Sivir is a surprisingly effective champion - often overlooked and underestimated. True, she is actually fairly difficult to play a lot of the time, and often you WILL get raged at just for picking her. Let's turn that around, and do some damn good TEAMPLAY! If the build is too long, too wordy or anything else just skip to the parts you are interested in. They should be clearly mapped out. Thanks!

Here are some abbreviations that may crop up in the guide:

AA = Auto-attack (Basic Attacks)
CC = Crowd Control (Stun, fear, slow, snare, etc)
FB = First Blood
AP = Ability Power
AD = Attack Damage
MD = Magic Damage
AS = Attack Speed
MS = Movement Speed
MR = Magic Resistance
ArPen = Armor Penetration
MPen = Magic Penetration
LS = Life Steal
SV = Spell Vamp
DPS = Strong Auto-attacker
MDPS = Strong spells; casters
CDR = Cooldown Reduction
OOM = Out of Mana
MP = Mana
HP = Health
MP Regen = Mana Regeneration per 5 seconds
HP Regen = Health Regeneration per 5 seconds

Greater Mark of Desolation and Greater Quintessences of Desolation - The normal build here, without any item set change, does NOT land you with much armor pen early game. You are HEAVILY reliant on your Q doing plenty of damage early on, and this damage is physical, hence why i build flat armor pen runes.

Greater Seal of Attack Speed - These runes help again with early game, and buff your attack speed a bit until you get the significant boost when you build starks fervor. I value them over health for the sake you can do significant fighting away from the main fray and should be OK so long as you play it safe.

Greater Glyph of Replenishment OR Greater Glyph of Attack Speed - Solely for mana regen, the total amount you get is very nice. Stacked with a meki pendant and your masteries mana problems are almost eliminated (again, so long as you dont spam and you play sensibly. If you choose attack speed, that is to buff your early game damage if you personally feel the regen sufficient as it is.

Offense is specced into because it is where you get your main damage buff allowing your attacks to be a lot more potent again until you start building the ADitems that are the core of this build. Notably, attack speed and armor penetration is prioritized over spell pen simply because your spell pen is not nearly as useful when you start moving into later game where boomerang blade loses a proportion of its effectiveness.

Utility is then taken but can just as easily be put into defense. This is because a lot of the time you will be going mid, and extra XP is almost essential when you do to keep up with or overtake your opponent and reach that vital level 6 a bit earlier.

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Boomerang Blade - Early game, this is your main damage output. As you can see, the boomerang, at lvl 3, does 170 dmg plus 75% of your AD, which is about 70. Thats 240dmg every 10 seconds, at a long range, and with the multiple target hitting (of coursse with less damage though). Exploit this ability, BUT DO NOT OVERUSE. It WILL sap your mana if you spam it on minions all the time. try getting champs eariler game. Of course, you're not actually going to always hit that much but the amount of damage you're putting out as a skillshot is absolutely ridiculous at midgame. Target the squishies who are yet to build any tanky items at mid game and it will literally rip through half their health if you're going well. Thats why this ability is maxed first.

Ricochet - Mainly this ability is what makes Sivir such a good pusher and backdoorer. The auto attack bounces off to multiple targets, meaning farming is incredibly easy and any champions standing near their minion wave risk getting harassed continually. Manawise it is quite heavy to sustain though, so use in moderation. The damage is worth maxing this second.

Spell Shield - "Whats that? Gangplank's moving towards me?" [Activates spell shield] "Oh, thanks for blocking that 500dmg crit and helping me stay in lane with mana". I rest my case.
This move is so good in many situations its criminal, especially at mid vs casters. It's like a free banshees to describe it to anyone that lasts up to 3 seconds upon activation. However, I max it last due to it only being necessary in one point earlier on. Change this as you will of course.

On The Hunt - A pretty nice ult with a long range encompass - easy enough to get an entire team, so use it during teamfights. Your starks aura will also be nice, so if your not picking up kills, you should be a grand assist to the team with this move anyway. It is also good for running the hell away from anything. Notably, if you activate it in a teamfight you will recieve about 5 assists if you win the teamfight - So it is a great way to gain and maintain stacks on Sword of the Occult if you choose to build it. Of course, max when you can.

This build is designed to give you survivability, AD and AS consistently throughout the game, whilst still allowing to restrain your hungry mana problems. Most of the things here are self explanatory, very similar to a lot of AD builds. You have extreme damage late game with powerful crits thanks to items like Infinity Edge, whilst also having a lot of lifesteal to maintain yourself in teamfights. YOU ARE VERY MUCH A TEAMFIGHTING PERSON YOU MUST ALWAYS BE THERE WHEN THEY COMMENCE!! Frozen Mallet gives you some CC which is always nice, and gives you a flat amount of health for you to lifesteal into to keep up a fight. Zeke's Harbinger is purchased as well to give you the aura that also goes with your ultimates aura - are you beginning tosee how essential and useful we are in a teamfight?

When/if you finish your build, buy every elixir including Oracle's Elixir. Why? Wards.

There is always huge possibility for alternative items dependent on the team. if you're facing heavy AP, Banshees Veil and other magic resist items like Hexdrinker are essential to help you live. You are predominantly a team player with your auras so it is important you keep yourself alive, therefore you should build what you need to to do so.

If you are against a heavy tank team, completely changing the build to substitute in a Madred's Bloodrazor and a Black Cleaver is by no means a bad move. This is a guide, not a Bible :D!

Warmogs impaler Sivir, where you build one or two warmogs with an Atma's impaler, is a bad idea

There are a LOT of builds on MOBAFire utilizing Warmogs-Impaler for Sivir. I'm going to clarify why this is such a bad move here:

Health without resistances is futile. Something like a Madreds or even normal attacks will simply melt you to the ground as all you have is health and no beneficial passives or actives like most tanks will be building. So let no one kid themselves that it helps you live - as it does not. Sure, it might help in the odd situation, but this is where my next point comes in:

"With this set up, you get a LOT of AD from Atmas". In a sense, this is true. BUT how are you going to use that? Lets say you decided to build Frozen Mallet and The Bloodthirster instead. You get a lot of health, but far more imporantly you are ALSO getting huge amounts of AD from the Bloodthirster and lifesteal to help yourself to sustain. It's 20x better than pure health and damage. The crit chance on Atmas also becomes useless as Crit Sivir is not the way to go (I build it mainly for AD and use on squishies).

Please, do not judge me for not following the crowd and building Warmogs & Impaler.

Thanks for reading my Sivir build ;). Here's a few tips and tricks to part one:

Flash through walls (Dragon, Baron, etc)
Call missing on people gone mysteriously, or prolonged time, from your lane. They could be going to gank someone.
Upvote this guide and leave a happy comment
Jungle buffs, especially Lizard, if nothing is going on. Dont disturb an ally Jungler though if you have one.
When running, duck into brush and double back and run out to confuse a chaser.then flash back if you really want to be annoying :P.