This is an interesting question. I think in hockey the quality of the roster and the individual player's form has far more impact on results and play then the system the coach employs. Generally, when a team does well in the standings and/or in regards to advanced stats, players should get most of the credit and when the team does poorly in those areas, players also (and/or the gm who built the roster) deserve most of the blame.
Most bad aspects about the team's play last season that people in this thread keep blaming Therrien for could be attributed to the players.
Last year the bottom six outside of Eller did practically nothing, we were very thin on young forwards pushing in the minors, we were clearly missing at least one top six player, and half the year we had Gilbert, Gonchar, the bad Emelin, a developing Beaulieu playing important roles on defense. Even with the excellent play of Subban, Pac, Markov etc., that still amounted to pretty average player quality in front of Price, so it should not be surprising that the team played so average. As soon as we got Petry and Beaulieu started settling in, the advanced stats improved, to a point where we had better shot based stats than Ottawa and Tampa in the playoffs. That's not the coach all of a sudden figuring out better zone breakout strategies. Roster improvements are what matters most.
Now, we have Petry for a full year. The fourth line looks much, much better than last year's. Whatever the third line is should have better players than last year's Prust and Sekac. Semin could be that top six player we lacked, and at the very least he seems like a creative puck handler who can help with our puck possession. We have better AHLers pushing at the door too to create some internal competition. Galchenyuk looks like a man compared to last year.
I bet if we stay healthy we'll look better this season and have better possession stats. Some will credit Therrien but to me the improved roster will be the main cause.