Hello there, I'm a typical Veigar main and I'm here to guild you to be a boss.
There is not much about me. I'm only in bronze. I only started to League of Legends about 6-8 month and I usually spend time on LoL for 2-3 hours days, So if you are not going to a guild from bronze then that's fine for me. But when it comes to Veigar I know better than an average people. And I also doesn't have English as the first language, sosome of these might not make sense to you guys.
I love Veigar before the mage update(it still nice), when I play against an AP champion, man I love one shots. But with the mage update it make Veigar kind of a execute champion type. It also make Veigar strong even if you play with several tanks.
This guide is going to be made by information that I gathered and my personal experience.
That's all I have to say for an introduction.

SPACESPACESPACESPACESPACESPACESP

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Pros

+ Very high scaling late game + An awesome AOE stun + Good DPS/burst + very easy to learn + Can kill tanks + Now good against everyone + ONE SHOTS!

With your passive being able to INFINITELY stack up AP by hit your abilities on enemy or last hitting with Baleful Strike, Makes you out scale harder than anyone else. As the game goes on the stronger you will be. With Morellonomicon, Zhonya's Hourglass and Abyssal Mask + runes with give you 45% CDR making you do more DPS. At 30-40 minutes mark you should have 1000+ AP and one shot their carry with only your basic combo(E+W+Q). Also remember that your ult now scale with target's missing health, so the lower they are the more damage they with take.

Cons

- Squishy - No real escape ability - Stun has to land - Low mobility - Vulnerable to CCs - Skill shot oriented - Not very good wave clear

Unless your build some tanky states you are going to be squishy as hell, you will die really fast if bruiser, assassins or carry can get on top of you. But with that being said buying and using Zhonya's Hourglass effectively will never let you die. Being able to do maximum damage will needs your stun Event Horizon land,because your W Dark Matter which is your main source of chunking their health down has a delay. Veigar has very low mobility and is a skill base champion so it makes you an easy target for high mobility champions.

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(Passive)Phenomenal Evil Power:Every time your hit enemy champion with any basic ability will gain you 1 ability power, hitting ult, getting kill or assist will gain you 3 ability power. This is what makes Veigarthe best or at least one of the late game scaling champion. Like Nasus's Siphoning Strike and Thresh's Damnation, this passive can stack infinitely.

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(Q)Baleful Strike: Veigar shoot out a small skill shot that hit first two target and deals 70 / 110 / 150 / 190 / 230 + 60% of your AP. Passively Veigar gain 1 stack for killing a unit and 2 stack for siege minion or large monsters. Try to maxing this ability first for lower cool down in early game for stacking AP. Use this to as effective as possible try to set up for two minions when you get every cannon. And when you push your lane try to take two small raptor camp, the gold aren't that much to put the jungler be hide.

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(W)Dark Matter: Veigar target a small area, after a delay of 1.25 second he release "Dark Matter" dealing 100 / 150 / 200 / 250 / 300 + 100% to all enemy unit.Max this ability last, because this ability is already scale with all of your ap + this is the hardest ability to land with the delay(rito pls). This is the the ability that set up your ult to the maximum damage. With its 100% AP scaling max this last, it will still do massive damage. This ability is the hardest skill shot to hit with 1.25 second delay and the area aren't that big. So use this when your enemy is stupid enough to walk into your stun. It is also AOE! hitting this ability to multiple targets will make huge different in team fight. This ability also grant vision on the area, useful for face-checking.

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(E)Event Horizon: Veigar target an area first then after a delay of 0.5 second he create an AOE cage. If any enemy unit walk or dash into the edge they will be stun for 1.5 / 1.75 / 2 / 2.25 / 2.5 second(s). This ability is basically another version of Jarvan IV's ult. It doesn't do any damage but it can set up for some easy kills. This ability make your gang bang potential high through the roof, either you'll get a kill or the enemies burn their Flash!!!. You need to max this ability second to increase the stun duration to Garentee(:3) hit Dark Matter. But if you choose to go for more damage get this ability to 3 points then max W second. Either way you want to use this ability as effective as possible, look at the cool down all the time.

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(R)Primordial Burst: Veigar throws a ball of dark energy at a target dealing 175 / 250 / 325 + 75% AP. The damage is increase by 1.5% for every 1% of the target's missing health. At below 33.3% of maximum health it will deal double the the damage included the scaling. This ability was the reason why I play Veigar the old version of this ability was a nightmare of all AP mage. Let just say RIP oneshots(;_;). The change made him pretty much can 1 v 1 any one if play right. You have to remember that the lower the enemy's health is the more damage your ult will do. Like all ult you would want to get a point on it every time you can.

