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Edit: you could potentially take both to maximize a more on-hit DPS style, instead of taking IE.
While in S5 and seasons past it was usually good to include a GA, Banshee's Veil, or the more aggressive Mercurial Scimitar, the preseason patch favors your last item to be an item to complete late game scaling OR to enhance survivability while still dealing damage. Mercurial Scimitar, Death's Dance, and Bloodthirster all fall into the latter category, while IE, Dancer, or any other AS/Crit items are for scaling.
(Response to the guy who calculated stuff)
THANKS SO MUCH! Glad you liked the build!
64% from Guinsoo's
40% from BOTRK
40% from Runaan's
35% from Q passive
30% from Greaves
25.5% from base scaling
14% from Runes
4% from Fury mastery
The example build has fantastic synergy with Kog and gives him 252.5% which reaches his 250.5% requirement to hit 2.5 ATK speed at level 18. W active and it's 5 AAs per second from 4 items. Very nice :D
I'd say Runaan's is superior in general as it gives Kog a small amount of on hit damage at 15 per hit times 5 AAs per second equals 75 on hit damage; for perspective, Fervor of Battle does 80 damage per hit when fully stacked. Runaan's with Kog's insane ATK speed late game is practically like having FOB doubled. Whereas Phantom Dancer gives 3% more movement speed and wastes 7% ATK speed late game whilst adding no damage albeit a small amount of survivability in the Lament passive. I'd pick Runaan's regardless of it's Wind Fury passive; especially as it means every item has an on-hit effect, something Kog thrives on.
With W active at 5 AAs per second, your DPS is 275% which keeps up/surpasses an IE enhanced AA of 250% like other ADCs. So the last item can be situational without gimping much damage, which is interesting... Particularly as he applies on-hit effects so much. Incidentally, I don't think you'll ever need Mortal Reminder as Kog's DPS is so much higher than any sustain, especially considering the BOTRK passive synergy with Lord Dominik's, meaning a LOT of health shred.
After trying a fair few builds, this one is VERY good. Some items I've seen that I feel are overrated in other builds as "core"
Wit's End - It's kinda like Runaan's but with magic damage and res steal. It synergises with W but less so in a team fight and has no kind of scaling unlike Runaan's. Runaan's is better in the long run.
Muramana/Essence Reaver - This combo does work but it takes forever to stack and fund. It gives us 25 on hit AD in the end for 5000 gold. That sucks in comparison to 2600 gold for Runaan's and 15 on hit damage in one slot with more crit chance.
Death's Dance/Hextech Gunblade - Death's dance is bad because Kog is mixed damage. Hextech Gunblade makes some sense but doesn't add as much damage or sustain. Bloodthirster's shield is invaluable and the AD more efficiently buffs his AAs than Hextech does due to the poor scaling on W. Mercurial Scimitar's active is situational superior for obvious anti-CC reasons.
Just some depth on why this guide is so agreeable :D