Build Guide by FallenDefender
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Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
This build focuses on Anivia's ability to harass and effectively deal large amounts of damage in very short periods.
Your main objective until you reach level 6 is to just stay alive and not use your passive ability (rebirth). You should use Flash Frost and Frostbite in conjunction to deal large amounts of damage to them if they come too close to you.
Once you reach level 6, it should be easy to kill almost anyone at this point because you have 2 spells that you can chill your enemies with and your frostbite is high enough to deal large amounts of damage to them.
Your main objective at this point is to help your allies kill their enemies, unless they are doing a good enough job themselves. Then you have to push and just keep leveling. If you can solo, do it. It is the best idea for Anivia to outlevel everyone (including teammates).
Your first item is a Pendant because it helps you stay in your lane longer...the only reason you should have to leave in the first bit of the game is to regenerate your mana. The Pendant will help you stay in lane.
Next time you head home, you get boots and a Tears. You still do not need to leave your lane. Just keep harrassing them.
By this time, I have reached level 6 and have gotten at least 3 kills. With those 3 kills and your gold income (amplified by runes and mastery), I have enough gold to buy Catalyst or Tears of the Goddess AND Boots of Swiftness. (Alternative - Kages Lucky Pick...it will help you get the needed gold. Anivia's items are very expensive)
There are two paths you can take at this point: Laning/Leveling, and Hero Killer. Either way you go, you get a lot of gold because Anivia's abilities help her farm minions quite well.
We will focus on Hero Killer:
Travel the map and find any place where an enemy champion is not close to a tower...you need help. Using combos of Flash Frost/Frostbite AND Glacial Storm/Frostbite will help you deal a lot of damage almost instantly. If they run, you can block them off with Crystallize or if you get overwhelmed, same thing.
Next time you head home, you should be able to buy Archangels/Catalyst (whatever one you didn't buy last time) and finish either Rod of Ages or Archangels.
From then on, you just keep picking off enemy heros and buying the items in the order I put them. The reason I get two Rylai's is because your slow becomes vicious (Rylai's slow is not a UNIQUE Passive) and it makes you Extremely healthy. I also go with a void staff instead of Magic Penetration boots because your masteries and your void staff give you about 50% Magic Pen. (Note - You could get a Guardian Angel just to be annoying and help survivability...if you want more AP, stick with my build.)
Have fun pwning your enemies and if you have any questions...feel free to ask. Comments are appreciated.