Abilities order

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You MUST max out Q first for lower cool down to spam for those stax. So it came to maxing W or E second. For me, I prefer maxing second because it make the stun time longer and since your W is already scale with all of your AP, your going to be still doing a lot with one point. But if you want more damage then get E to 3 points then start maxing W. And getting point on ult every time you can is pretty obvious.

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Yasuo's Wind Wall : Seriously dude if you have never face a Yasuo before , then I think you just only play bots or you are just not playing league. Like freaking hell dude I'm so done with Yasuo. Just too much. Anyway, his wind wall is just so annoying all you can do is just use your W and that's it. If you try to finish him off with ult? NOPE, WIND WALL! Wanna try to engage with Ashe arrow? NOPE, WIND WALL! Wanna try to snipe them with Jhin or Caitlyn? NOPE, WIND WALL EVERYTHING! Maybe if RITO make the ability not being able to block ults I'd be very happy.

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Morgana's Black Shield : Just one of the most annoying thing for control mage. This shield is just your bane of existence. Its just not allowed you to make any play and the shield makes me want to die... Just kidding dudes.

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Ferocity tree Tier 1: sorcery - Make your damage from ability power spells by 2%. I was a little confused if this mastery gives you 2% of your AP or make spell 2% stronger. but actually reading it, it does make your spell 2% stronger...nothing much. Tier 2: Double edge sword vs. Feast - DES makes you do 3% more damage, but you take 1.5% more damage. Feast gives you 20 health when you kill a unit. Which one is better? TBH I'm not really sure. DES is for someone who can guarantee that they are going to surviving the laning phase. In alternative feast is for god like sustain since you you don't have life steal or spell vamp, it will help you not recall for millions of times against those poke champion. But in the end it all come down to your choice, I just prefer feast. Tier 3: Natural talent - gives you 2 AD and 3 AP + 0.44 AD and 0.67 AP per level at level 18 you will get 10 AD and 15 AP. Compare to vampirism this mastery is much better in my opinion. Spell vamp isn't your option because its so little that I haven't notice if it affect my game play or laning phase. In the other word, just take this matery. Tier 4: Bounty hunter vs. Oppressor - Bounty hunter makes you do 1% more damage for each DIFFERENT champion that you kill. This mean that if you kill each one of their team you will do 5% more damage. Oppressor makes you do 3% more damage to impaired movement champion, which in this case; your E the stun. I think Oppressor is the best option here because... IDK. Sure you can kill each one of their team, but if you don't then the mastery is useless. Plus I think it reset when you die.

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Cunning tree Tier 1: Savagery - Makes you AA or single target spell do extra damage to minion and monster. nothing much...just helps you last hit those minions. Tier 2: Secret stash(cookie) vs. Assassin - Secret stash makes your potion turns into cookies. When you use it, it will instantly heal for 15 health and give 15 mana and the healing last for a bit loner. Assassin make you deal 3% more when you are alone...simple. In my opinion Cookie is better because my play style is based around team fighting, so Assassin is useless if you whole team is around you plus you already do too much damage anyway. Tier 3: Merciless - Make you deal 1-5% more damage(scaling with level) to champion that is below 40% health. This mastery help you so much since your ult scale with missing health. Tier 4: Dangerous game - Restore 5% of your health and mana when you kill or assist a kill. This mastery helps you survive some finish off things like ignite. Good stuff. Tier 5: Precision - Gives you 3% + 0.3% per level hybrid penetration...that's it. Key Stone: Thunder lord's decree - Dealing damage to champion within 3 seconds will calls a thunder strike down dealing magic damage in the area. The damage is 10 per level + 30% bonus AD, 10% of total AP. This is the tool to do tons of damage. Do easy thunder proc by AA + Q + AA. If they hit stun W + Q + AA, if low enough PRESS R. EASY!

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Morellonomicon Stats: 100AP, 20 CDR and 400 mana. Passive : killing or assist restore 20% of your maximum mana. Dealing magic damage to champion will apply Grievous Wounds for 8 seconds. Grievous Wounds : Reduce 40% of the receiving healing, regeneration and also life steal. The grievous wounds passive help very much again healing champion such as Soraka or Swain or just healing over all. But in my opinion you have to get this item no matter if they have no heal. Because of the 20% CDR and the 400 mana help you farming in lane easier to get those stacks. 100 AP also help when you fight. The path is either going for Lost Chapter for more mana sustain or Fiendish Codex for more CDR to spam Q.

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Sorcerer's Shoes Stats: +15 Magic penetration Passive : +45 Movement speed That's it...

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I will update it so often. <3