There are various mathematical proofs and logical arguments for the non-existence of Elo Hell. These proofs are entirely accurate and largely ineffective; fighting personal anecdotes of injustice with math is rarely a fruitful pursuit. The purpose of this post isn't to engage in that futile debate, but to use math, logic, and a little common sense to help improve one's Elo.
The first, and most important, mathematical point to be made is simple: Every game is worth, on average, 22-28 Elo. If you win a game you are only 11-14 Elo higher than you were before, but you're 22-28 Elo higher than you would have been had you lost. Because every game you win is also a game you didn't lose, and vice versa, the stakes on an individual game are higher than most players realize.
In practice this means that any improvement in play, even a minor one, can lead to fairly large increases in Elo. If improving your last hitting leads to 5 additional wins out of 100 games played, then instead of ending that series at 1200 Elo you'll be 1310-1340 Elo. Add an additional win for learning to consistently keep Baron warded, two for knowing when you're overextended, and a couple more for timing buffs/objectives and you're 200 Elo higher than you would have been. The key to increasing your Elo is to improve your play.
The hard part is identifying one's flaws and correcting them. It's easy to tell when you CS poorly, but most other flaws are tiny, infrequent, and unquantifiable. Did you lose that fight at Dragon because of poor positioning or because you pulled Dragon? Did you pick the wrong champion or were you outplayed? Could you have saved top lane if you'd rushed that way instead of continuing to farm? These are the little things that kill, small decisions which are innocuous but critical to the outcome of a game.
The single easiest step you can take to help yourself is to install LoLReplay. With the replay files it saves you can observe your games objectively, separated from the moment to moment stresses of actual play. Flaws that might have escaped your notice during an intense match are much easier to see when you're relaxed and detached from the proceedings. Best of all, you can share these replays with friends and mentors and get their input. Skimming through your past games may not be the most exciting activity, but it's better than repeating your mistakes and turning them into habits.
As a final philosophical point, focusing on increasing Elo is a detrimental mindset. It makes it harder to identify mistakes, make observations, and learn. In the short term focusing on improvement might lead to losses, but in the long term you'll see substantial Elo gains. Whether you think your true Elo is 500 higher than your current Elo or don't care at all, improving is the surest way to move up the ladder.
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