Like the 4 S's of Scouting (5 if you count mine!), coaches have a handful of categories to evaluate
[*]Tactics: Xs and Os; I need someone who can identify the strengths/weaknesses of a roster and build a playstyle accordingly with an eye towards playoff hockey
[*]Adaptability: maybe a subset of Tactics, but adjusting to the results and circumstances in a game/series with the personnel on hand
[*]Motivation: via inspiration or fear or what have you
[*]Development via Deployment: a subset of motivation, do players grow their games?
[*]Media Management: there is a lot of face time, especially in Toronto; does he wield the media as a tool, or is does he crumble under the scrutiny?
[*]Management Management: does he collaborate well with the front office (roster, analytics)
[*] Officiating Management: the game within the game
Keefe:
Tactics were aligned with Dubas, who tried to get ahead of the current metagame, but it petered out in the playoffs routinely and Adjustments were either non-existent or consistently stupid (play Matthews with Marner MORE).
Motivation was always done through process and minimizing emotions, which reads well on paper, but hockey players aren't really the cerebral type in general, and certainly not in a group setting, so we often so the Leafs lay eggs in big game moments. He also couldn't really get Marner (and the rest of the core) to budge on working to generate offense playoff style because they continued to have regular season success. Credit to Keefe for identifying it early on (2021 is the earliest evidence) but demerit for not whipping the team into shape to leverage that knowledge.
Development via Deployment is largely a dud as well (look at all the players we didn't have time for who went on to have immediate success elsewhere); only Matthews and Nylander visibly grew their games, but they're constantly tinkering on their own.
Media Management is where I can give Keefe tremendous credit; as a rookie coach coming in on the heels of Babcock and that poop-storm, Keefe's relatively stoic approach gave the media next to nothing to spiral off to damage the team and brand. Management Management was also quite good, as he took on ideas from his new GM and just made them work (took half a season).
Officiating Management: haha, Keefe was not good at this at all.
New Coach:
I don't think there's much out there in terms of tactics that's revolutionary.