I'd guess that in that situation they are close on term as well, so it's just one year difference either way.
Settling on AAV is very GM focused, in that Treliving likely has a long term plan for how things have to align. Term is always good to push for of course because the cap percentage goes down every year. Also in Toronto's case they likely will make a run for McDavid in 3 years so maybe they want that Matthews deal to overlap a bit, at least to 4 years, so they don't have to re-sign Matthews at the same time as they have to give an offer to McDavid.
As a neutral I would be very surprised if Edm doesn't lock up McDavid to some absurd contract the first day they're allowed to. McDavid is the best player in the world, he plays exciting hockey, elevates in the playoffs, puts butts in seats, you don't let those players go.
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Also as an aside, most ppl here are forgetting that Matthews has all the leverage. Full NMC that has already kicked in, UFA next summer, you can't trade him unless he agrees to it (doubtful). I'm sure he's also thinking (probably correctly) that he'll get more than 13.5m next summer when the cap goes up, so from his perspective he's leaving money on the table just by considering an extension now. In other words if for whatever reason he doesn't like the deal Leafs are offering, why not just wait a year he'll almost certainly get multiple better deals from everyone including the Leafs.
And then he can decide for himself whether he wants to stay in Toronto or go somewhere like Vegas or Boston who, unlike Toronto actually has a history and culture of winning -- looking a bit further these are both realistic scenarios bc Boston has cap space if they trade one of Zacha / Coyle while not re-signing their 5th defenseman (both doable), Vegas can make something work if they put Stone on LTIR (also doable depending on Stone's back). At this point, it's not too crazy to think both teams (as well as others) would make a pitch for him, if they do it's not too crazy to think maybe Matthews might end up on any number of teams.
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TLDR -- I'm not saying Matthews will definitely hit UFA, and even if he does, he still very well may re-sign in TOR (see Landy in Colorado). But I
am saying that if he's not currently seeing a deal he likes, why not just wait a year, he'll get better deals when he hits UFA.
Leafs have absolutely no leverage with Matthews and to me it seems dumb to pretend otherwise