A copy of my Forum post about this topic (http://euw.leagueoflegends.com/board/showthread.php?t=939766). When I calculted it, it turned out to be far worse than I ever feared:

I know, I know, they say Elo hell doesn't exist. I won't go into standard arguments now. This post is purely calculating.

First, we start with someone with bad luck in placement matches (I was one of those). My games went like this (this post is NOT about self pity, it's just that I am a perfect example for the point I'm trying to make):

15/6/20 Defeat because the internet wiped out at our AD carry. Not his fault, just bad luck.
2/7/20 Victory. My score would've been better if our AD carry wouldn't have carried us 110% sure (I started overextending while not needed).
I don't remember the score of my third game. I do remember that someone had an attitude that negative we simply had no chance with all the whining.
0/4/7 Victory, my score was that bad because I was never in time at the lanes as jungler. My allies already made the kills all the time.
10/7/4 Defeat, I played AD carry, got 4/0/3, but Amumu and Morgana were fed thanks to a bad ally, they focused me every teamfight.
17/8/7 Defeat. It should say enough that I had kill or assist in 13 of the 15 kills at some point. While the other team had about 25.
3/1/12 Victory. Not much to say about, carried by Diana.
0/5/8 Defeat. I was useless as support, plus two people fed.
0/3/1 Defeat, I had to solo bot with Vayne vs Sona and Caitlyn, as the support was playing on a calculator at best...
8/10/8 Defeat, we had an AD carry that did not speak a word English, rushed a Last Whisper on Ashe (while noone was even building armor), and constantly overextended, plus she couldn't farm.

All of the seven lost games are lost because of either bad luck, or a player who doesn't know what he's doing. Now, the rating this costed. Say that I would have won 3 of those games without the bad luck/bad allies. That'd be 3 times 40-50 rating won instead of lost, for a difference of near 300 rating. It might've been even more, if in the first game we wouldn't have had the dc, in that next one not the whiner, etc. All those things that are what people call Elo Hell, and what I call bad luck when you get most problems from it.

Now, the calculations I talked about. Imagine 10 people, who all have 1000 Elo, in one game. They have all played exactly 100 games, nine of them belong at 1000 Elo, one is, through bad luck in his placement matches and maybe a few more bad luck games (in fact he doesn't really need that, as this example will prove) at this Elo, while he should be at 2020. That's a big difference, 1020 Elo. Right?

It isn't. Imagine 2 players, who play 100 games against each other. If the difference in win rate is 67% to 33%, that means the player with 67 wins has had 34 wins more, equaling to 34*2*15 (say that you gain/lose 15 Elo per game) is 1020 Elo higher. Over 100 games.

Now, this already shows that a 2020 Elo player, who started at the same 1510 Elo as the other player, will still lose every third game from this 1000 Elo player.

Next, and this is my main point, let's calculate the win chance of this player in the 5v5 where the other nine belong at 1000 Elo. The others, compared to one enemy, have a 50% win chance, this player has a 67% win chance. (4*50+67)/5=51.7%, and the enemy team 48.3%.

That's it. Those few numbers show, that if you are playing 1000 Elo below your level, you only have 3% win chance more than the enemy team. So for every 100 games, you gain 45-60 Elo. Let's say 50. To get to your true Elo, you'll need 20*100=2000 (A FREAKING TWOTHOUSAND) games. You don't have that much time in a year.

So, what should solve this problem? It's easy. As I showed earlier, starting 300 (or maybe even more, it can be up to 800, depending on how much you lost due to bad luck) Elo too low thanks to placement matches is perfectly possible. At the same time, the system only cares about your win or loss, not about how well you did. You can go 50/0/30, and if all your teammates went 5/30/5 or something among those lines, you most likely lost.
I have two easy solutions:

1) Remove placement matches, as this is the most important thing that puts people at a totally wrong Elo, as it's far too luck dependant on if you get allies who actually know what they're doing, and on unintentional disconnects.
2) Base rating on KDA instead. Now, before you all start about kill stealing, I say, make a kill and an assist count equal, but make a death count heavier to avoid everyone rising to 2000000 Elo. If you go 15/6/20 but lose, like I did, you would at least get Elo, as you got the best score of the game.