I do not have time to work on this, I just wanted to get it out there and managed to scrounge up the time to do it (I do enjoy playing the game but between everything in life and relaxing, this does not really count as relaxation to me). I will periodically check it, but it wont be rewritten by me. If anyone wants it improved then take it upon yourself to write up (BBCoded if you so desire) until you reach your heart's content, then either post it in this threads discussion and/or PM it to me as well as explicitly stating that I (A.R.M.) can use the material provided in this guide ("Watch Them Burn" by A.R.M.). Any criticism about how I should improve my formatting (but do not offer the finished formatting themselves) will be taken as Ignorance to what I have explicitly stated here, thus ignored; I will welcome any constructive criticism about gameplay mechanics (including items, spells, runes, masteries, positioning, timing, anything for it.

Note: This is not rigor tested outside of ARAM's, and it took awhile to rigor test it inside of ARAMs for the champions are random. Trying to get people to welcome the idea of going through with this bot lane is quite difficult, I do not like rigor testing things like this with randoms because in my experience in most cases no matter how you do at least half of them get upset, if you do bad they are told you so's that rage and report... although those are not valid test cases for they didn't want to see you succeed in the first place. Considering I had a bad experience when I first started playing for people raging at me because I was really good with one champ that I mained so had a higher than I should have had normal (hidden) elo, then tried new champions and absolutely failed... so I got reported by my own team (even though I told them in champion select the situation (I never played champion before I want to learn it)... so I got banned for "Intentional Feeing." I did go something like 0 and 13 on sion being the worst stats out of them(and some ones from when I initially started playing that were residual, and of course the reports lack date stamps) ... from then on I haven't tried new champs except for when I have at least 2 other friends playing with me... for there is always the propensity to fail (which is why I fear trying new champs in PBE, especially with its stricter offense banning rules ("intentionally feeding"), anyways now that you have that word of caution (even though the tribunal has changed since then), lets get to the topic at hand.

I am going to assume whoever is viewing this knows the basic mechanics of Kog, and if not, one will learn, I advise seeking out other guides/resources to learn how to play him.

This guide is for ARAM, but if you want take the build and do an alternative build order in the other game modes. Keep in mind even AD Kogs do primarily magic damage, so you can go bot lane, for the days of solo Kog'Maw are over, just make sure there is ad elsewhere.

This guide basically states:

Kog mainly does magic damage despite the type of build.

Ginsues is a great sustain item (if he falls below 50% hp) and Kog can keep that active up infinitely if proper teamwork and patience is employed. 20% attack speed, 10% life steal, 10% spell vamp until exiting combat (until the timer that recognizes you (or your burns) as hurting anything expires)
One can indefinitely keep the passive up if proper teamwork and patience is employed too. +32% attack speed and +32 ability power

Kog should never overextend, but this build allows Kog to take (most) (<-- assumption that this will not always prove true on the basis that I can not possibly tested this vs the best player for each and every champion all the permutations of scenarios, let alone get anywhere close) anyone down that gets close to him.
This should also allow Kog to stay with his team rather than his team stay with him, although as with any carry, he still needs to be peeled for; point being is that he is not as team dependent.

Liandry's Burns like hell, and if the enemy gets close then your void ooze will cause an extra 6% (magic) burn prior to your additional (for they are now in range) 5% physical damage burn of the blade of the ruined king.

Rabadons makes the difference of 200ap (2% of health bonus magic damage) to (5% of health bonus magic damage), decide if cc/penetration is worth the loss of that 3% (how much health are your enemies packing). Ther eis also the fact that all his spells scale off AP

Ignore what is below for this guide is not proof read not is it formatted well, what is in this preface are my main points.

If you wish to do this outside of ARAM go bot with a support (or rather someone that will let you farm). Build in this following order: a chalice, a liandry's, sorcerers shoes, ginsues, blade of the ruined king, rylai's

Never spam your ult to poke, it is ok to do so if you are in a teamfight, just do not go overboard, for your cd's are not ridiculously long, and your other spells tend to be overall more effective in a teamfight landscape, use common sense (can you afford to go oom at this time, how much longer are you likely to live, and how much longer do you expect the fight to last (cost benefit analysis, the benefit being conserving mana to do more damage in the long run (if it make sense to as defined prior))).

I know this is a mess, the gist of it is the build as a whole. Ginues offers great sustain, his ult's cd (for mana cost resets) is slightly under that of ginsues cd for stacking it's passive, so this results in a state of predictability(Kog will ult) but also in a state of constant sustain and fear for the opponent for Kog has 8 stacks of ginsues. Once you upgrade the chalice to a grail you increase your cd thus your level of predictability decreases enough strategically speaking. Ginsues drop below 50% health passive of sustain and attack speed yield insane sustain, and since the burns of your items count as damage dealt, it is constantly running, as long as you do damage to something every so often (ult mana cost cd) you are good to go (ad as anyone can imagine it is easy to keep ginsues up on SR, TT, and Dominion because there always are minions around, ARAM all minions die immediately and most champions are either fighting when vs a kog or dead (or Kog's tier 3 ult is not up and the enemy is too fast to keep pace with, although it is not the worst thing I the world to not have it, but it is one hell of a buff).

