Talk:Tristana/@comment-25187669-20141019095748/@comment-13660209-20141020050749

here's my two cents

assuming she has a pd, a last whisper, and a infinity edge regardless of whether she has the bt or botrk

the bt has 55 more ad, with 55(2.5x0.55+1.0x0.45) = 100.375 damage on average considering the critical hit

The botrk proc will deal 8% current health, but it will never deal 0 damage, because if the opponent would have any less than ~253 health than her auto attack base damage will kill them

(253 was calculated from tristy having about 265 base damage, multiplied by (2.5x0.55+1.0x0.45) for the critical hits, then divided by about 1.91, which is physical damage reduction from a target with about 140 armor, being penetrated by 35%)

Thus, the damage botrk's proc will (attempt to) deal, on average and without armor reductions, to a 2000 health target, will be about fnInt(0.08(2000-x), x, 0, 2000-253)/(2000-253) = 90.12

Unfortunately, the usage of 253 is not strictly correct, as botrk will also apply damage for the finishing blow, making the minimum health that botrk will do damage at something higher than 253.

as you can see, 100.375 is greater than 90.12, but only by 10 attempted damage per autoattack. the average damage per auto will be that damage plus 483.625, making that 10 damage per auto a very, very small damage increase. In addition, this is a very conservative estimate of botrk's damage, as the target only had 2000 health.

Botrk's attack speed, while not stacking multiplicatively, should compensate for the 10 damage loss per auto. Of course, being a percentage of the target's current health, and increasing in average damage depending on the auto attack's base damage, it is probably a less effective first item than bloodthirster, though to my knowledge no one rushes either anymore anyways.

TL;DR botrk deals insignificantly less damage per auto than bloodthirster, if my math is correct