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Penalty killing is hard work. As a unit of four (or even sometimes three) you are trying to prevent a goal against from an opposing team that has more skaters on the ice than you do. But, instead of just trying to squelch scoring chances, what if you never even let the other team get into the offensive zone in the first place?
That's what the Kraken are striving to do with a new system on the penalty kill. And it's working.
Let's dig in.

Just like in even-strength play, a penalty kill has a forecheck strategy that it uses to apply pressure to other teams with the goal of regaining possession or, at the very least, stifling their offensive attack.
Last year, the Kraken's forecheck on the penalty kill was a 2-2 formation. This season, they've moved to a 1-3. That means one of the two forwards on the ice plays in the middle of the neutral zone as a bit of a disruptor to other teams' transition (and sometimes a director of play to the left or right), while the three remaining penalty killers form a line at or near the blue line.
The goal is to take away speed by offering a checker high and showing a wall of skaters to try to get through which also challenges the other team's ability to retain control of the puck.
It looks like this.

KrakenPK

While this is a more passive form of forechecking, it can be very effective in not letting other teams pass through into the offensive zone, and even if they do, they definitely have trouble doing so with control.

MIN Entry Denied

"We're not giving opponents easy entries right now," Carson Soucy said.
To that point, the Kraken have the eighth highest rate of dump-ins against when playing short-handed (.76 per two minutes of play according to Sportlogiq). That means that opponent's power plays are electing to send the puck in loose which opens up the opportunity for a puck battle that now either team can win.
To that point, the Kraken aren't just disrupting entries and creating dump-ins, they are getting to loose pucks, winning battles, and getting the puck back out of the zone neutralizing any offensive attack against.

Generating Dump Ins

Right now, no other team is clearing the puck successfully more than the Kraken are when playing shorthanded (3.01 per 2 minutes of play), and their overall success rate on those dump-outs is third best in the league (81.2%).
So, the Kraken strategy isn't just keeping other teams' power plays away from generating attacks, they are also eating up time and opponents' energy by sending the puck often all the way down to the other end of the ice requiring skaters to cover a lot more ice to regain possession and regroup for a breakout.
In fact, there's so much in and out of the zone as well as back and forth that the Kraken penalty kill allows the fifth lowest offensive zone possession time by opponents (34.4 seconds per two minutes of play).
Now, of course, power plays do find a way through - especially if they can find a seam for a pass or sharp cut through with possession. This is where Kraken skaters feel they are doing a good job following the structure they've built for in-zone play, too.
"We've had success as of late," Morgan Geekie said. "I think it's communication. Being predictable. We don't ad-lib too much out there. We're doing the same things every time so it makes it easy to read off of, make plays, and count on each other. It's being reliable to each other and being solid as a group."
When other teams' power plays have the puck, the Kraken apply pressure and work to clear possession out of their own zone or at the very least, challenge any scoring chances.

PK Pressure to Clear

In addition to the hard work and pressuring that Seattle penalty killers are doing there's a lot of blocked shots and clogging shooting and passing lanes. As a result, according to Evolving-Hockey.com, the Kraken are allowing the fifth least amount of shot quality by opposing power plays (6.21 expected goals against per 60 min of play).
There are going to be goals against. That has happened in seven Kraken games this season. But three of those games were the first three of the season. A time in which, as Soucy noted, the team was still adapting to the new systems on the penalty kill. Conversely, there have been nine games when the Seattle penalty kill has been perfect, including six of the last seven matchups.
"We're four guys working hard out there," Soucy said. "The dedication is there and it's paying off."