How to raise division/MMR without playing better

1. Allow your teammates to carry you. You are playing to win, not to be a big shot who carries every game. In fact, you probably cannot carry every game unless you are smurfing. If you are 1-9 but your teammates are all 9-1, don't bitch about your score - just stay safe, relax, listen to calls, and let your teammates win the game for you. 
2. When your teammates are throwing, remember your opponents can be just as likely to counterthrow. The matchmaking algorithm dictates that your teammates and your opponents have similar skill level. If your teammate is throwing, your opponents can throw too. Until the nexus falls you can always seize the opportunity to win.
3. Don't question bad plays. Remember your teammates also want to win - they are not intentionally feeding your opponents as an attempt to make your life harder. When they make bad plays, they already feel bad themselves, so there is no need for you to spray salt onto their wounds. I recommend you say absolutely nothing about it and keep your mouth shut. You are here to win the game, not to belittle some random person on the internet who made an honest mistake.

URF mode win rates

I collected over 200k URF mode games during the ~2 days so far. These games are so popular and go so fast that it was extremely easy to get these data.

Here's the win rates on  URF mode per champion, from the highest to lowest. I am sure a lot of these numbers are no surprises to you. 

Champion	Win Rate	Popularity
Sona	77.973%	21.151%
Soraka	66.283%	18.427%
Hecarim	62.403%	16.908%
Kayle	61.177%	13.126%
Nami	59.342%	7.727%
Nidalee	58.921%	39.039%
Alistar	58.744%	18.688%
Galio	58.528%	2.968%
MonkeyKing	55.568%	12.385%
Janna	55.261%	6.522%
Skarner	55.069%	5.482%
Karma	55.058%	9.888%
Morgana	55.024%	9.774%
Ezreal	54.839%	35.902%
Fizz	53.871%	16.277%
Malzahar	53.767%	5.810%
Sivir	53.577%	7.949%
Shen	53.576%	6.013%
Jayce	53.175%	13.668%
Orianna	53.061%	5.160%
Sion	52.787%	6.384%
Talon	52.293%	6.319%
Taric	52.058%	4.835%
Lulu	51.810%	11.946%
MasterYi	51.769%	20.481%
Swain	51.630%	8.759%
XinZhao	51.488%	5.586%
Sejuani	51.263%	1.605%
Karthus	51.110%	12.528%
Lucian	50.875%	8.343%
Fiora	50.870%	6.080%
Maokai	50.839%	9.645%
Poppy	50.818%	6.219%
Leona	50.811%	8.123%
Yorick	50.729%	5.637%
Evelynn	50.482%	9.004%
Ziggs	50.480%	18.999%
Brand	50.285%	7.982%
Jax	50.040%	8.617%
Lux	49.823%	30.431%
Warwick	49.810%	6.070%
KogMaw	49.747%	7.268%
Zyra	49.690%	8.459%
Syndra	49.580%	7.202%
TwistedFate	49.507%	7.539%
Nautilus	49.506%	2.396%
Ashe	49.463%	15.728%
Draven	49.253%	6.611%
Veigar	49.153%	12.286%
Urgot	48.893%	9.095%
Graves	48.872%	2.427%
Katarina	48.621%	14.914%
Malphite	48.464%	7.278%
Zed	48.409%	19.374%
Rengar	48.174%	8.020%
Ahri	48.088%	16.980%
Heimerdinger	48.083%	9.833%
Blitzcrank	48.082%	17.546%
Amumu	47.988%	4.624%
Shaco	47.948%	13.161%
Twitch	47.941%	3.448%
Nasus	47.845%	11.352%
Annie	47.748%	8.589%
Kennen	47.497%	3.239%
Teemo	47.492%	20.477%
Diana	47.423%	3.677%
Riven	47.309%	12.731%
FiddleSticks	47.149%	9.802%
Vladimir	47.104%	5.942%
JarvanIV	47.040%	2.755%
MissFortune	46.900%	3.399%
Viktor	46.785%	2.632%
Darius	46.598%	6.092%
Caitlyn	46.452%	7.153%
Quinn	46.298%	1.904%
Lissandra	46.197%	2.830%
Akali	46.058%	9.591%
Varus	46.014%	11.778%
Gangplank	45.746%	13.274%
Irelia	45.513%	2.021%
Mordekaiser	45.410%	3.126%
Renekton	45.308%	2.916%
Chogath	45.209%	5.448%
Gragas	45.082%	8.540%
Tristana	45.026%	7.058%
Jinx	44.737%	12.420%
Tryndamere	44.663%	8.045%
Velkoz	44.556%	10.165%
Rammus	44.450%	3.086%
Xerath	44.342%	5.096%
Khazix	44.295%	9.595%
Volibear	44.294%	2.148%
DrMundo	43.983%	5.327%
Singed	43.957%	4.048%
Vi	43.925%	3.543%
Pantheon	43.391%	9.234%
Nocturne	42.896%	4.339%
Leblanc	42.850%	17.175%
Zilean	42.673%	7.370%
Vayne	42.210%	7.817%
Trundle	42.072%	1.610%
Corki	41.884%	2.354%
Shyvana	41.317%	1.527%
Udyr	41.008%	3.867%
Cassiopeia	40.961%	3.290%
Nunu	40.561%	4.709%
Olaf	40.262%	2.297%
Garen	40.187%	4.435%
Zac	40.058%	1.041%
Elise	38.946%	1.568%
Anivia	38.353%	3.612%
LeeSin	38.294%	9.646%
Aatrox	37.822%	1.298%
Rumble	36.821%	0.876%
Thresh	36.243%	5.305%
Yasuo	33.686%	6.165%

What I do NOT find surprising:

- Nidalee, Soraka, Sona, Jayce, Helicopter-Pony win like crazy.

- Yasuo, Rumble, Cassiopeia suck, since they gain very little from the 80% CDR.

- Lux is mediocre. Her R spam is decent, but no match for the sustain from some of the better champions.

What I DO find surprising:

- Galio wins like crazy. This is probably due to his W spam and his MR scaling against a meta that is almost all magic damage poke.

- Nami wins like crazy. Not quite sure what happened here, especially if you consider the fact that her E is not too useful and does not scale well with CDR. Perhaps due to a combination of sustain from her W and her damage/CC from Q + R.

- LeBlanc is played often, but she isn't too good. Despite what Riot said during the TSM vs C9 match, you cannot perm root someone with her E spam. 

Note:

- Unfortuantely, ban rates are not available. I do suspect Nidalee and Sona are actually banned quite a bit. When Nidalee gets picked, for example, around 1/3 of the games will have Nidalees on both sides.

- Win rates are calculated only in games which the champion in question is played on one side. This makes sure an overwhelmingly popular champion does not have close to 50% win rate.