When Kog was first released his Ult did 200/300/400 damage to champions

With a 0.3 AP ratio and no bonus AD ratio.

He was widely considered terrible until Riot replaced the old Q passive (free %armor pen) with attack speed.

But they accidentally gave him multiplicative attack speed, meaning he could hit 2.5 attack speed with runes and two IAS items. That was fixed pretty quick, but in the process Riot bugged his W, causing it to double his bonus AD whilst active (lulz). After that was fixed he was considered bad again.

Then Riot increased his W duration to ten(!) seconds, gave his Q magic AND armor shred, and gave his Ult a bonus AD ratio. That resulted in nerfs, of course. Kog lost 40 attack range, two seconds off his W, and 40 damage off his Ult. He was fine for a while, but then the old Unholy Grail (80 AP and everything) was released and suddenly AP Kog was absolutely unstoppable. His Ult's stack limit was increased as a result to prevent him from spamming forever.

Next up, Riot removed the mana cost on Kog's W and remade his Q from a dueling tool into a tank-busting tool (okay?) Nothing really came of that-

-until Riot remade Bloodthirster, launching the game into a hyper-carry clusterfuck. Kog ended up losing a chunk of his base speed, a bunch of HP, as well as another 40 damage off his Ult by the time the dust settled.

Then came the remake! In which Kog ate seven nerfs and most of his kit nuance in exchange for being an immobile turret. OnHit itemization was broken as a result and Riot 'reverted' Kog because he was too strong in the hands of mere mortals and totally ignored by competitive. The revert, of course, didn't revert everything. Kog's base stats were still ass for the most part, his W cost mana again, and his Ult was still a shell of its former self.

And next up!

Kog's Ult is going to get returned a bit. More damage against healthy targets, less damage against injured targets. Generally a buff to his mid-game power. Maybe a nerf to late, we'll see. Depends largely on whether or not the ratios end up changing, too.

Honestly...

All this nonsense makes me pine for the old Kog.

I mean the old Kog, here. Like, before the buffs that resulted in even worse nerfs sort of old Kog. Because that seems to be what happens to him. Riot tries buffing his damage somehow and holy shit suddenly Kog is unstoppable and they have to nerf the parts of his kit that make him unique. Or, barring that, at least try to give Kog an identity beyond 'does all the damage' because that has resulted in knife-edge balance and head aches. Kog really needs to offer his team something other than just raw damage. Something unique. Something no other ADC really brings to the table. That was the whole point of the Marksmen pass, wasn't it? Giving them all a reason to be picked?

Because 'needs to have a team built around him' isn't a reason to pick Kog. That's a weakness. You can build a team around MF or Twitch, too, and they'll be better off for it, but they can function on their own, too. 'Hyper-carry' isn't a niche, either. That's a success curve. And one that isn't unique to Kog.

Instead of monkeying with Kog's damage, focus on the parts of his kit that aren't damage if you guys want to buff him. His ability to grant vision. His ability to shred resistance. His ability to lay down persistent slowing fields. His totally unused Lore hook regarding eating stuff. Anything besides his damage. Because fiddling with Kog's damage output often just makes the situation worse. There's quite a history of that, in fact.