Its common knowledge that the choice of the stage can have a great impact on the outcome of the match. But in the grand scheme of things, just how much of an effect does this really have?

While a matchup can be 6:4 on one stage and 7:3 on another, does that mean that overall that the matchup is 6.5:3.5? Maybe, maybe not.

But in order to truely grasp the matchup knowledge in order to give an accurate estimate on the matchup advantage ratio, should the matchup be
analyzed on ever legal stage? Should we average them together?

I would like to see your opinions on the subject, as well as maybe discussions about how specific matchups play out on different stages.

Lets take a look at the current anther's stage list for reference:
Starter:
Battlefield
Dreamland
Final Destaination
Pokemon Stadium 3
Smashville
Tower Of Salem
Yoshi's Story

Counterpick:
Castle Seige
Dracula's Castle
Jungle Hijinx
Mirror Chamber
Sky Sanctuary {disgusting}

Knock yourselves out, theorycrafting is the funnest part of the game!

I'm confused on why Sky Sanctuary is legal and Wario Ware isn't

Well if this relates to matchups on that stage, do you think Wario Ware is most fair than Sky Santuary, and then after that, do you think it should be fair/unfair?

Remember that a little bit of unfairness is the point of counterpick stages.

Matchups are stages are intertwined. I think there is merit to comparing the abilities of two characters while trying to ignore stage choice, but the fact is that if Character A hypothetically beats Character B (ie is way higher on the tier list) but every single stage benefits Character B, then it is hard to argue that the stages do not affect the MU.

So when looking at MUs I think it is a good idea to look at the stages and how they impact it. When I did a MU chart for Falcon a year ago, I gave an opinion on a MU number but if I felt like certain stages were really good for either character in the MU I included info about how much better/worse the MU becomes. I didn't usually go with hard values (and if I did, it was just to give a ballpark estimate) because it's hard enough to decide on ONE MU value let alone another 12 lol.

So if Wario has a stage that makes the Falcon MU 50-50, but it's the only stage that is like that (the rest he loses, all hypothetically) then I suppose you should average all MUs but that's a lot of work for not much increased accuracy. Instead I would just say "Falcon wins this matchup 60-40 on every stage except for stage X where the MU is even since it is so good for Wario..." instead of trying to analyze the MU in detail on each stage. Getting the main details of the MU down and giving a brief overview of how each stage affects the MU is 80% of the useful info, there isn't that much need for the last 20% considering how much extra work it is.

It's kinda like learning stuff like KB constant/growth and trajectory and stuff on a move in addition to the move's frame data. While all of that extra stuff is nice, knowing the frame data and the general idea of where the hitbox is is like 80-90% of the useful/practical data. The rest is just extra stuff that doesn't hold that much value, you already have an idea of how strong the move is or what trajectory it sends on.

Theoretically, you could have a matchup chart for any given stage correct?

Suppose you wanted to create an accurate matchup chart (to the best of our anylitical abilities) which would involve gettign the matchups from a given stage. Would you say that you could potentially do this for some major stages and be mostly accurate?

Are their any key stages that we can use to more or less predict how the matchup would go on similar stages?
[maybe somehow categorize certain stage features and design schemes or something?]

Personally, I think that something like that (key stages) might be doable on project m, but SSF2's stage list is extremely varied in comparison.