In short you don't have crazy mana sustain as AP Kog, but with proper management your more effective than AP Kog. Ginsues gives you sustain and damage for it is a given that someone will always get to you, and gone is the day of an AP Kog that can beat anyone that reaches him (lich bane is gone and Kog cannot ascertain 1k AP anymore). Blade of the Ruined King will buff your health a bit plus is a slow, thus your spells burn even if you have no other slow item and have no e.

Kog Must have liandry's for it almost makes up for his ults nerf, although if you don't know about that, then rather his ults lack of power. You do not need a slw item on ARAM, for more often than not you can hit them with void ooze (for they hav to fight or be poked to death), and that will give them 12% burn, then just keep hitting them whilst they're on it, plus you have the blade of the ruined king.

If you just cannot consistently land your ults then I advise rylai's. If you can but they get close and are high physical damage and life steal, then get iceborn gauntlents (If need be). It is always nice to have rylais for it yields in 12% burn (minus resistance), which is still absurd.

If you are doing this build outside of ARAM I advise a Rylai's as a must have for that added crowd control, plus if you blind skillshot anyone, it is harder for them to run away or engage.

I have touched base on the items if you want to use them in ARAM, this section is for outside of ARAM.

Outside of ARAM I advise always rushing a chalice, then liandry's (get tier 1 boots somewhere in here). Then get sorcerers shoes (for Kog is slow, if your having issues with mana then conserve it a bit more, if your still having issues then get Elise's miracle (by level 15, philosophers stone of course prior for that gp10). Get ginsues next, if you are running hybrid pen runes get the pickaxe, if you are running magic pen runes get the blasting wand. Once ginsues is finished get the blade of the ruined king. Once you get the blade of the ruind king get rylais. Finally upgrade the chalice to a grail.

Ginsues allows you to effectively fight those that get unwelcomingly close, and the blade roots this into reality, attempting to fight those that get close prior to this is more or less futile (judge for yourself for it is situational) and resources are probably better spent trying to kill their carries as your team is.

If you are adverse the idea of more AP (a rylais) then grab a mercurial scimitar if cc is an issue, if movement speed or attack speed is an issue go a phantom dancer or a trinity force. If you desire more AP and don't like my other options there is always lich bane (as much AP as rylais but with movement speed and bonus damage rather than a slow).

If you chose to get sorcerers shoes upgrade them with furor.

Read the description, but basically Kog no matter how you build him does mainly magic damage, I opted hybrid penetration runes to increase the effectiveness of the blade of the ruined king and the smidget of ad I had as to make it harder to be counter built. It works great against the champions that lend themselves to be both high (magical) resistance and heavy sustain.

This guide is for ARAM, but if you are repurposing it I advise exhaust, for people will get close to you, and exhausts resistance reduction as well as it's movement impairment and damage nerf give you the upper hand even if they ignited you for you have overall more healing than ignite will do (you'll probably hit half hp then heal lie mad), plus your hybrid thus wrecking them from all angles especially if you use the blade of the ruined king.

After exhaust comes your preference of flash or ghost. I prefer ghost for Kog is clunky as it is, you can run away with ghost via void oozing (e) in the direction your running and run that way whilst the enemy is stuck on the slow ground, or you can chase down (within reason) anyone who dares try to run away. Flash is one of those spells so many use that if you flash they flash, or you flash to reposition but it is such a sort distance that it is irrelevant if they truly are killing you that fast (I believe it is better to fight to the death than it is to *****foot around).
Ghost is great for getting back into lane with whilst you have tier 1 (or the lack of) boots.

It is a given you always get Kog's ult when it comes available.

Once you have ginsues and you are trading with the enemy, ult every time the mana cost cd ends (right before the ginsues stack resets, even if you are not going to hit anything). Once ginsues hits 8 stacks you are ready to fight and go on your teams mark. Never overextend as Kog. When you have ginsues passive sustain active, always attempt to keep that up, you can do this by the same measure that is suggested to keep ginsues stacked, rather you always have to hit something you can damage.

If you are in an ARAM rush ginsues, if not, build in this following order (or as your game necessitates): a chalice, a liandry's, sorcerers shoes, ginsues, blade of the ruined king, rylai's.

ARAM:

If you get the pickaxe first, focus on leveling your ult, then your w, then your q, then your e, your going to want to get at least one point in your e early as to provide cc, the reason I level it in entirety before my q is that it has great base damage, and the cd on it is invaluable to myself.
If you get the blasting wand first then buy two companion faerie charms and a mana pot, focus on your ult, then your e, then your w, then your q. The same reason still applies for the q.

Other (modes/maps/possibilities):

Since your basically running apc (to start) with a support bot lane, you are going to want to level your spells in the same fashion I described for it you started a blasting wand on ARAM: focus on your ult, then your e, then your w, then your q. The same reason still applies for the q.

For SR:

If you want to be a stinker, someone who defy's the meta, something that no-one thinks would work (good reason or bad), and find the proper situations that it would be feasible, start nothing and have a strong starting "support," (you still get gold but they have the power to keep the enemy at bay), then as soon as possible go back to base for a pickaxe (or blasting wand, again your preference), then finish the ginsues... In other words build as advised for an ARAM, thus level your spells as you would in an ARAM under that build structure as well.

Just note that for anything other than ARAM switch that 1 point in defense to wherever you respectively need it for your spells. Keep in mind you do mainly Magic damage but want to do both. If you want you can switch over to the Archmage from the Brute force if you want, for you will get overall more AP than that initial AD boost.