Joe Snively skates for Yale in 2016. (Rick Scuteri/AP)

Joe Snively remembers sitting in his dentist’s waiting room for a routine cleaning before hockey practice when he spotted one of his favorite players, Washington Capitals sniper Alex Ovechkin. Snively snagged his gloves out of the trunk of his parents’ car and asked for a signature.

Roughly a decade later, Snively took the first step toward becoming Ovechkin’s teammate Monday when the Herndon, Va., native and coveted undrafted college free agent signed a two-year, entry-level contract with the Capitals. The forward’s deal begins next season.

“You grow up watching the Caps, [and] you dream of playing for them,” Snively said. “It felt really great to sign a contract with the Capitals, but my goal is to play in an NHL game with them, and I’ve still got a lot of work to do before that.”

Snively played at the Capitals’ practice facility in Arlington as he came up through the organization’s Little Capitals development program. He remembers Brooks Laich joining his youth team for a practice, and he has watched the Capitals since their uniform colors included black, bronze and blue. He looked up to center Nicklas Backstrom most, awed by his passing and playmaking. His parents, eye doctors in Vienna, have season tickets, and Snively celebrated Washington’s first Stanley Cup last season like scores of other local fans. He is evidence of the “Ovechkin effect” — the influence that the Russian scorer’s arrival has had on hockey’s popularity in the region.

“Yeah, it’s pretty cool for this area, for fans and for kids," Ovechkin said. "They see the progress that hockey did in the United States and, obviously, in D.C., and it’s pretty cool.”

Snively, 23, recorded 36 points (15 goals and 21 assists) in 33 games with Yale this season. The 5-foot-9, 180-pounder led Yale in points in all four years he played there, tallying 58 goals and 81 assists in 129 career games. This season, Snively was a nominee for the Hobey Baker Award, given to college hockey’s top player. Before he went to Yale, he played three seasons in the U.S. Hockey League and recorded 125 points (50 goals and 75 assists) in 159 games with Sioux City.

More than 20 NHL teams reportedly were interested in him, but Snively said he talked with only five. He is the second local player to sign with an NHL team in the past three years; forward Sam Anas of Potomac, Md., also played with the Little Capitals before signing with Minnesota out of Quinnipiac University. He is in his third season in the American Hockey League.

“When the Caps started to become successful, you could just see the amount of people in the local rinks, it started to increase," Snively said. "More kids wanted to play hockey. ... It became a hockey city. It’s been really cool to witness and be a local [from] Northern Virginia and just see how the hockey community’s just gotten so much bigger.”

Organizational forward depth is a weakness for the Capitals, who have few high-end prospects in the AHL. Washington signed Shane Gersich and Brian Pinho out of the college ranks last season, and Snively could join the Hershey Bears on an amateur tryout agreement this season. But because he is finishing his senior year at Yale, he is unsure whether playing with the Bears will conflict with his class and exam schedule.

Snively’s best asset is his skating, making him well suited for the direction the NHL is heading. He is a good penalty killer with strong defensive-zone habits, and offensively he has an accurate shot; is willing to go to the hard areas, such as the front of the net, to score; and has good vision.

With entry-level contracts largely the same from team to team, the Capitals may have had the sentimental advantage with Snively.

“Obviously a unique situation with a local kid, which is phenomenal,” Coach Todd Reirden said. "But it’s very competitive to sign those free agents out of college, and we’re fortunate to be able to add someone [who’s] almost like a free player. And just a really great story in terms of being a local player, playing in this rink growing up. To me, he’s [evidence] of generations of players that are starting to come around thanks to Ovechkin and Backstrom and the growth of the organization. It’s going to be fun to watch the next few years, the impact that they’ve been able to have on young hockey players and building the game of hockey in the area. It’s just going to keep growing from there from what we were able to accomplish as a team last year. …

“It’s pretty neat to see it all kind of come full circle. Happy for Joe and for his family, and looking forward to hearing about how he does in Hershey.”