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The author only bought 1 Doran's Ring. That puts his level 18 AP w/a 0 stack mejais at 205, 245 if you really wanna give him 5 stacks. With 5 stacks, it's still 30 damage difference, and still asks why this guy is rushing Lich Bane.
Lux's max base attack damage at level 18 is 109. That means Sheen procs deal 109 damage (pre-18 levels will do a bit less). If the author had bought a few Doran's Rings or something instead, the Lich Bane proc would be over 200. If you get mejai's and only a meagre 5 stacks, that amount can climb very quickly.
I don't like building LB first, but this build has enough early AP to make it worth it if you really wanted to. It's definitely worth the upgrade if for some reason you didn't want to get your Deathcap earlier.
But hum, let's see. Let's say I'm level 16 by the time I get a Lich Bane.
Sheen damage: 154
Lich Bane damage: 184
Oh, you're correct by 30 whole damage! My bad.
Although, this calculation reinforces that Lich Bane is a bad item to rush for an entirely different reason, as you would practically have 2x as much AP if you had gone Deathcap instead.
You also grab a Lich Bane before you build any significant AP item which would make Lich Bane stronger than Sheen.
By the time you get Lich Bane in this build, you will have a minimum of approximately 170 AP from runes, masteries and items WITHOUT ANY MEJAI'S STACKS. More than likely you will have several stacks by that point, bringing us to a theoretical total of around 200 AP. That's twice as strong as Sheen's passive, without even a Deathcap yet.
I'm not advocating this build, but if you're going to make a claim like that, at least check your facts to see if it's true.
QUESTIONS:
If you answer my questions, I'll +1!
+REP if I helped. ^.^
GJ, You've been updating! :) +1
1. You forgot to upgrade your hextech revolver at the end into a Will of the ancient.
2. How the heck r u going 2 get 600-700 ap late game if ur build only give u at most 400, go take a look at ur stats and either amp up ur build or don't brag as much.
3. Tell them why u dont want them to get rylai's crystal scepter and banshees, honestly they rnt bad items but they r only useful in certain situations.
4. Make it prettier.