Friday, February 4, 2011

Common Misconceptions About Items - Infinity Edge vs. The Bloodthirster

Another article today from Jebus McAzn on item theory. Today, I'll be talking about the war between two items that many DPS carries want to have, but only need or can afford to get one at a given moment. These items are Infinity Edge and The Bloodthirster, respectively. While you all should certainly know the stats for these items, if you don't, here they are:

Infinity Edge
+75 Attack Damage, +20% Critical Strike Chance
Passive: UNIQUE - Critical hits now deal 250% damage instead of 200%
Cost: 4080 gold
Recipe: B. F. Sword+Pickaxe+Cloak of Agility

The Bloodthirster
+60 Attack Damage, +15% Life Steal
Passive: Gain an additional 1 Physical Damage and 0.25% Life Steal per kill. Maximum of +40 Damage and +10% Lifesteal. Bonuses are lost upon death.
Cost: 3200 gold
Recipe: B.F. Sword+Vampiric Scepter

So we can see that when you farm a Bloodthirster up to its full stacks, its stats actually become:
+100 Attack Damage, +25% Life Steal
These stats seem to be far superior to Infinity Edge. You see a lot of carries mistakenly get The Bloodthirster just because it has more raw damage. Because of those numbers, they mistakenly assume that they'll be dealing more damage with The Bloodthirster than with Infinity Edge. Let's do some calculations. If you've read my previous blog on Madred's Bloodrazor, you know that I like to do math here in simple terms, so everyone can understand.

Let's take two ranged carries who attack once every second. They have no base damage, so the only damage they'll be doing is from items. One gets an Infinity Edge, one gets a Bloodthirster and fully stacks it. Let's ignore gold costs for now. Say that each carry attacks 5 times. How much damage will each do, approximately?

The carry with The Bloodthirster will deal 100 damage with each attack. With 5 attacks, that's 500 damage. She averages... 100 damage per attack, obviously.

Now let's consider the carry with Infinity Edge. She has 20 base crit, so she attacks 5 times and criticals once. That's 4*75 + 2.5*75, since Infinity Edge does raise your critical damage. In total, that's 487.5 damage, or 97.5 damage per attack. You see that even though The Bloodthirster has more base damage, Infinity Edge only falls 2.5 DPS short of the other item. Now some of you may be thinking, "Wait, doesn't Infinity Edge cost 880 gold more?" This is true. But you're also not taking into account the other items you'll be buying.

Infinity Edge only gets better as the game goes on. With more and more base critical chance and higher base damage, the extra 50% critical damage really starts to add up. Let's take some calculations again, this time with Phantom Dancer added in the mix. Phantom Dancer, if you don't know, gives 20 movement speed, 55 attack speed, and 30% critical strike chance.

The champion with Phantom Dancer and The Bloodthirster has 100 base AD and 30% critical chance. In 20 attacks, she will critical 6 times for 200 damage and attack 14 times for 100 damage. This amounts to 2600 damage in 10 attacks, or 130 DPA (damage per attack).

The champion with Phantom Dancer and Infinity Edge will have 75 base AD and 55% critical chance. In 20 attacks, she will critical 11 times for 187.5 damage and attack 9 times for 75 damage. This amounts to 2737.5 damage in 20 attacks, or 136.875 DPA. With just one critical chance item, Infinity Edge is already starting to out-damage The Bloodthirster.

Finally, let's take champion base stats into account. Assume that a ranged carry champion reaches 100 base damage by level 18. Let's use the same examples again.

The champ with PD and Bloodthirster has 200 base AD and 30% CrC (critical chance). In 20 attacks, she will critical 6 times for 400 damage and attack 14 times for 200 damge. This amounts to 5200 damage in 20 attacks, or 260 DPA.

The champion with PD and IE will have 175 base AD and 55% critical chance. In 20 attacks, she will critical 11 times for 437.5 damage and attack 9 times for 175 damage. This amounts to 6387.5 damage in 20 attacks, or 319.375 DPA.

