Why do the Habs play so much better in the second period?

In the hockey analytics community, we take for granted that NHL teams, by and large, play differently according to the score on the Jumbotron. The same team with the same players could go from getting 50% of all shot attempts when tied, to 55% of shots when down a goal, to under 40% when up by two goals or more. We see it all the time, and we account for these situations when estimating a team's true ability level (via score-adjusted possession metrics, for instance).

As our understanding of hockey analytics deepens, perhaps we will be able to come to similar conclusion about teams putting up dramatically different results depending on the period of play. Note the following table:

(data via war-on-ice.com)

Isn't it strange how the Canadiens go from a bottom-five team in the first period, to a top-five team in the second? Isn't it stranger that the same variation does not seem to affect the Senators throughout the course of a season? And isn't it stranger still that the Habs have carried over that possession advantage into the playoffs against the Sens despite unfavorable numbers against Ottawa coming into the postseason?

We won't find a definite explanation for this phenomenon just yet, but we can start by looking at the fundamental difference between odd (first, third and the second overtime) and even (second and first overtime) periods in a hockey game: the long change.

Focus 1: Stretch passes out of the defensive zone

Here's a play from the second period of Game 1. Tom Gilbert has possession of the puck and is preparing a zone exit for Montreal.

With coaches preferring 30-45 second long shifts in today's NHL, players are changing all the time. The Senators' bench is just outside the Montreal blue line, so the forwards, especially, have to take themselves out of the play in order to get off the ice.

With Mike Hoffman (OTT68) going off the ice and his teammate not yet in the passing lane, Gilbert sees Brendan Gallagher at the far blue line and hits him with a long cross-ice pass.

Gallagher does really well to read the bounce off the boards and absorbs the hard pass. At the same time, he makes a pivot and carries the puck into the Ottawa zone.

He has a step on Cody Ceci (OTT5), but the defenseman is closing fast. Plekanec and Galchenyuk are following up on the play, but they'll have to get to the middle of the ice in order to become viable passing options.

Ottawa has recovered and is setting up their man-to-man coverage. Ceci is well-positioned to prevent Gallagher from either cutting to the middle or crashing the net on his backhand.

Wiercioch has good body position on Plekanec; ditto for Turris on Galchenyuk. Neither Montreal forwards will be able to get to the red box for a drop pass and a high-percentage shot from the slot on Andrew Hammond.

Gallagher's out of time and space, and just puts a low wrist shot on net. The play turns out to be relatively harmless due to sound positioning from Ottawa defenders. But it still generated a shot, and now the Habs get to face off deep in the Senators' end.

A team which does this enough times in a hockey game will get its share of offensive-zone draws, shots on net, and, eventually, goals.

Montreal is not the only team which likes the long pass. In fact, the Senators used the second-period long-bomb to great effect against the Habs in a regular season matchup on March 12, 2015.

The play developed in a very similar manner as the one we just looked at, but Erik Condra did a much better job at creating space on the zone entry by cutting across the ice, and linemate JG Pageau was there in the "red box" to take the pass and go in unchallenged against Carey Price. The end result: a Senators goal. (FULL VIDEO LINK)

Focus 2: Unsuccessful dump-outs leading to icings against

Remember that the first overtime period plays just like the second period in terms of the long change - it's much tougher to get to the bench after being hemmed in your own end. What's more, the stakes are high and the players are mentally and physically exhausted from three periods of playoff hockey.

Essentially, it's really easy to make a bad judgement call and ice the puck, which is not a good thing.

Here, Eric Gryba is swinging out from behind the Ottawa net and spots Mark Stone at the Montreal blue line.

The pass that he attempts is directly down the left wing, as opposed to cross-ice like the two previous examples I brought up. There's less of a chance for it to get picked off in the neutral zone, but it also has a much higher chance of going all the way down for an icing call.

And that's exactly what happens. Stone can't get a touch on the puck, and Jeff Petry only has to beat him to the hashmarks to get the icing call. Michel Therrien stays with his forward line of Galchenyuk-Plekanec-Gallagher, but sends out P.K. Subban and Andrei Markov for the key O-zone draw.

Ottawa wins the draw and Stone has the puck next to the sideboards. He's under heavy pressure from Galchenyuk and is looking to make a soft chip off the boards to Clarke MacArthur (OTT16) for the immediate line change.

It's tough to say for sure what thoughts are going through his head at this moment, but "get the change" and "don't screw up"  might be two of them.

Uh-oh. The puck takes a bad hop and goes right through MacArthur. Then Markov steps up and hits him hard. It's another icing.

The Ottawa players are now stuck in a vicious circle. They've been out there for a while and can't skate the puck out. So they dump the puck out but can't get off because of the icing. Rinse and repeat.

Some coaches may take a time-out here in order to slow things down and to put their preferred matchups out on the ice. But you only have one time-out per game, and it also gives your counterpart a chance to get organized. So most of the time, you just sit back and hope that you don't get scored on right off the faceoff.

To further compound the issue, this is the possession chart of the players on the ice for that faceoff (lower & to the right = better, thanks @IneffectiveMath):

So really not an ideal situation all-around for the Sens, their worst possession units on Friday isolated against the Habs' best five skaters.

The ref drops the puck, and this happens about five seconds later: