By what metrics are a players skill decided?

Personally I think an accuracy/damage ratio metric would be ideal, but it'd have to be filtered into different categories. I say that because if you only have one ratio of accuracy compared to damage, it doesn't take into account the range at which you're playing at. My accuracy with an R99 is not reflective of my accuracy with a Longbow. (I haven't grabbed that gun since Armed & Dangerous.) 

So you'd filter the weapons into different groups based on range. Obviously it wouldn't be perfect because then what happens when you use a weapon outside its intended range? We've all hipfired with a G7, and some of us might've gotten cheeky long-range precision choke Peacekeeper knocks. I don't have an answer for that, but ideally, it'd basically count towards whatever range you're looking at. 

You'd have three groups of an accuracy/damage ratio, one being close range, one being general use, and one being long range. For example's sake I'll put R99 into close, R301 into general, and G7 into long range. So let's say you primarily play close range, aggressive pushes with the R99, snapshots with the Peacekeeper, etc. etc. Your accuracy/damage ratio would be reflective of how good you are at each individual range. With that info the matchmaker would match you with either same, slightly lower, or slightly higher ratio players. I think that'd be a good indicator of overall skill, and being able to see the statistics on their banner would help your team be more cohesive as a unit. Someone with a high ratio for close range probably plays aggressively and can hit their shots and make picks for your team, so you'd play around that. A long range player with a lower ratio probably has practice hitting shots (obviously you can't hit them all) and you'll want to play around pressuring the enemy before closing in for the kill. Someone with a high general accuracy ratio might just do whatever and follow your playstyle, so they might just be all around reliable. Obviously there's multiple interpretation issues regarding this, but ideally I'd base it around something like that, while also factoring in their total games played / total game time, etc. etc.

In my eyes sizing up capability comes down to just overall experience. Things like, decision making, use of terrain, cutting off enemies, etc. etc. I don't necessarily need you to land shots, I just need teammates who can follow up on what I do, or make choices that lead to beneficial situations for us. I come across way too many people who've played the game for hundreds of hours and just, don't know what they're doing and can't hit any shots. Things like, should we fight or disengage, which way should we go while the ring is closing in on us, how can we outmaneuver the enemy, how can we use the ring to our advantage, etc. etc. 

Also I'd definitely have a player run reputation system. Nothing punishable, just quirks you'd watch out for and maybe be able to filter in matchmaking. 3 Positives, 3 Negatives, tagged onto the players banner that you can see, but they can't see. Pros being things like, communicates often, has good aim, shares supplies, etc. etc. The three most tagged positive qualities would be shown, and the 3 most tagged negative would be shown as well. Negative qualities would be like, loot hog, toxic, doesn't communicate at all, etc. etc. On top of that, if you're friends with them, or you add them, or they add you, or they invite you to their party of whatever, you're no longer allowed to tag them for positive or negative. There's going to be no way to influence their tags once you start playing with them, because you saw their tags first in random matches and decided that they were tolerable enough to play with them. The only people who can influence your tags are randoms, so if you want to be tagged fairly and positively, you play fairly, and positively. It's also definitely going to have a number next to each individual tag to show you how many players tagged them with X quality. There's no merit to seeing the tags without knowing how frequently they're being tagged that. Also most definitely some of the tags will cancel out. If you're rated toxic by 120 people, and get rated non-toxic by 30, you're definitely not going to have the "non-toxic" tag listed. 

Edited because apparently c-o-n-s is censored.