Every few weeks, some new champion or method of play comes into existence that just seems impossible to beat. A few weeks ago it was Evelynn and Maokai, and in the past week or so it's shifted to Cho'gath and Draven. Though they can be seriously frustrating to battle, especially in solo queue, there is hope!- so fear not, Summoners, and hearken to my advice.
Draven is probably one of the scariest picks to see in bot lane, especially if he has an aggressive support like Taric or Leona. However, with proper planning and teamwork, he is manageable. Go for an extremely passive disengage/farm lane against a Draven, because you will not be able to out-trade him at early levels. The way to really "win" against a Draven lane is to not feed him. He falls off extremely hard once team fights begin, so if his team doesn't garner a significant early gold advantage, then they will probably lose.
Supports that are good against Draven lanes are Taric (for the armor buff), Alistar (for the disengage and decent healing), and even a well played Janna (fantastic disengage, and her shield will block an axe-auto attack). Supports that are not good against Draven lanes are Sona (squishiest champion in the game, weak sustain), Lulu (also extremely squish and can't help very much pre-6), and Soraka (any Draven that isn't awful will be able to kill her before level 3 unless she completely zones herself).
AD carries that are good against Draven lanes are pretty much anybody with an escape and/or the ability to farm from afar or waveclear at tower effectively. This includes Ezreal, Corki, Graves and Caitlyn. These champions are also strong pokers, and you should try to poke as often as possible to prevent him from going all-in. AD carries that you should *never* play against Draven lanes include Vayne (weakest early game of any ADC), Kog'maw (similarly bad laning phase and no mobility), and Tristana (her harass is too short-range to trade, and she has to all-in to get kills, extremely unsafe against Draven).
Laning against a Draven can be extremely frustrating, especially if you have an aggressive playstyle. If the Draven has an extremely aggressive support, starting cloth armour and potions is always an option. Request that your support buy a pink ward and use it to facilitate an early gank. If you force him to go back to base, or get a first blood, then Draven falls off really quickly and your support can begin to zone him. Don't feel bad about asking your jungler and mid to set up camp bottom because Draven is nothing more than a lane bully that does not translate to team fights, especially if he doesn't snowball in lane. A Draven that is camped is a useless Draven more so than any other AD carry because of this.
If you don't manage to shut the Draven down early, then your best bet is to let him push to tower and try to farm under it. In this case, I would recommend building double Doran's Blades and a lifesteal scepter, especially if your lane has little or no sustain. If you are having particular trouble, you can even buy Ninja Tabi (sell them back later for 'zerkers). If he takes your tower early, let the creeps push closer to your second tower and freeze the lane to farm and catch up for a while. Be sure to let your team know that he will be roaming with his support- getting ganked by Taric and Draven is pretty terrifying! If he continues to try to push, facilitating ganks will be extremely easy, especially if the jungler has chosen to invest in an Oracle's Elixir.
Another option is to play a high-sustain top lane champion like Yorick or Cho'gath and ask to swap lanes with bottom. Your AD carry will probably be able to push down the enemy's top tower fairly quickly to make up for losing bottom tower fairly early, which at least keeps the global gold even. After the towers go down, you can go back top and farm, or make a move on Dragon. Though it may be a bit scary and you may be zoned a bit, a slightly behind tank is better than a crushed AD carry.
Cho'gath in the mid lane is another extremely snowbally terror. With his knockup, three second silence, and several hundred true damage nuke at level six, he can generally one-combo-kill his laning opponent. Not only that, but he pushes the lane harder than most mid lanes early game due to his vorpal spikes ability, which costs no mana. Oh, I forgot to mention the fact that he is also one of the highest sustain champions in the game. These attributes combined make him an extremely formidable opponent. However, as with Draven, he can be handled.
Mages that can lane against Cho'gath are Ahri (she can wave clear almost as hard and has passive regen, and is mobile enough to dodge his skill shots), Casseiopeia (can level her poison to spam on him at early levels to force him out of lane or pick up an early kill; it also gives her high enough mobility to dodge him, and her ult can disengage his combo pre-silence), Anivia (her egg gives her a safety net and her stun can help to disengage), and Galio (his passive magic resistance and high wave clear basically turn it into a farm lane). Mages you shouldn't play against him are champions with no mobility or safety net, for example, Twisted Fate, Karthus, and Ryze. Alternatively, you can swap the mid and top lanes and send a bruiser like Warwick, Olaf, or Yorick.
You should always start with boots as your first item against Cho'gath so that you can dodge his skill shots. I also recommend setting up a rune page with movement speed quintessences. Because he has such a large amount of lock-down, the enemy jungler will also probably camp your lane. As such, you should always buy 1-2 wards with every return to base. Ward both sets of wraiths and you should be fairly safe, assuming that the other lanes have also warded appropriately. You should rush an early Chalice so that you can keep your wave pushed and prevent him from roaming, and to maybe have enough MR to live through his combo if he catches you. After the chalice, your build is up to you, but I would consider this mandatory. Also, don't stand near the creeps while he is trying to push them forward. His vorpal spikes fly quite a ways, and do a decent amount of damage. You could also get hit by one of his skills for some free damage.
There is no such thing as poking a Cho'gath down. Don't waste your mana on trying to harass because he will regain his entire health bar on the next creep wave. The only way to kill him is a super hard all-in, and probably with a lot of jungler assistance. Each time Cho'gath kills something with his ultimate, he gains a stack (up to six) of a buff that gives him more HP. This is the reason why he seems so tanky with no items, but he loses half of his stacks upon death. With a cooldown of about one minute on his ultimate, this buys you enough time to bully him a bit while he re-stacks it. If you see him use his ultimate on a creep for a stack, then he is vulnerable until it comes back up because he can not do enough damage to kill anyone without it. You should try to all-in and force him back, or maybe even set up a jungler gank and get another kill.
If the Cho'gath decides to go with the push and roam strategy, you have two choices. If you know where he is going, you can follow him and turn it into an even fight; or you can call MIA and push the tower down early. I generally prefer to push rather than follow against Cho'gaths because even numbers won't win. His combo is most likely going to instagib somebody and that somebody is probably going to be the squishy mage trying to follow him. I generally only follow if the jungler is also coming to set up a counter-gank.
Thanks for reading my first blog post; feel free to send me any comments, questions, or requests for what to write next! xD