After extensive Kogging, here's what I've found

The boost to Koggy's W base damage is a pretty big deal. You want to abuse that if you're rolling with Koggers. Typically, a Wit's End rush would seem like a pretty uninspiring start, but that's largely because you're doing it wrong. Instead of the typical AD/attack speed nonsense, start with 14 magic penetration. Between Runes, Wit's, and Koggy's Q, you're packing enough shred to knock someone from about 60 down to zero. If you thought Vayne hitting you with 12% max HP true damage every three attacks was bad, wait until Kog is blasting you for 40 + 7% on every single attack. That's 120 + 21% per three attacks for those in the audience who find math hard.

Follow up Wit's with Ninja Tabi and Phage. You're now moderately tanky and you can survive enough focus such that even a chimpanzee smashing his ass against a keyboard would have enough time to react and peel for you.

Rageblade comes next. Whenever possible, try to stack Rageblade ahead of time before a fight breaks out. Use it to force dragons (dragon force?). Turn around, pop that W, and lay waste to whoever is unlucky enough to get immobilized by your team's CC (your team has CC, right? Why are you playing Kog on a team without any lockdown?). Once Rageblade is down, finish up Trinity. Once Trinity is done, round out the build with Black Cleaver and BoRK in whatever order will be more helpful for the game. You now have three Rage passives. That's three times the rage! Go make Tryndamere quake in fear because with that much rage, Koggles is finally angry in addition to being hungry.

You now have 2.5 attack speed, two seconds of downtime on your W, and one second of downtime on your Q to make sure the enemy team is as miserable as your lane phase was. You have enough bulk to shrug off anything barring a direct hit from a Mage's full combo. You deal so much damage so quickly once Rage is stacked that if you swap over to a soft target after whomping on a tank for a while they'll typically flash just in time for a 16% Max HP true damage slime wad to reduce them to a boiling puddle. And if they somehow manage to survive that a 680 damage Ult backed up with magic pen typically seals the deal.

Koggy is still SUPER situational. He still needs a team that can peel for him and he still needs a player with the patience to capitalize on his team's good plays as his opponents bad ones if he's to succeed.

I still think Kog could use a Shyvana level touchup. Putting more focus on amping his teams damage through Q and possibly a debuff on his Ult would be a solid identity for him. And I would be totally okay if that required nerfing his W stat-check button. That said, Riot finally manage to balance Kog again.

It only took a fucking year.