Pop-culture bad boys turned Broadway luminaries, Trey Parker and Matt Stone are sitting in a place they never expected to be: the lobby of the Ellie Caulkins Opera House.

And the pair readily admit that, although they have deep roots in Colorado, that wasn’t the guiding reason that the unlikeliest Broadway hit in years, “The Book of Mormon,” is launching its first national tour in Denver on Tuesday night.

Famous for the cable comedy “South Park,” the pair co-wrote with Robert Lopez the irreverent musical about two young Mormons sent on their mission to Uganda.

But they had reservations about their play beginning its road trip in Denver. The duo may have started out here, but their work has taken a beating by local critics over the years.

“We were like, ‘We don’t know if that’s a good idea.’ We haven’t been treated well,” says Parker.

Producers, however, couldn’t resist the sentimental hook of opening the show on the old home turf. More important, the timing was right for Denver, too.

The arrival of “Book of Mormon” underscores the increasing national stature of Denver Center Attractions, the Broadway arm of the Denver Center for the Performing Arts.

In the past decade, the Denver Center has picked up steam as the launching pad for national tours. “Osage County” kicked off its travels here, as did ‘”Disney’s The Lion King.” Next season, Denver will launch 2012’s Tony-winning play “Peter and the Starcatcher.”

When tickets went on sale for “The Book of Mormon” in January, the run sold out in five hours. The success warranted a return engagement, set for the Buell Theatre in October 2013.

“I’m so glad we chose Denver as our first city,” says Anne Garefino, the duo’s longtime producer and one of the producers on the musical. “It couldn’t be a better welcome for the tour show. And I think we were proven right.”

Tuesday, 2½ hours before the curtain rises on “The Book of Mormon,” Denver Center Attractions will hold a lottery drawing for 24 tickets. Each day of the run, the ritual will be repeated.

Lotteries aren’t new to the Denver Center. “Spring Awakening,” “Wicked” and “American Idiot” had drawings. But the organization has never had a lottery for a sold-out show. Expect demand to be high.

Still, it’s hard to figure out exactly what sort of hit “The Book of Mormon” will be as it crosses the country or where it will rank among Denver Center hits. Meanwhile, the metrics for success go beyond money.

“This is going to sound cheesy,” warns Garefino. “But when we do ‘South Park,’ we put the show out into the world and we don’t really have that feedback that you can get with a live audience, the laughing at what you’ve written.

“You can go stand in the theater and see people reacting. That’s our measure of success.”

Of course, there was that surreal night in June 2011 when “The Book of Mormon” earned nine Tony Awards. Among the honors: best musical, best book and best score, which Parker, Lopez and Stone shared. Parker tag-teamed the award for best direction with Casey Nicholaw.

“We’ve been involved with a cultural thunderclap before, where something just becomes part of the conversation,” said Parker. “We thought we could pilot our way through that without getting too emotional. But it was totally trippy being the talk of the town.”

Now, the town is Denver.

Indeed the gang’s all here: Parker, Stone, Lopez, Nicholaw.

As theater newbies, Stone and Parker were often told by vets that “theater is alive; it’s a living thing,” says Stone. “Now we really get it. Because now we feel like we have this child. We were done with ‘Book of Mormon’ a year and a half ago, and it’s still out there. If we don’t pay attention to it, it can start acting out.”

Parker interjects: “It’s on right now in New York.” If the curtain hadn’t gone up at the Eugene O’Neill Theatre that day, it was about to.

“It’s so crazy, we now have the Broadway child and this. Bobby (Lopez) said to me, ‘At some point, you just have to stop caring.’ Because once it becomes this thing ….” Stone trails off a with the look of a parent overwhelmed by the commitment.

How the musical will play on the road is a fresh adventure.

” ‘The Book of Mormon’ has been so much broader than we thought it would be,” said Parker.

When in New York, Stone and Parker sit in the back of the Eugene O’Neill to watch the musical and their audience.

“There are old ladies with pearl earrings and gray hair, and we’re singing ‘f— you, God,’ and they’re laughing,” Parker says. “Old people are the dirtiest people in the world.”

For guys who have made a princely sum on the cheeky, the naughty, the offensive, beginning with the Emmy-winning “South Park,” the Broadway reception has left them marveling.

Which isn’t to say it’s everyone’s cup of joe.

“I’ve seen a few people walk out in this one song that’s literally an hour and 50 minutes into a 2½-hour show,” Stone said. “We lost you here?!”

As for the response to the musical by Mormons who have seen it?

“There is a big contingency of Mormons who come see the show and embrace it as their ‘Fiddler of the Roof.’ It doesn’t make them leave the theater going, ‘Yeah, our thing is screwed up.’ They leave saying, ‘Yeah! We’re Mormons!’ And there are people who go and say ‘I love my family. I love my faith. But, yeah, I have problems with that,’ ” said Stone.

“Of course, there are plenty of Mormons who’ll never come see and plenty of Mormons who’ll be offended by it,” Stone said, as the sound of a male voice powers its way out into the lobby of the Ellie during a rehearsal.

Parker interjected a sort of punch line: “The best thing is, even if they don’t like it, they’re Mormons; they’re going to be nice about it.”

Lisa Kennedy: 303-954-1567, lkennedy@denverpost.com or twitter.com/bylisakennedy