In competitive games, rating player skill is a very hard to solve problem. Not simply because player skill is a very broad concept, but because players have unrealistic views of their own skill level.
Skill in a game can best be approximated by a player's ability to influence the outcome of a game favorably. This can take the form of anything from mechanical skill, to the ability to communicate. Sometimes, you'll see players who are mechanically skilled but socially inept be unable to succeed in team based games. Then they end up complaining about their teammates and blaming their teammates for their losses.
Players tend to overestimate their own skill level in a Dunning-Kruger fashion. The majority of players think they are well above average in skill, which is a clear impossibility. Part of this comes from players not wanting to accept responsibility for failure. It's much easier to blame other players or circumstances when you lose. Another part of this comes from most games being designed to make the player feel good about how well he does. Games reward you for every little thing you do right.
I have seen countless posts on various gaming forums for countless games in which players complain about the skill rating system in the game because they feel that it does not work in some fashion. There's actually quite a lot of math and statistics behind modern skill rating systems that show that they actually do work.
Nowadays, game developers have resorted to hybrid progression / skill rating systems, which allow players to have the convenient excuse that they simply don't "grind" progression as much as the other players who are at a higher level. Players who play a lot and are truly competitive will reach their appropriate skill rating, whereas the players who play less can pretend that their lower skill rating is due to them playing less. Of course there is some truth to this, since skill improves with practice.
If only the masses understood skill.