BOTRK rework idea

I used to dislike - it didn't synergize with AD ratios on Jinx, Sivir, or Varus (my most favourite "caster" ADCs to date) and it didn't synergize with crit. To put that last bit into perspective, I liked crit so much, I explored the possibility of winning lane with crit chance runes or crit damage runes so I could pick up an IE, 2 PDs, and ramp my DPS to silly levels late game. I disliked seeing BOTRK that much on everybody who didn't rely on auto attacks as much as say, Reksai, who's main damage ability is her above ground Q, or Aatrox.

Threads about how cost and damage efficient the passive was, even with crit making actual AD more valuable, a few games of ADC Kogmaw, and surviving a Hecarim with the passive, have converted me. Still, it frustrates me that this item just craps on everyone- it's good on auto attack bruisers for being an excellent source of damage with little further damage itemization, ADCs for ripping tanks a new one, assassins for 100-0 ing, I've even contemplated building it on Leona in games where I'm not consistently edging death, but a bit of damage would be great.

I got an idea to make BOTRK very effective against only tanks, so tank killers have a go to item, but first, some math (excluding runes) to convince the non-believers of it's damage. It will be done with level 18 stats of Varus who's decent with AD and BOTRK, 2 phantom dancers, and an infinity edge to simulate real conditions, because no self respecting auto attack reliant ADC won't go with a phantom dancer, or a shiv and IE. This one takes an extra PD, again, to maximize DPS. Crits are averaged out and treated as a multiplier.

Stat bonuses from PD & IE 80 AD 85% crit chance 100% attack speed 50% bonus damage to crits (2.50/2.00 = 1.25)

DPS formula with stat bonuses and champ states above plugged in: (((180 + bonus AD) * 1.85 * 1.25) + on hit effects ) * (0.993*(1+1.00 + bonus AS))

DPS with BT (((180 + 80) * 1.85 * 1.25)) * (0.993*(1+1.00)) =(260 * 1.85 * 1.25) * (1.986) =1194 raw dps

DPS with BOTRK (((180 +25) * 1.85 * 1.25) + 8% tchp ) * (0.993*(1+1.00 + 0.4)) =((205 * 1.85 * 1.25) +8% tchp)(0.993(2.4)) =(474.0625 + 8% tchp) * (2.3832) = 1130 + (2.3832)(8% tchp)

A little more math to isolate and solve for the average damage of 8% tchp... 1194 = 1130 + (2.3832)(8% tchp) 64 = (2.3832)(8% tchp) (0.08)(tchp) = 26.85 tchp = 336

And there we have it, the point at which BOTRK dps breaks even with BT dps on that build with Varus. I suspect my maths might be wrong, please pinch me if I got it wrong.

Anyway, an anti health item based off current hp is useful against everyone with more then a pinch of hp left in the bar. What I have in mind is a new BOTRK that scales very hard off bonus HP. This way, we have a hard counter to health stackers, particularly ones with no armor, while leaving squishies who don't itemize for hp relatively unharmed by the passive. To further distinguish the new BOTRK as a tank killing item, it will have pay offs in that it has little to no synergy with skills, that is, no AD. The active is also gone, that way, the item's "power budget" can be pumped into making it a tank killer.

NEW BOTRK 15 % lifesteal 60% attack speed UNIQUE passive: Deals 15% of the target's bonus health as physical damage

I suspect it's overtuned, though, keep in mind it is a tank killer item.