On his way to No. 700, Ovechkin recently passed several of the game’s scoring greats, including Mark Messier (in front of an Ottawa crowd chanting, “Ovi!”) and Steve Yzerman, the former Detroit Red Wings center who is now the club’s general manager.

“You’ve had a tremendous career to date. It looks like you’re going strong and you might play forever,” Yzerman said in a video addressed to Ovechkin. “If you ever do break Wayne Gretzky’s all-time record for the most goals in the league,” Yzerman added, “after watching your Stanley Cup celebrations, I want to be invited to your party.”

Those celebrations, after the Capitals beat the Vegas Golden Knights in five games, included revelry at a nightclub and playing in a public fountain.

“Even after that many goals, every goal he scores is like his first goal in the N.H.L.; he’s jumping around and he’s very excited,” said Jari Kurri, who retired as the N.H.L.’s leading European-born goal scorer, since passed by Teemu Selanne, Ovechkin and Jagr.

Ovechkin is best known for possessing perhaps the most dangerous one-timer in hockey history and for the childlike joy with which he celebrates. The shot has factored into his extraordinary success on the power play, where he has frequently double-shifted and played the full two minutes. His 259 power-play goals rank third, and it seems a mere formality that he will break Dave Andreychuk’s record of 274.

Ovechkin was reared by athletic parents in a hardscrabble neighborhood on the fringe of Moscow. His mother, Tatiana, was one of the great point guards in Europe, winning two Olympic gold medals in basketball with the Soviet Union. His father, Mikhail, was a professional soccer player, and his oldest brother, Sergei, was an accomplished wrestler. Sergei died after a car accident when Alex was 10, and Ovechkin frequently celebrates goals by kissing his fingers and pointing skyward in memory of his big brother.

Ovechkin was selected No. 1 in the N.H.L. draft of 2004, just before the league lost a full season to a labor dispute. When he finally made his league debut, in 2005-6, he scored 52 goals and collected 106 points, which both rank him third for an N.H.L. rookie.