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It's just me! I really dislike maths mistakes :p.
However, great job for a first guide. I hope I'll see its upgrade.
Good luck!
First of all, thanks for posting an other build of veigar on mobafire.
However, I must downvote this build for the many logical mistakes in it.
I don't dislike you build, what I dislike is the maths behind it that makes it much better than it really is.
Let me explain :
It doesn't help you much in early game! let's do some maths :
Most heroes have 30 MR early game. (you can check that)
therefore if there is no magic penetration, they take 76.9% of the damage output.
now let's apply the marks penetration.
Your opponent has now 27,4 MR. (30*(1-0.0855) = 27.4)
hence the opponent takes 78.47% of the damage output.
therefore your gain in damage is about 1.97% !
So at level 1, with only baleful strike, which deals 108.27 magical damage (90 + (15+14.85+0.6)*0.6), you do 2 more damage !
Great increase in harass, isn't it ? It will take about 2 seconds to most heroes to heal that back.
You can argue that I forgot the Archaic Knowledge bonus.
Alright, but I must tell you something, it doesn't make a 23.55% magic penetration !
Magic penetration is not additive, it's multiplicative! Therefore what you said about void staff :
it's wrong again! It seems that you think that magic penetration is additive, while it's multiplicative. What does it mean ? It means that if you combine your marks with Archaic Knowledge, you have 1-(1-0.0855)*(1-0.15) = 22.27 % magic penetration not (0.0855)+(0.15) = 23.55%.
Doesn't seem to be much of a difference ? let's add the void staff passive.
With additive, you'd get 23.55+40 = 63.55% Magic penetration (btw you had forgotten to take into account your marks in your result).
With multiplicative, you get 1-(1-0.0855)*(1-0.15)*(1-0.4) = 53.36%. It starts to make a lot, don't you think ?
But let's come back to early game, you have Marks and Archaic Knowledge, so 22.27% magic penetration. Hey that's a lot ! Maybe I will harass them a lot with that ... Well, not so much.
After application of the magic penetration, the opponent has 23,32 MR.
Therefore he takes 81% of your damage output, and your increase in damage is around 5.14% !
If we suppose you're at lvl 1 again, with your 108.27 damage baleful strike, you make 5.56 more damage, so barely nothing.
Besides, how do you intend to harass and farm ? You have a very low mana regeneration.
Considering you have a Doran's ring and your natural mana regen, plus the meditation masteries, plus perseverence, you have 16.12 mana regen per 5 sec. Therefore, if we imagine your mana is almost empty, you'll have 23 mana regen per 5 sec.
Therefore you will need 14.1 seconds to refill your mana, in order to cast a baleful strike. Therefore if you farmed a little and if we suppose you start your harass at lvl 3. You'll have to focus your opponent during 2 full minutes to be able to kill him, which means he will go back to base when low life and come back 30 seconds later. While you harassed him, he could get some free farms, that you gladly sacrificed in order to harass him. In the end, when he comes back, you'll have gained 2 more AP, and he will have made more kill creeps than you, having more money than you, he can spend some of it in health potions. Besides you will be low mana, while he will be full health and full mana, as you are squishy, it will be time for you to go back to base, and you'll have not much money (and AP), as you didn't farm.
Veigar is not an harass player, forget about that.
One more thing : you sacrifice your quickness masteries, in order to pick the expanded minds masteries. I suppose your calculation was to enhance your mana regeneration ? Well it doesn't makes much of a difference, and if your build is complete, you only gain more 15 AP. It doesn't really improve it in early game : you gain 0.7 mana regen per 5 sec...
And in the end, you'll have over a 100 mana regen per 5 sec, when your mana pool is full and even more when empty, if you can empty it.
By the way, you only have 3 quintessences, not 9....