Koggy is rocking a 63% win rate under experienced hands
Now I'm going to begin here by pointing out that I main Kog. I've mained Kog since his first free week. I've logged well over one thousand Koggy games, so don't think for a moment that I'm just out for the Void Puppy's purple blood.
This has been an issue for a while, honestly. There has always been a vast divide between how good Koggy is in the hands of relatively casual players and the hands of those who understand his nuances. Especially when a good Koggy player is being guarded by a team who knows how to protect him. But it wasn't quite so bad when Tanks were nonexistent and Assassins abounded to feed on him. Now that beefy front-lines are back in vogue Koggles is in his element, and that element is killing everything horribly from way the hell over there.
Just layering on nerfs isn't going to do the trick. That might bop his win-rate back down to a managable level amongst those who really understand him, but it'll just totally destroy him in more casual play. When there's a huge skill level gap like this (and believe me, a difference of 12% is pretty huge) just tossing around buffs and nerfs all willy-nilly is dreadfully unwise. One need look only as far as the changes to his Q last year to see this.
What Kog needs, what he really needs to be healthy at all levels of play, is to have have his pre-Q change dichotomy not only returned, but further defined to smooth out his learning curve. A fifty one percent win rate on average might be fine, but a sixty three percent win rate among long-time mains absolutely is not.
So... I'll start by saying that any numbers mentioned below are tentative. I don't have the ability to play-test concepts and iterate on builds to find balanced numbers. Consider the concepts here only.
Regardless!
How do we do this?
We'll start with Koggy's old champion hook 'Long range (WER), but he packs a nasty bite up close (Innate and Q).' This was changed along with his Q. Now he's even MORE dangerous at range when he has a solid front line and his ability to chunk soft targets without fail for a big portion of their resist if they jump him was removed. Basically, his primary play pattern was made even stronger (which can be abused by those who know him well) and his fallback pattern was nerfed (which makes him even harder to pick up). So to reintroduce this dichotomous play style, we begin with his W.
Bio-Arcane Barrage becomes a toggle which alters Koggy's whole kit. The damage and cooldowns of all abilities are shared (which means no double Qs, looking at you Nid) but the range and targeting style changes drastically. For the sake of being adorable, we shall henceforth refer to this character aspect as 'The Koggle -Toggle'.
Koggle-Toggle off: Kog'Maw's basic attacks and abilities deal bonus damage equal to 2/3/4/5/6% of the target's maximum HP in magic damage. Koggy's attack range is reduced to 450 while the toggle is off. The base damage on his QER would probably need to be reduced a bit to keep things from getting overwhelming. Koggle-Toggle on: Koggy gains 150/175/200/225/250 bonus attack range.
What's this mean? It means Koggy can have his face melting damage OR his crazy long range attacks, but not both at once. The goal here is to make his backup play pattern stronger at the expense of his primary play pattern. And now on to how this alters the rest of his kit.
Innate (Koggle-Toggle Off): Koggy can bite an enemy champion in place of a basic attack at close range, dealing (current Innate) bonus True Damage. This Innate is refreshed when Kog'Maw returns to the fountain or dies. This improves the usability of Koggy's Innate against melee-assassins that decide he needs to eat it. Innate (Koggle-Toggle On): Each consecutive attack against an enemy unit increases his range by 20, stacking up to five times. Switching targets removes the stacking attack range bonus.
Q (Koggle-Toggle Off): This ability becomes a 600 range targeted nuke that eats 6/12/18/24/30 of the target's resists. Short range, good for dueling squishy folks who decide to jump on Koggy's face. With the toggle off, his Q would work exactly as it does on live, including the %shred rather than flat shred. Remember, both skills have the same base damage and share their cooldown ala Mini/Mega Gnar.
E (Koggle-Toggle Off): This ability becomes a 600 range targeted nuke that blasts the primary target with Void Ooze, damaging them, slowing them, and causing them to leave a Void Ooze trail wherever they walk for 4 seconds. Again, this gives Koggy a reliable slow to deal with enemies trying to pounce on and chase him. He loses the AoE damage of the Toggle On E, but he gains a much more reliable soft-peel. The Toggle On would be identical to Live Void Ooze.
R (Koggle-Toggle Off): This ability becomes a missile skillshot (think Galio or Corki) with a range of 800/850/900. This means that landing Koggy's Ult at close range becomes significantly easier, though at the obvious expense of most of its excessive range. As with the above examples, this gives Koggy more of an option to peel for himself with his sheer, overwhelming damage. Again, with the Toggle on Living Artillery would be unchanged from where it is on Live.
So overall?
We're looking at a damage nerf across the board at long range in exchange for a significant damage/reliability buff at medium to close range. This would allow Koggy to react more favorably to foes jumping on him in the only way he knows how. By devouring them via his overwhelming damage. These changes would reduce how oppressive Koggy is at very high skill levels while making him much more accessible to a broader range of League players. This remake would, I believe, make it MUCH easier for Riot to balance Koggy.
TL;DR: Improve Koggy's close/medium range damage/reliability in exchange for a damage nerf where he's most oppressive, at super-long range.