Bloodthirster vs IE - Math Included

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The Bloodthirster Cost: 3500 (1150) +80 Attack Damage

UNIQUE Passive: +20% Life Steal UNIQUE Passive: Your basic attacks can now overheal you. Excess life is stored as a shield that can block 50-350 damage, based on champion level.

This shield decays slowly if you haven't dealt or taken damage in the last 25 seconds.

VS

Infinity Edge Cost: 3800 (645) +80 Attack Damage +20% Critical Strike Chance

UNIQUE Passive: Critical strikes deal 250% damage instead of 200%.

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Trying to compare these two things is impossible without reducing it all down to quantifiable stats. The obvious solution is to just flame people who don't go the meta route of IE but are you sure your even flaming for a good reason? Let's find out!

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is easier so let's do that first. It gives a base 80 attack damage. Then it gives +20% crit chance. That means that 1/5 attacks on average should give double the AD which is 160 AD. But wait, there's more! The unique passive actually increases this to 200 AD. If you spread this bonus AD over 5 shots that means you get an average bonus of 40 AD. This brings the total average AD given by IE to 120 AD.

is tougher to quantify. It gives the same base AD of 80 but the passives are confusing. The 20% life steal gives you back HP which means it would negate the damage done to you which means it essentially steals 20% AD which is another way of saying it gives +20% AD. So with that added on you get an AD total of 96. Still left is the even trickier life steal shield. It says it can give between 50 and 350 damage shield. The average of that is 200. That means it gives you an average of +200 HP. The problem is it only absorbs once since its HP. It's not like armor where it provides an easy to quantify reduction. The trick is to find out how long it would take IE to catch back up to BT once the shield is depleted. We find that out with an equation of (x * 96) + 200 = x * 120. This makes both IE and BT an even comparison since they are set to equal each other. The answer to the equation is 8-2/3. At the point in which both opponents make 8-2/3 attacks they have both did equal damage do each other. BT average shield (200) absorbs 1-2/3 attack of IE 120 AD which means it gives BT 1-2/3 extra AD which is worth 160 AD. Spread that over an even fight of 8-2/3 attacks and you get around 18.5 AD. Which gives BT a total of 114.5 AD.

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Uh-oh.... have you forgotten that the prices are not the same? BT costs 300g less than IE.

IE is 3800g for 120 AD = 31.67g per AD. BT is 3500g for 114.5 AD = 30.57g per AD.

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Oh my god! What does this mean?!

Here's the breakdown: IE gives slightly more AD at a slightly more price than BT. They are almost exactly the same worthiness.

Except one thing: BT provides sustain and IE does not. BT not only helps kill your opponent but also keeps you alive. IE only helps kill your opponent. IT doesn't keep you alive.

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The clear winner is .

Remember that this is a purely 1v1 scenario. This is in no way saying you shouldn't ever build IE. This is ONLY saying if you and your opponent each have the opportunity to choose between one of these items...

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VIDEO COMPARISON http://youtu.be/qVH3oEVk0mo

Decide for yourself.