Now the damage increase between Infinity Edge becomes really obvious. The higher base damage or critical chance you have, the more efficient Infinity Edge becomes - that 250% bonus starts to pay for itself quite easily. So while you may look on it as losing out on 880 gold, you end up with almost 60 additional damage - more than a B. F. Sword, for less than half the price.

But here's something else that you're wondering - what about the lifesteal from The Bloodthirster? Doesn't that make the item worth it? Well, it's decent for laning - and that's about it. The reality is, by the time you've saved up for a Bloodthirster or Infinity Edge, you've probably entered the mid-game, where it's much harder to keep laning and you'll most likely enter team fights with full health anyway, if you have a good support on your team. The only time lifesteal will be even remotely useful for you is during a team fight - and marginally so.

Some people out there are die-hard lifesteal fans. I know it. I've watched Master Yi go into a one-on-one with a Nasus or a Trundle and just not die because of his lifesteal, even though he initiated at 20% health - he actually leaves the fight with more health than when he entered.

But let's face it - as a DPS carry, you don't take that much damage if you're playing right, staying in the back behind your tanks. Almost the only time you should be taking damage is when their AP carry decides to focus you. Almost all AP carries have some sort of stun - Anivia, Annie, Veigar, etc. They also generally have a "Hadouken" combo that will completely burst you down in a matter of seconds. No matter how much lifesteal you have, you will NOT be able to negate that stun-and-burst combo.

Let's say that you survive with 30% health. With a lifesteal item, you need to get back into the fight to replenish your health. But at this point, it's incredibly risky for you to go in. Their tanks are on the front line, usually with hard CC, and are ready to slam your ass the minute you decide to go back in with such low health. Going back in means suicide - so you have to port back. Your team loses the team fight and you're unable to hold your mid tower all by yourself.

One random tangent now that will relate to this - Has anyone ever watched Day[9]'s stream about Starcraft 2? Even if you don't play the game, he has some incredibly insightful comments that actually relate to a ton of games out there, whether it be Halo, Call of Duty, World of Warcraft, or League of Legends. What he offers at one point during a Newbie Tuesday tutoring cast:

Let's say you're losing a game. Your opponent has had a larger army than you the whole game, and he's been pushing your base and containing you for a long time. You usher up as many forces as possible, but you still lose. Don't ask yourself how you could have countered his army - ask yourself why his was larger than yours. A failure to have a firm grasp of the basics is what caused your defeat. Don't think in the now - always think ahead. Be proactive, not reactive.

This just hits the nail right on the head, in my opinion. If you're in a team fight as Ashe and you're suddenly nailed by a Flash-->Tibbers-->Incinerate-->Disintegrate combo and now have 15% health, don't think "Oh, I need to heal this damage with my Bloodthirster and hope I don't die." What you need to do is prevent the damage from happening in the first place. While in really good teams, you can prevent the AP or AD carry from focusing you down just by relying on your teammates, you always need to take the initiative whenever solo queuing or going against a team of equal or greater skill.

Think about this - while a Bloodthirster's lifesteal may bring you back from the brink of death, if you get shut down by any hard CC at all, it's useless. A Banshee's Veil, on the other hand, stops the crowd control and actually lets you tank much more magic damage.

Do note, however, that I am not saying that The Bloodthirster is a terrible item. Far from it. There are several scenarios in which The Bloodthirster is extremely useful - here are a few of them.

1. If you play Sivir, Pantheon, or other ability-reliant AD DPS champions

Sivir is a champion who relies heavily on her Boomerang Blade and Ricochet damage during a team fight. Ricochet does not crit. Boomerang Blade scales off of AD and also cannot crit, while both get gradually weaker based on how many enemies they hit. Therefore, it is vital for Sivir to have as much base attack damage as possible, to make the best out of her abilities and team fighting abilities. Sivir excels at tower pushing as well, and you can't crit on towers. Because Sivir's main damage comes from the AoE that her abilities cause, it is not beneficial to grab critical strike chance on her.

