Looks like many people like to down rate before even trying. SAD. That is not helpful at all. And they are misleading the readers who are trying to get good advice.

Right after I saw 0 positive vote, I will try to prove my point. Just played today, my first game and below is the stats. Take a look at the kills, deaths, assists, damage dealt to champ, damage taken, and largest critical strike. The most important stat to look for any carry is the "Damage To Champs" stat. Not the "win" or "lose" stat. That is exactly what defines a "carry".

Kills, Assists are expected from AD Carry, no big deal. Most of Kills are around the end of the game after Kog has become a super ADC.

Death is low while taking a lot of damage from multi champs ganks. Check the stats on damage taken. Thanks to Flash and Ghost I escaped many deaths from ganks! Most of my deaths because I tried to be super aggressive (like dashing cross enemy's turrets to get my kill, didn't listen to my own advise...). Can definitely be lower if played more defensively.

Damage dealt to Champs is 63K. Double to Katarina's who is our AP Carry. Why Kat has more kills and way less damage? Kat's kills are early game thus lower Champs damage. AP Kat is not as effective as Kog's super ADC late game. And as Kat need to be in the middle of enemy's champs to be effective, she can get killed easily after enemies have their core items ready. Thus Kat tend to play more cautiously. As time pass, Kog on the other hand became more aggresive with long range attacks.

The 2x difference in damage is the trait difference between a regular Carry and a SUPER Carry.
The difference will be more striking the longer the game is. Being the top damager is the aim for a carry, whether you win or lose.

Here, without the sixth item, Kog's maximum critical damage is 802. Although this looks weak compared to Shaco's 1008, this is the damage Kog's basic attack is dealing; very frequently at very fast attack speed and very long range. In a period of [[bio-arcane barrage]'s 8 secs, this Kog can deal more than 12K damage if he can auto-attack continuously throughout that 8 secs. Garen's tank don't stand a chance against this Kog. With full health he spinned and when he stopped spinning, he was dead.

I have not completed my last item build. Trying to get Warmog to absorb Caitlyn's high damage Ace in the Hole. One of Kog's counters I mentioned below. She reserved that move only for me. I got hit by it all the time. I fully understand why.

I am obviously their first target in the end game. Because if I am not dead, they all be dead. Unfortunately to them, that was what happened.

I hope all these make sense and influence you to play the FAST and FURIOUS Kog.
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Before I start, let me warn you that Kog is one of the difficult champ to play.
If you are a player who
1. like to charge enemy single handed
2. like to chase a low-health champ by yourself
3. like to be super aggressive right from the start
4. like to wander around by yourself
Then Kog is NOT the champion for you. Err... maybe I am wrong, but the chance of you getting anything good from the above is minimum.

Kog's best starts showing only after mid-game. And will be a super AD Carry at the end game. Kog is a team player. If your team does not team play, your team will lose because Kog can not function alone.

Kog has to play defensively at the start, focusing on farming and farming and farming. Not killing champs. Even when trying to help your allies, do not get beyond the safety areas. Watch out for allies who love to go on suicide missions; DO NOT FOLLOW HIM/HER! You'll get your kills alright, but not yet.
Of course if you get fed right from the start, the game will be over very soon. Your opponents will know it by you killing every single champ you see. They will surrender very quickly.

Now fast? and furious? How can that be? Kog'Maw is known for its slow movement speed! Inability to escape ganks etc etc etc.

Let's get going first before I explain.

I guessed you already see why this Kog's build is FAST and FURIOUS. Hahaha.
Why attack speed only and no other attack runes or defense runes?

Kog is supposed to be standing far away instead of fielding damage, so attack runes is better suited for him. For lesser damage taken, just try not to get hit. A successful gank against Kog is a death call anyway. Even +100 Armor or +100 Magic Resistance will not help much. I tried it. Don't lose heart if you got killed. Kog's best is at the end game.

Attack Damage, and Armor Penetration may be good alternatives, but I prefer Attack Speed (AS) because Attack Speed sometimes can make a difference between killing or getting killed. And it definitely scale with your increasing damage. With the Attack Damage you have as carry, and the Attack Damage your enemy has as carry, either of you can die very quickly. If you are a bit faster than enemy at AS, it can get you the kill instead of being killed. A +30 or so additional damage is nothing compared to a faster last hit with 600+ Damage. If you missed the last hit by a bit, the Icathian Surprise will usually do the job.

Start with Boots and 3 x Health Potion. You need the additional +25 movement speed because otherwise you will be just too slow. Make sure you play defensively, don't die, and make the health potion last till you get 1550 Gold. If you die or have to go back to base before this, take additional Health Potion (max 3) and go back laning. Focus on getting the gold asap.

