Lucian double procs it.
This is the only thing you are right about in your comment, but thank you for the correction. For some reason I was under the assumption that his passive was 2 hits scaling for 20%/25%/30% AD, but now I see its just one for 40%/50%/60% AD. He still absolutely abuses on-hit itemization when its paired with physical damage, but it's a little tiny bit less bullshit.
Very few ADC's build 2.5 as.
Great? I talk about 2.5as only one time to show the max possible from a 4% BotRK, and to show how ludicrously strong 4% current hp as a passive which is priced at less than 200g fucking is. RIOT blatantly and egregiously undervalues % hp damage and how fucking strong it is.
The rest is based on "ADCs can get 2.0 attacks a second with little difficulty if they have an inbuilt AS steroid and a fairly normal build." which is absolutely true at 4-6 items.
Armor just got buffed to give more, reducing the % hp damage.
Because ADCs never get armor pen, right? And the armor pen item that was just buffed, LDR, totally doesn't also increase the damage BotRK's on-hit does. Additionally with items like Stoneplate tanks have been itemizing for more health, particularly in teamfights, which causes, guess what? More damage than before, not less. Not to mention, the armor values were barely even increased in the first place.
The spell version gives spell pen, which bork does not, meaning it also improves burst damage and gives a little extra to the sutained damage.
You mean like how you get lifesteal on BotRK and a nuke + anti-kiting active that has no parallel on the spell version? You have attack speed, on BotRK as well as attack and it's passive for sustained damage, you have attack damage and its passive and its active for burst, plus it even has a better build path AND multiplicative scales off the rest of the ADC's itemization instead of having direct anti-synergy in the case of Liandry's.
Fuck, give Liandry's an active and spell vamp, and CDR then we can talk about how BotRK doesn't have a bit of flat armor pen.
Also, 16% current hp/sec is innacurate, after the first one, the second shot drops by .64% of where there HP currently was. 100 .92 .92 =/= 100 - 8 -8.
Notice I had put "~" before the 16%? That's an important part, you can't just ignore because you feel like it. I literally cannot do any actual math as we don't have as information as I would need just to figure out how much damage they would hit for in addition to the Blade hit, let alone what sort of mitigation and hp pool we are even talking about. It's still 8% current hp two times, but it is different from 16% of the hp at the start.
+
+
and 
all into 1 item with no stat or passive loss
is gonna have a field day with this
and every other ADC champion right now abuse it and doign great with it the only adc that dosent is 
