I was going to post this as a comment in the FTB, but it was too long apparently.
I'm a little curious as to whether or not there is any credence to "Carlyle pushes shots to the outside" narrative, so I fiddled around with theninjagreg's shot tracker and I found a few things:
All shots EV
All shots PK
It's obvious that whatever is going on, shots are being taken from further away than last year. Carlyle haters (such as myself) would say "quantity is way up!", but we're only allowing one more shot per 60 minutes than last year (31.8 this year, 30.8 last year). A 3% increase in shots allowed and a 5% increase in average shot distance allowed. Is that worth it? I have no idea.
Corsi has also been much worse, implying that opposing teams are missing the net quite a bit or that the Leafs are blocking many shots or a little of both. Assuming that the Leafs can sustain their ability to block shots, the decrease in Corsi isn't that big of a deal if it has only resulted in one more shot per 60 minutes. That being said, some personnel changes would do wonders for possession stats (more Gardiner, less assholes, Bozak/Kadri or Grabbo swap).
The PK has become pretty good and shottracker shows that. Assuming that I did the math right, they're allowing 43.1 PKSA/60 this year while they allowed 53.6 PKSA/60 last year. Allowing 20% less shots from an average of six feet further away has resulted in a top 5 PK. Who knew?
Everything is coming from further away this year - shots, saves and goals. In theory, it would make sense to say that a 5% increase in average shot distance would probably inflate EVSV% by some amount, without controlling for shot quality beyond average shot distance.
My point is that, despite how much I hate Carlyle, I think he could be a good coach if he underwent a Hitchcockian-like transformation. He needs to stop with the team toughness bullshit, play the best lineup availible and stop holding players accountable if he can't be held accountable himself. However, he seems to have a working formula on the PK and, to some degree, he is able to "push shots to the outside" consistently.
Edit: I should note that I only used road data, which obviously affects the sample I drew from.