Just before Thanksgiving in 2013, Mike Petri and his wife, Lauren, were browsing in a bookstore in Bethlehem, Pennsylvania. Lauren was due to give birth to the couple’s first child in a few weeks, and so the couple were looking to fill out their collection of children’s books. They grabbed plenty of standards — “The Very Hungry Caterpillar,” some Dr. Seuss titles — but Petri was looking for something specific.

“They had kids’ alphabet books about baseball, football, basketball,” he said. “But nothing about rugby.”

Petri said this did not surprise him (“I’m not an idiot”), but as a soon-to-be dad, a high school math and science teacher in New York and a key cog of the U.S. team, Petri felt a need to fill this hole in the canon. He and Lauren began playing around with words and rhymes (what rhymes with “scrum?”). Soon, Lauren encouraged him to start writing down his thoughts.

He did. And after some fits and starts, and plenty of scribbling during his daily rides on the N train from his home in Brooklyn to his classroom at Xavier High School in Manhattan, Petri was able to read “R Is for Rugby” to his daughter, Evie, in late May.

Petri is particularly proud of a few of the rhymes. O, which is for off-load (flipping the ball to a teammate as you’re being tackled), advises that “at the end of the run” a player should “pass the ball to a mate and continue the fun.”

Petri also struggled for a while over what to do with X, primarily because the obvious solution seemed to be “X-ray” but going that way “might have sent the wrong kind of message about our game,” he said. In the end, he used X to describe a rudimentary strategy in rugby whereby two players run crossing paths (like an X), and settled on this rhyme: “The most basic play/Is an old-fashioned switch/One guy will strike/But it’s hard to tell which.”

“I’m not saying it’s Pulitzer Prize material or anything,” Petri said. “But we’ve sold more than 1,000 copies in a few months, and I’ve heard from people whose kids love it or who even use it themselves when they’ve watched rugby.”

Teaching about rugby comes naturally for Petri, whose day job is lecturing on algebra, physics or biology and then, after school, coaching Xavier’s varsity rugby team. He also squeezes in his own training, often making for workdays that start at 6:30 a.m. and do not finish until he walks through the door after 10 p.m.

On the U.S. team, this is not altogether uncommon. Unlike the so-called Tier 1 rugby teams (powerhouses like New Zealand, Australia, England and South Africa), the United States — which is one of the lower-ranked Tier 2 nations — has a large number of players with full-time jobs outside the sport.

Some players do play for big clubs abroad, such as Hayden Smith (with England’s Saracens) or the star back row player Samu Manoa (with France’s Toulon). But about half of the 31-man roster here is like Petri: begging time off from a jobs as contractors and sales reps while living out rugby dreams.

Realistically, the United States has no chance of winning the tournament (no Tier 2 team is expected to make any deep run), but that does not mean the Americans, who are known as the Eagles, do not have ambitions. Petri, who is playing in his third World Cup, said the team tried to be as myopic as possible — focusing only on the practice or the game in front of it. He turned a bit wistful when thinking about the team’s locker-room tradition after a win.

“We sing ‘America the Beautiful’ together,” he said. “Other teams have other victory songs, but that’s ours. And singing it here would be amazing.”

American fans who are less familiar with the sport will quickly recognize Petri, whose position, scrum-half, means that he constantly has his hands on the ball. The Eagles have bigger stars — Manoa is an imposing physical presence and the captain, Chris Wyles, has a significant pedigree — but Petri creates the rhythm of the United States’ attack, pulling the ball out of the scrum and getting it moving in the right direction.

It is a job that the U.S. coach, Mike Tolkin, likened to a point guard in basketball. Petri is largely taking strategic orders from elsewhere but has to rely on his own decision-making and distribution skills to give his team’s offense any kind of flow.

He also has to run, a lot, as he moves wherever the action is when his team has the ball. Tolkin said that during his last game, Petri ran more than seven kilometers — about 4.3 miles — and is “one of the fittest guys I’ve seen.”

Smith also noted that one less-obvious part of Petri’s job was his role as a sort of free safety on defense. While a scrum-half is not often tackled — because he’s usually passing the ball quickly — he does have to occasionally attempt a tackle on an opponent. Consider that Petri, at 5 feet 9 and 185 pounds, may be trying to take down players who are half a foot taller and nearly 100 pounds heavier.

“They’re also usually running pretty fast already, too,” Smith said. “It’s not the best part of the job, I don’t think.”

Petri confirmed that way of thinking — “I’ve eaten my fair share of dirt” — but also said he reveled in the task.

“I don’t have a rhyme for this,” he said. “But it’s just something that’s part of anyone who plays rugby. I wrote the book for the same reason that I wanted to play for the Eagles again at this World Cup: Rugby is such an important part of me that I just really, really want to see it grow.”