the second round by the Tampa Bay Buccaneers and now out of the league] was everything. But in reality, what was inside there? It's a hard job."

The Chiefs will face another franchise Sunday that has fielded well-respected special teams for a long time. But the Patriots have ranked in ESPN's top five a total of six times in the past 13 years, less than half that of Toub's achievement. What he has done in Kansas City, and in Chicago before that, will go down as one of the most remarkable feats of this era.

Whether he eventually ascends to a head-coaching job should not cloud his impact on the game.

ESPN's Seth Walder contributed to this story.