Entering Thursday’s game at Barclays Center against the archival Rangers, Capuano has amassed 188 victories with the Islanders, more than any other coach except Al Arbour, who led the Islanders to four straight Stanley Cups in the early 1980s. Arbour, who died at 82 in August, helped the Islanders win 740 games — an N.H.L. record for a single franchise that seems safe.

After Arbour announced his retirement in 1994, the Islanders had little stability, or, for that matter, extended success until Capuano came along. Before Capuano was hired in 2010, the Islanders had 11 coaches in 16 years, including Arbour, who returned for one game in 2007. Mike Milbury and Lorne Henning held the job twice.

“The one thing I haven’t changed is who I am,” Capuano said. “I’m not going to change my personality. I’m firm but fair with guys. I believe in the system that we have to play to win games. But I learn every day. If we’re asking our players to get better, not only for myself but for my coaching staff here, we have to do the same thing.”

Capuano has led the Islanders through a renaissance and a transition, from frumpy Nassau Coliseum to Brooklyn. Only five of the 20 players who dressed for Capuano’s first game as coach, a 4-2 loss on Nov. 17, 2010, are still with the team: Tavares, Matt Martin, Josh Bailey, Frans Nielsen and Doug Weight, who has since become one of Capuano’s assistants.

“The team was a lot different when he took over,” said forward Kyle Okposo, a first-round draft pick who began playing for Capuano in Bridgeport. “Now we’ve established ourselves as a top-echelon team in the league, and doing it pretty quietly. We play an exciting brand of hockey, try to play up-tempo, and he’s a big part of that. He wants us to be structured, but he wants to us to make plays. He’s done a really good job of that.”

Capuano replaced Scott Gordon, a more heralded coach who had jumped to the Islanders from the A.H.L. before the 2008-9 season. At the time, Garth Snow, the Islanders’ general manager, said he was unsure if Capuano would even finish the season. But he is still here. (Gordon is coaching the Lehigh Valley Phantoms, the Philadelphia Flyers’ top farm team.)