BUFFALO — To see the Islanders ranked No. 1 in the NHL on the penalty kill and to see them carry a streak of 39 consecutive advantages killed off into Thursday’s game here against the Sabres are impressive sights.

But that’s not the full story. The Islanders’ penalty kill was historically bad for the first four months of last season, last in the league and hovering below 70 percent efficiency — a number that would have been terrible in the high-scoring days of the 1980s and downright hideous in the defense-first era we now experience.

So how did the Isles’ PK get here, sitting at 87.8 percent efficiency atop the league?

“I would say we’re understanding what coach wants us to do,” Frans Nielsen said, referring to assistant coach Greg Cronin, who joined the staff before last season and had a bit of trouble implementing his penalty-kill structure. “We struggled with it last year and now, we just play. Hockey is one of those things, when you’re thinking, you’re usually a step behind. The PK guys, we’re just reacting right now, there isn’t much thinking.”

Goaltending is clearly a big factor and the Jaro Halak/Thomas Greiss duo has been superb on the penalty kill — among goaltenders with at least 15 starts this season, Greiss is second in the league with a .919 PK save percentage, Halak is third at .898.

“There’s always some luck in there, too,” Greiss said. “A puck bounces off a leg and goes in and then you’re not successful even though you’re still doing things right. But our whole unit on the PK has been doing a great job cutting down on chances.”

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There was only one noticeable change back in February, when the Isles became a shut-down penalty kill. The forwards became more aggressive in pursuing pucks and bodies to the side walls in the defensive zone, with a sort of triangle-and-one mentality — one forward pursues and hounds, the other stays in the middle to cut off the seam pass, which was something that was hurting the Isles in their four-month funk earlier last year.

While last year’s terrible stretch was bad, it was closer to the norm than this year’s — the Isles haven’t even been in the top half of the NHL on the penalty kill since 2010-11, when they finished 12th, and haven’t had a top-10 season since 2003-04, when they were fifth.

“No. 1 in the league, it speaks for itself. We’re doing the right things,” defenseman Calvin de Haan said. “I never felt like we were the worst PK in the league at the start last year, we just seemed to be giving up goals when we shouldn’t have been. We didn’t change all that much, but it seems to be working.”