Talk:Blade of the Ruined King/@comment-2003328-20140415221936/@comment-24055932-20140527224839

1.Vayne builds her set around her w, not around her q - assuming she uses her q to procc Trinity harshly cuts her survivability as you can't use tumble to dodge.

2. Using Vayne as example to prove BotRK is overrated is kinda clumsy, as Vayne got the highest AD of all marksmen thanks to her ult-AD-Steroid.

3. Assmuning a 6 item aggressive build is only important if you care about the game after 40 minutes - unluckily, most of the games don't even last that long, and even if, there is rarely any situation where you'd go full glass - for usual you build 1 defensive item to survive longer, as you can never dodge anything, and a simple undodgable skill could be your end (e.g. Swain q+e will take 50% of your HP - or more).

For the general calculation let's assume a champion with 120 base, 15 from runes, 14 from masteries (+0.05 AD on extra AD), 1.00 attack speed and 0.666 base AS. Builds:

a) Berserkers, Infinity, Last Whisper, Phantom Dancer, BotRK ==> 287.5 AD, 1.73 AS, 0.55 Critchance

b)  Berserkers, Infinity, Last Whisper, Phantom Dancer, Bloodthirster ==> 371.5 AD, 1.47 AS, 0.55 Critchance

As both builds got identical armor penetration, armor can be left out. The damage per hit is calculated per AD*(1+1.5Critchance) (=AD_Dmg)*Attack_Speed + On_Hit_Damage.

As equation:

a) HP( HP0, n):=   0.95^n * HP0 + ( 907.73* 20*((19/20)^n-1))

b)  HP( HP0, n):=    HP0 -  996.66* n

Now we set a=0, b=0, solve them to a(HP) and b(HP), then set a = b, solve for n. HP0=2612

This means, if you happen to duell a champion with more than 2612 HP, you're better off with BotRK even without its active, though only if you happen to have no abilities with AD scaling or innate AD steroids.

So technically you're right - even if perfect conditions are given, BotRK is, even with its passive, for most marksmen a bad lategame choice if you only look on the damage and want to build crit. Though, directly after the purchase, BotRK clearly outpowers BT and favours you with a better early to midgame, till you got IE and at least a little bit more.

Special cases would be non-crit builds and builds containing Runaans.