The contest between McDavid, Gaudreau, and Matthews for the Hart trophy this year is very tight. (I leave out Josi because I think we can assume he'll win the Norris, and there is no award for "best forward", so the Hart nearly always goes to a forward.) Of course, Huberdeau also has his champions.
The scoring difference between these four forwards is almost a non-factor, to me. The PPG of these four (currently) is: 1.54, 1.45, 1.44, 1.41. That amounts to a difference between 126 points and 116 points over an 82-game span. Which is nothing.
Still, just going by PPG and total points, McDavid is the front-runner since he'll probably win another Art Ross, even if it's not at all a decisive win. Still, the Art Ross winner often wins the Hart, as we know.
With Hart trophies, you always look at team narratives, which need to be there for a player to win (esp. a non-"canon-ized" player like Huberdeau or Gaudreau). McDavid and Matthews don't really have a strong team narrative this year -- the Oilers are about the same as last season overall, and the Leafs are quite strong but have been strong for a few years. Huberdeau has the advantage of his team being 1st overall, though they were already great the past couple of years, so that narrative is similar to Matthews. Gaudreau has the best team narrative of the four, I think. The Flames were mediocre last year, and are dominant this year, and he's been very consistent and is their best player.
Then there's the "sex appeal" / media-frenzy factor, which of course favors Matthews. (If a candidate plays for the Rangers, he automatically wins this.) Matthews (a) is having an elite season in elite-starved Toronto, which automatically favors his chances, and (b) has reached 60 goals, which nobody has done for 11 (?) years.
Then, there's the literal-definition-of-the-award factor; i.e., the player whose team would suffer the most in the standings if he were not there. This is obviously subjective and not easily measurable. I don't have time to do a deep-dive into it statistically (one would hope the voters will... but they probably won't), but I can do a very simple check of a few things:
Players' point-total as a percentage of team's overall goals:
43.3% -- McDavid (122/282)
39% -- Gaudreau (113/290)
34.4% -- Huberdeau (115/334)
34.2% -- Matthews (106/310)
Then, let's remove Power-plays from that:
Players' ES point-total as a percentage of team's overall ES goals:
38.8% -- Gaudreau (88/227)
37.2% -- McDavid (77/207)
33.2% -- Matthews (77/232)
28.1% -- Huberdeau (72/256)
Then:
Teams' total GF/GA with player on/off the ice:
+122 McDavid --- McDavid on: +79 McDavid off: -43 (Edmonton 282/246 McDavid 150/71)
+118 Gaudreau --- Gaudrea on: +103 Gaudreau off: -15 (Calgary 290/202 Gaudreau 155/52)
+73 Matthews --- Matthews on: +66 Matthews off: -7 (Toronto 310/251 Matthews 147/81)
+42 Huberdeau --- Huberdeau on: +70 Huberdeau off: +28 (Florida 334/236 Huberdeau 149/79)
Taking the bulk of these "most valuable to his team" things into consideration, I think McDavid is the favorite, but Gaudreau is just behind him. Both players' teams are overall in negative goal differentials when they are not on the ice. Edmonton, however, is a bad team when McDavid is not on the ice, overall. (The Flames are also mediocre at best with Gaudreau; in fact, somewhat poor.)
The above stat gives a little less credence to the Matthews' argument, and certainly less to Huberdeau's (which is largely a result of his team being so high scoring). The Panthers are still a strong positive team when Huberdeau is on the bench.
Finally, of course, there's this:
Plus / Minus (i.e., ES results overall)
+63 Gaudreau
+35 Huberdeau
+27 McDavid
+20 Matthews
Plus/Minus is more so a team result than a player one, but there's no denying Gaudreau (and his line) in Calgary are having an amazingly dominant season at even strength. Here, Huberdeau and McDavid look about what you'd expect, and maybe Matthews a little less so, though still good (as seen above, Matthews has been on the ice for the most goals against of the four).
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Of course, the above stats aren't taking into account ice time, situational usage (though these four are surely all pretty similar?), etc., but I think it gives us some good info.
In my opinion, with 2-3 games left in the season, the Hart trophy should go to McDavid or Gaudreau. Considering McDavid is the scoring leader, and Gaudreau is near him and on the most dominant ES line (with a great team narrative, to boot), AND considering these two's teams depend on them the most to be competitive, they have the strongest arguments, I think.
I think the stats above, and my casual knowledge of him, almost rule-out Huberdeau. His performance is Hart worthy, certainly, but taking into account all factors, including value to team, I think he's clearly below the other three discussed here.
Matthews is in a middle-ground. I know there's the argument that "60-goals-gives-him-the-advantage", but does it? Historically, the Hart trophy very rarely goes to a goal-slanted scorer who isn't, say, 1st or 2nd in League scoring. Sure, Matthews might be 2nd (or 3rd) in scoring if he hadn't missed games, but the Hart doesn't take into account missed games for value. And while the Leafs certainly needed Matthews to be in 2nd place, they needed him less, I think, than the Oilers did McDavid or the Flames Gaudreau.
So, it's a tough one, but I lean towards McDavid or Gaudreau, trying to take all things into account. McDavid's disadvantage, of course, is voter fatigue. I wouldn't be upset if the final awards were:
Hart -- Gaudreau
Lindsay -- MacDavid
Richard -- Matthews