“You get to run the ball a lot. I love running the ball when you play rugby. Tackling, everything, I love it,” he said. “It’s like you’re always in the mix.” As the “eighth man,” Paea would play up front like a lineman, “and you also get to be in the back with the skill guys so you’re kind of in between, which is cool.”

The USA Eagles would probably need a few N.F.L.-caliber athletes to have any chance of defeating the All Blacks at Soldier Field, given the gulf in class between the two teams. But Hansen said American rugby is very likely to grow and that the Eagles are likely to improve on the back of rugby’s inclusion in the Olympics.

“They’ve got tremendous athletes throughout their colleges who don’t make the gridiron or they don’t make the sports that they aspire to, and there’s an opportunity now for them to play rugby and maybe go to the Olympics,” Hansen said. “That can only be beneficial to their 15-a-side game.”

Staying one step ahead of their competitors remains the big challenge for the All Blacks, who continue to be the most dominant team in world rugby. They have an overall success rate of more than 76 percent, which makes them one of the most successful teams in any sport.

Being willing to look at other sports for inspiration and information has helped give them a competitive edge.

In recent years there have been visits to the Sydney Swans Australian Rules team, various National Rugby League teams in Australia and the N.B.A.’s San Antonio Spurs, who have embraced international talent. The New Zealander Shawn Marks played, was an assistant coach and recently was named an assistant general manager for the Spurs.

“There are a whole lot of things you look at,” Hansen said. “Strength and conditioning is one. You look at team culture. You look at structures.”