Don't know what you are doing wrong? Stuck in BRONZE or SILVER?! Come here.

I think Sivir is the most mechanical champ out of the three. Jinx and Kog are really the same champs ability wise; they both have a offense, utility, skillshot, and skillshot ulty blast. Sivir is like Draven where you have to have a lot of practice with skillshots and timeshots to really get the advantage from playing her. She just takes a lot more practice to master. In order of difficulty to master (as in play to full potential) hardest to easiest: Sivir, Kog'maw, Jinx. Both Sivir and Jinx I have seen dominate games. Kog'maw not so much. So for your go to champ, to get to Silver 3, I advise you always pick Jinx. Know all of her abilities in and out. She's not particular hard to master and is a really strong champ. I'm not sure I've ever seen her banned either.

TL:DR = Play Jinx.

With that said, make sure to realize that a champ select is never going to auto lose the game. Always pick the champ your best with no matter what. Even if your team flames you.

Some games you lose. Simple as that. It's probably one of the hardest aspects of League to grasp. Here is the best ranked Challenger in NA right now: http://www.lolking.net/summoner/na/65009356 Look at how many games that person has lost. 124 flippen losses.

The trick is to keep a positive attitude. So you lose one game because someone feeds? Big whoop. Guess what, you'll most likely never see that feeder again and maybe it was just a terrible snowball game for them anyways. I've had terrible games and I know you have too!

If a draven is 15-0 in 10min the game is most likely over in all practical senses unless no one else is fed at all then you build a thornmail and he'll kick his own ass. Usually what happens is that the Draven helps other mates snowball as well which is the end of the game.

The question you should be asking yourself is not why do I get paired with idiots but how did that Draven get fed? Address the root of the problem. Is the Draven just much better skilled somehow? Then suggest the jungle camp bot and the other lanes ward against incoming ganks and farm for mid-late game. Don't forget that top and mid lane can push their lane and then venture out and gank too! Is the Draven not that good but your ADC just sucks really bad? Suggest he play safe and focus on farming. Tell him/her that it's OK when they die but to be more careful next time. "We got this, be safe! Do you need help bot?" As long as you can prevent your ADC from dying you probably can kill the Draven easy and win the game. Maybe the ADC got stuck in ADC when he mains top or jungle? Could you have prevented this? If someone suggests a role they like to play do your best to avoid picking that role because it will give you better chances at winning if the other random players get a role they know how to play.

TL;DR = Keep a positive attitude. Always. The best players are the ones who stay positive in their worst games, not their best.

As for your champs: Blitz is pure god mode in anything below gold IF you know what to pull and when to pull it. He's usually banned in low elo for good reason but if he isn't banned then grab him every game. Folks rarely main support in low elo so its a win win. Talon is a strong pick as well. Kassadin just got stomped on this patch and Azir was nerfed a lot as well so I suggest you ditch those champs for now.

Stick with support. As a support you will lose the ability to carry games but you will gain something much more valuable: filling the void and making a difference. Filling the void is very underrated. In Silver and Bronze, may be higher, support is usually frowned upon. Nobody wants to do "that job." People are used to Call of Duty type games where you are pure damage and get killz. So you'll be that guy who takes the role nobody wants and your other 4 randoms will usually get the roles they want. That's good for you. That means a higher win chance because your other 4 randoms will be comfortable and so will you. Support is not just a role that has to be filled by default. Your job is to protect the squishies from the assassins and keep an eye on objectives.

Another benefit of playing support is not having to play the grind fest of last hitting minions. You sit there and wait like an assassin. You wait for the mistakes and you pounce (in lane I mean). Then during team fights you progress into a protector of the squishes.

Blitz, Thresh, Leona, or Sona (DJ Sona just got released too!) are very good choices. Blitz is almost a guaranteed win if you are really, really good with him. Low elo does not know how dodge properly (as in the squishes won't stay back far enough... or sometimes they don't even strafe side to side... etc...) I don't want to be misunderstood here. You certainly don't pick Blitz and win. You pick Blitz and know EVERY DETAIL of EVERY ABILITY, have read 10 guides, know what to build, who to pull, and when to pull... then, at Bronze or Silver, you are practically guaranteed a win. It's not really until Gold that people know how to deal against a Blitz. Thresh, Leona, and Sona all have AOE CC. You get to make the enemy team useless for a very little bit of time. The trick is knowing when to pop that ulty.

Look up guides on how to play these champs and practice their skill shots and when to time your moves properly.

It's much better to be really, really good at a few champs then to try to master all the roles. Look at LCS. They certainly aren't masters of all roles. They have the benefit of playing the same role every game. Make that your benefit.