Pantheon is an extremely bursty champion who is reliant on combos, the most common one being Aegis of Zeonia-->Heartseeker Strike-->Spear Shot, which can often take a squishy from 75% health to zero in no time flat. Rarely will you see Pantheon actually autoattack until the major team fights, but to be honest, his role in those big fights is to jump on the enemy carry and take them out without dying, then to rinse and repeat his combo. Thus, items like Sword of the Occult and The Bloodthirster are incredibly common on him, while Infinity Edge is rarely seen. Finally, Pantheon's Heartseeker Strike does raise his critical chance to 100% against enemies with under 15% health. This does end up making your critical strike chance irrelevant against enemies with low health, ending up wasting a significant portion of your money.

2. If your champion is based off of hard-hitting, slow attacks instead of fast, constant DPS

It's very hard to come up with an example of this kind of champion, but the best illustration is Trundle, in my opinion. Tanky DPS Trundle typically gets a Triforce and generally tries to deal as much burst damage as possible in team fights with his Rabid Bite while supporting his carries with Pillar of Filth and destroying tanks with his Agony. During a team fight, he will NOT be attacking often, but will be gimping carries and bursting them down.

So what's the point of getting Infinity Edge on him? I-Edge relies on a constant stream of attacks with a relatively high crit chance, in order to really milk out that 250% damage proc. An analogy - if you flip a coin twice, it's still somewhat likely that you'll get heads twice in a row. However, flipping a coin 1000 times will yield results much closer to 500/500 heads to tails.

Likewise, a good critical rate needs a good stream of attack speed. The less you attack, the less you critical, and the less you're gaining from an Infinity Edge. Thus getting The Bloodthirster is acceptable on bursty champions that don't capitalize on attack speed.

3. If you've invested in defensive items or already have an I-Edge

Say you did go ahead and get that Banshee's Veil or you already have that Infinity Edge. Now you need more damage. The more base damage you have, the more Infinity Edge pays for itself. This is a huge theme that you NEED to be aware of. You are not buying The Bloodthirster because it's the best item for an AD carry - you're buying it because it offers the most raw attack damage, which in turn is what benefits Infinity Edge the most.

That Banshee's Veil, in the meanwhile, is saving your life in fights. Since you didn't invest in an attack item, you don't have as much attack damage as you'd like - although your team has been winning team fights simply because you've been staying alive. Now is the time to capitalize on their inability to kill you buy getting that damage up. The lifesteal is just a bonus. While carries will often get other options, like Phantom Dancer, The Black Cleaver, or Madred's Bloodrazor, The Bloodthirster is still a viable choice for champions who like raw damage to dominate the game.

When considering the issue of Infinity Edge vs. The Bloodthirster, it is always necessary to consider which one is better suited for the champion you're playing. Are your abilities really central to your champ? Is he more centered around autoattacks? If so, how fast does he attack? How much crit chance does he have? Can your survive a fight long enough to make that damage useful? Always, always, always keep these points in mind.

That brings us to the end of this blog. Next time, I'll be writing about AP carries and another common issue that so many are painfully unaware of - the usefulness of magic penetration in general on an AP carry, and why Void Staff isn't always the best option to get for that particular field. Anyway, that's all for today, and I will see you guys next time!


  1. i really think that black cleaver is the best first item to get for champs like ashe and so on. arp>crit

  2. "raw attack damage, which in turn is what benefits Infinity Edge the most"
    Crit chance IS what increases your damage the most with IEdge.

  3. Searz read the whole thing before making comments like that. He was saying in THAT PARTICULAR INSTANCE when you've already gotten all your attack items and that is the last big ticket item left with tonnes of dmg on it, you then get the Blood Thirster for it's raw damage increase.

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