On Hit Rune
Honestly, before you go screaming this is pointless or op, hear me out.
Greater Quintessence of On-Hit Damage: -Effect: Auto-Attacks deal 2 Physical Damage -Price 1025 (6 with 3)
Greater Glyph of On-Hit Damage: -Effect: Auto-Attacks deal .2 Physical Damage -Price 210 (1.8 with 9)
Greater Mark of On-Hit Damage: -Effect: Auto-Attacks deal .8 Physical Damage -Price 410 (7.2 with 9)
Greater Seal of On-Hit Damage: -Effect: Auto-Attacks deal .5 Physical Damage -Price 410 (4.5 with 9)
Total would be 19.5 compared to the 21.69 Attack damage you get from a full Attack damage page.
On Average however, most people don't build a full page of anything (except maybe the full crit 
xD) I'd say the majority of people will build the 13.2 On-Hit Damage using the Marks and Quintessences; letting the rest of the page be somewhat standard.
For Ex.
3 Greater Quintessences of On-Hit Damage
9 Greater Marks of On-Hit Damage
9 Greater Glyphs of Magic Resist
9 Greater Seals of Armor
With that said, why would anyone build On-Hit damage instead of Attack Damage? Well with certain champions, e.g. 
,
, and maybe even 
, On-Hit would benefit their kits even more than AD would. Also with the introduction of the new 
, these runes would give these champions an even better mid game spike while hurting their early game. Also, these runes would make tower taking harder, thereby making their pushing power weaker as well. This gives them counter-play but a bigger reward mid game.
IMO the champs who would benefit most from these runes (but may not necessarily need to use them) are as follows:
It may be stupid, and probably won't ever see the light of day. And my numbers are probably too low or too high (most likely high). I just wanted to bring it up to see what people thought.
Thank you <3
