Did you read the article? Have you taken a college/graduate level statistics class or understood what you are trying to refute? The more samples taken the more the actual values approach their theoretical values.
OK, I am just going to pick apart your argument.
An "average" is essentially the peak of a bell curve.
There is no reason to assume the Elo in LoL is a bell curve. In fact, I'd be willing to bet it's not a symmetrical bell curve. It most likely is a bi-modal curve due to the great amount of very low Elo players and the players at 1400 due to Elo decay. Any statistics you have for a bell curve are essentially null and void now.
There are always outliers. There are always people at the far left and far right. People who get carried to an ELO they don't belong in, and people who are below the ELO they do belong in.
Yes, there are outliers, but you are stretching the concept of it to new widths. This occurs when there is a
small sample of games/actions taken. When the numbers are drastically increased, the probability of you having bad members on your team vs the other team having those crappy members is 50%. There may be streaks either way during that time, but as a whole after a substantial amount of games, it's 50%. This is true for everyone, independent of Elo or skill in the game. This isn't opinion, this is mathematics, founded on logic and the Zermelo-Fraenkel Axioms of set theory. If you refute this, then this may be one of the greatest finding in the history of math.
Just because you magically throw out the word "average" doesn't mean it applies to everyone.
Why am I not allowed to use the word 'average' as pertaining to an entire set, namely the players of LoL. It is a perfectly valid claim; any sort of quantitative statistics can use averages and the value of that average relates to the
entire set. I don't know why you are averse to me using this valued term in our debate.
While it is somewhat acceptable to agree with the idea that people who don't win a lot are bad, it is in fact a logical fallacy.
What fallacy? If two players were to play numerous matches against each other, and the first player won significantly more matches, would we label him the 'better' player or the 'worse' player? 'Better', obviously, because in this game, where the sole objective is to win the game, those who win more are considered 'better'. We did not create this labels arbitrarily and they have been used since the dawn of competition, online or real life. This is no fallacy.
This game isn't designed well enough to rate people on their individual abilities and their team abilities.
Why not? You give this conclusion with no actual evidence or backing. On average (a solid average, due to millions of people playing this game and many more millions of games being played) the players with higher Elo will most likely win more games than those of lower Elo. This isn't opinion, it is fact and is represented by the wins and loses tallied by every player. And as you'll see from the previous paragraph, players that tend to win more through a sample of numerous games are considered 'better' players.
This is a team game after all, and I'm sure everyone has experienced those good games that are lost simply because one person on your team is bad.
Here, you fail to acknowledge the games where you [everyone] plays poorly and happens to be carried. This happens with the same frequency as feeders on your team; matching does not have a bias towards you or any other player. Feeders can happen in relatively long streaks, but so can being carried and, by the LLN, the line will even out.
In terms of real world example, it is curious that no real, sustained, professional athlete in a major league would match your example of an outlier, even in team games where the result of the game does not rest entirely on his shoulders. Given that real life sports has a much, much larger sample size than LoL, this would be considered incredibly improbable. What is much more likely is that 'bad' players are behaving according the the
Dunning-Kruger Effect, a cognitive bias where incompetent people are so incompetent to the point that they can't recognize their incompetence and therefore overestimate their skill, denying them the ability to see their mistakes in full.