Once you get 1550 Gold, get B. F. Sword
If you get this early enough, with +45 AD and Kog's range, the pressure will be on the enemy. And you will farm more effectively with this weapon.

The next 2 items are Giant's Belt and Zeal. The priority will depend on enemies on your lane and your comfort level. If you are taking more damage than you are comfortable with, take Giant's Belt, otherwise take Zeal.

Infinity Edge and Phantom Dancer are the next 2 items you MUST complete. Up to you which one first. Once completed, this will make your AD so frighteningly high that you will find out that enemies keep a distance from you. That is good for you and bad for them!

How about boots? Naah... not yet! With the Flash & Ghost, or combined, you can outrun anybody at this time. Again, Kog is SQUISHY!! Unless you know what you are doing, use them for escape only! Don't waste the summoner's spell for chasing enemy's champ.

Once you have the gold, get Frozen Mallet. Kog's fun starts right there. Once hit with Kog's long range basic attack, enemies movement are slower than you! Lalalala La! Just walk slowly, turn on your Bio-Arcane Barrage spitting Living Artillery and Void Ooze while you continue to let your basic attacks finish the job.

The next item is Boots of Swiftness and Bloodthirster. By this time, when Bio-Arcane Barrage is on, you can see many damage of 500-800 per hit. That will melt even the strongest tank away. In team fights, if your enemies are not aiming you as their first target. Then BYE BYE enemies!

The last item is up to you. My game usually ends before I can get the last item. Another Bloodthirster or Black Cleaver or another Phantom Dancer wouldn't hurt, or would REALLY HURT! Warmog's Armor or Banshee's Veil will sustain you a tad longer. Whatever you need at that time. My preference is of course increasing Critical Chance, Attack Speed or Attack Damage. I find Statikk Shiv is cheap and great! LOL!

My first one is

The damage is minimum early game. But because enemies can see the ooze, they tend to stay away from it. Good for you, bad for them.
Some people like to have Bio-Arcane Barrage first. Void Ooze cause more damage to multiple minions and it is faster to get experience if you choose this. Overall, not too much difference, but I like it this way.

The second one comes pretty quickly.

This is your main killer ability. Max it as soon as possible.
Of course when is available, take it. Damage is also minimum. I use it only to harass and for vision to prevent ganks. For this ADC build, the damage is ...err, not interesting to mention, although many times I used it to last kill low-health minions or champs.

When you are given a selection of Void Ooze or Caustic Spittle
choose

You'll find that you will have no Q until well into mid or late game. That is fine because you are expected to be so far away from enemy that Caustic Spittle will have no use anyway. In most games, unless a gap closer melee champ is against me, I almost never use Q. Which is great for me. One less key to worry.

will help you with Attack Speed. But otherwise, it is not that useful. But since you are fast enough, take it only when you don't have a choice.

It is said that Kog does not have too many escape option. Void Ooze can help at times, but when you are ganked, this won't help.

So I decided to use the standard escape mechanism available for all champions using Flash and Ghost. The moment you saw a gank (or in a team fight where you are the first to get attacked), flash away, usually to home base direction, and if they start chasing, use ghost to run away. At this time Void Ooze and rains of Living Artillery will make your enemies think twice of chasing you.

If you are in a team fight ( in which your allies are very close to you ), and your enemy charge at you first (common scenario as you are the ADC), Flash out! Your enemy will be stuck in the middle of your allies while you are now outside spitting at him. With your super potent attacks, this is a sure death for your enemy.

Together with your mastery +4.5%, and Phantom Dancer +5%, Boots of Swiftness +60 movement speed, and +27% Ghost; unless your enemies have Ghost and want to use it for chasing you, they can hardly catch up!!! Kog is slow, but at critical times, it can be unbelievably super fast.

If you are slowed or stunned... you can cross your finger and pray for forgiveness. So don't get too near enemies at any time including during team fights. Keep a good distance so that you can attack and escape when you need to.

The other spells may be useful, but nothing is comparable to these two. These 2 actually make Kog complete. Now, did I hear that Kog does not have escape mechanism?

Kog's last resort is jungling. He is too slow and too squishy at the beginning that jungling makes no sense. Mid to end game, Kog is a supreme jungler. He can kill dragon by himself.

Kog's best lane is mid.
He can 1v1 anybody early in the game, and gets better over time. If played well, due to the long distance attack, he can reduce enemies effectiveness on farming minions. I saw many times enemy champ decided to change lane because they just couldn't get the gold without being hit.

Kog can neither solo top nor bot. I tried, sometimes it works, but most of the time it is way too difficult. Not worth your time trying it.

