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Yeah not playing carry or support is what got me out of hell. All it takes for a carry to succeed is basic map awareness, not dying in lane, and the rest of your team not collapsing in the first 15 minutes. Despite the potential to face roll later on, carry is a comparatively low skill ceiling and not what you should be picking if you're stuck in a division beneath your ability.
Supports? I've often heard "good supports win games". This is usually from support players who need to feel important. Good PLAYERS win games, and a support is only as good as the players he's supporting. A good team can overcome a poor support much better than a good support can prop up a poor team.
So the secret in ranked is to always call mid or top first. Jungling is better than carry/support, but it's still not as important as top or mid (again, a good top or mid can overcome a poor jungler better than a good jungler can prop up a poor top or mid).
Copy "top" or "mid" to your clipboard. Immediately paste it into chat as soon as champion select comes up. The most important thing you can do in ELO hell ranked game is to take that important slot away from the public randoms.
What if someone calls those roles before you? If you get to pick before them, steal it. Some people might say this makes you a jerk, but in ranked you're out to win. If you want to play nice and make friends, play unranked. In competitive sports you don't pass the ball to a poor player in a poor position just to make him feel better. So just pick your top/mid champ, announce it, then explain that you will win. If he still complains that he called it, repeat that you pick first and this is the best way to win. He has plenty of time to pick another role or counter. If he's still raging then he'll probably queue dodge, which is just as fine because a player that inflexible and ragey will probably have lost you the game anyway.
What if you get last pick and are stuck with carry/support? Well, if you really want to improve your ranking as much as possible, I'd say give serious consideration to dodging. Go do something else or play unranked while your dodge timer resets.
Has one of your teammates picked Twisted Fate, Karma, Soraka or announced an AP Shaco? Dodge. I'm not saying there aren't players who can make those work, but they're so few and far between that it's probably not going to happen, especially in ELO hell.
If you're part of a team and know you're one of the more rocky players, or you're playing unranked then by all means go carry/support if you feel like it. But solo ranked? TRUST NO ONE. I went from a 55% win rate (that would have taken FOREVER to advance) to around 75% once I realized this.