Nashor's Tooth and other On-HIt Procs that scale with AP

Before I begin my rant, here's a comparison between AP AS and AD AS versions of Teemo and Fizz.

AP AS Teemo Compared to AD AS Teemo AP AS Teemo (no Masteries or Runes): 158 Physical Damage + 192 Magic Damage (including Nashor's Tooth and Toxic Shot initial on-hit proc) = 350 Mixed Damage to one target per second for 6800 Gold pre-mitigation AD AS Teemo: 287 to 718 (523 average) Physical Damage + 45 Magic Damage = 332 to 763 (568 average) Mixed Damage to one target per second for 7600 Gold pre-mitigation.

AP AS Fizz Compared to AD AS Fizz AP AS Fizz (no Masteries or Runes): 163 Physical Damage + 241 Magic Damage (including Nashor's Tooth and Seastone Trident active on-hit proc) = 404 Mixed Damage to one target per second for 6800 Gold pre-mitigation AD AS Fizz: 283 to 707 (517 average) Physical Damage + 50 Magic Damage = 333 to 757 (567 average) Mixed Damage to one target per second for 7600 Gold pre-mitigation.

Now, you may have noticed that AD AS beats AP AS in terms of expected and max damage and barely loses in terms of min damage. This makes sense: after all, the AP AS has a stronger burst than AD AS (at least for these champions), why give them better sustained damage too?

Despite this, however, AP AS builds suffer two critical flaws compared to AD AS builds: lack of impact from life-steal and spell-vamp, and lack of synergy with anti-tank items (Blade of the Ruined King, Liandry's Torment, Armor Penetration and Magic Penetration items).

First, on spell-vamp and life-steal: this should be fairly obvious, but life-steal does not scale at all with AP and spell-vamp rarely scales with AS.

In a similar vein, AP AS builds have an identity crisis when it comes to anti-tank items. Blade of the Ruined King is strictly better than Liandry's Torment in terms of tank-busting potential for AP AS builds, despite the latter providing AP; and Void Staff and Last Whisper only help one type of damage, which for AP AS builds does not help when Physical Damage is only slightly less than Magic Damage.

I feel the most effective solution that I can come up with for both of these issues would be to do the following:

• [NEW Item] Twilight Razor (Recurve Bow + Needlessly Large Rod + 500 gold)

• • +40% Attack Speed, +80 Ability Power
• • Unique Passive - Dealing mixed damage to an enemy champion reduces their Armor and Magic Resist by 4% for 5 seconds. This effect stacks up to 5 times.

• [REWORKED Mechanics] On-hit procs are considered Damage over Time spells for effects that trigger upon dealing spell damage such as Spell Vamp, Rylai's Scepter, and Liandry's Torment.