If Kog has to go top or bottom, try laning with tank like Blitzcrank, Volibear. Try not to lane with Akali, Master Yi or Katarina, because you can't get the gold from the minions. They will. Moreover they are so aggressive and expect you to cover them that you lose your time for farming. Without gold, you will not only stay squishy, but also become a weak ADC. Then your team will most likely lose. If you are behind in build, jungle, farm from other lanes and forget team fight; without enough build, you can't help except dying anyway. Wait till you get to both the Infinity Edge and Phantom Dancer before you join team fight.

Kog's counter are mainly the gap closer like
Akali
Fiora
Xin Zhao
Wukong
Katarina
If you are laning against these champs, your best bet is to buy Giant's Belt as you third item. They deal a lot of damage and you want to stay alive after they gap close. Good enemy player will even attack you while you are under the turret and then they run away. Try to stay a little behind your turret, spewing Void Ooze if you see them trying to gap close. If they hit you around the turret, your void ooze will prevent them from moving away quickly, and they will sustain a ton of damage from turret;. Harass your enemy with Living Artillery so that they are psycologically afraid to get near to their gap closing range. If you do not have health to sustain their gap closing damage, run away! Let the turret go.

The best way to play against them is if you have a tank with you, like Blitzcrank, Nunu & Willump, Dr. Mundo or Volibear. Alawys hide behind them, and attack the enemies from there. If you see 2 of them in the lane, and both are playing well, ask your ally to change lane; otherwise you will see yourself getting killed a lot of times and unable to build effectively. Unless, of course, your ally try to cover you all the time, which I find rare in solo game.

Other counters are super long range champs like
Caitlyn's Piltover Peacemaker and Ace in the Hole
Nidalee's Javelin Toss Massive damage!
Orianna Never see any opponent using her, but if played well, this girl is hell for Kog, and everybody else. Her ball is super annoying.
Ziggs's Bouncing Bomb
Teemo's Camouflage If you got attacked suddenly by Teemo on camouflage, your survival chance is close to zero.
Kog'Maw I hate playing against another Kog! Esp those who read this guide.
You have to keep moving around left and right to avoid their ability attacks. (Forward and backward does not help). But once you start using your living artillery effectively on them, they tend to stay away from you.

AT LATE GAME, all these counters do not matter because with 3-4 long range Bio-Arcane Barrage attack, they'll die. Build and play Kog well and you will become the ultimate counter to any champions in this game.

Attack speed increase is +28% from runes and +4% from masteries. It has +32% attack speed off the start. With +50% from Phantom Dancer, it gives +82% AS. At lv 18, Kog's attack speed is 1.75x a sec. That is very decently fast.

With the movement speed of 330 + 60 Boots of Swiftness, and +4.5% runes, and +5% Phantom Dancer, Kog's movement speed is 434. This even out the lack of speed he has. When needed, you can add the boots enhancer Enchantment: Alacrity or Enchantment: Furor.
To escape, you have your Flash and Ghost.
And did I say that we have Frozen Mallet? If you have Enchantment: Furor, you can run, turn back, attack, run, turn back, attack, VOID OOZE, Living Artillery rains, run.... you know what I mean. One time I was chased by 3 champions while having only 20 HP left. And I killed them all.

The most interesting one is the Attack Damage. At Lv 18, Kog has 100 AD. Decent.
With all the builds, it has +70 Infinity Edge +30 Frozen Mallet +70+ Bloodthirster, total 270+. However, with easy critical hit from Phantom Dancer and +150% bonus damage from Infinity Edge, it will deal max a whooping 675+ damage. On top of that with Bio-Arcane Barrage, you will deal additional 6% of enemy's max health as magic damage. And when your attack distance is +210. Holy cow ... hole-ly enemies!

SCARY number? Wait a minute... I completely forgot to count the sixth item! I leave it up to your imagination on what you can do with the sixth item. You can actually kill any carry champ with 3-4 hits (2 secs), or a tank with 5-6 hits (3-4 sec).

Getting the upper hand and chasing your enemy? Combination of Bio-Arcane Barrage, Void Ooze, Ghost and Frozen Mallet will not fail.

With such a fast attack speed, high attack damage, slow effect, fast movement speed, super long range and great escape mechanism sometimes I find myself asking ... where is the enemy?

It takes experience to be good at Kog, esp to prevent and to escape ganks. But once you get it. It will make enemies shiver.

At late game, you exert so much pressure on the enemy team that you will definitely be the #1 champ for them to kill. So be prepared for it.

Oh by the way, if you can't stay far away from enemies, make sure you are protected by your allies, and get your Flash and Ghost ready. You are still squishy throughout the game.

'If that's just hungry, I don't want to see angry.'
-- Tryndamere, the Barbarian King

Have a lot of FUN trying this! And let me know your feedback.