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The item Atma's Impaler has a unique passive as follows:

UNIQUE: 1.5% of your maximum health is granted as bonus attack damage.

The item's combine cost is 780g, and the total item costs 2300g. How much health do I need to make Atma's Impaler a cost effective +attack damage item? That is to say, how much health do I need in order to gain more bonus attack damage than if I had spent the gold on +AD items alone?

I'm trying to decide what to do when situations merit the armor bonus the item provides, but I still need to build damage.

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Please edit your question since it is no longer 2% –  Adam Arold Jul 3 '12 at 14:08
    
@edem Quite honestly, I'd forgotten I'd asked this question! You don't need me, though - next time, why not suggest an edit yourself! –  Raven Dreamer Jul 4 '12 at 2:36
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I wanted to edit but I had to edit 6 or more characters and this is just 2. I did not want to change anything else. –  Adam Arold Jul 4 '12 at 8:10
    
I think that Atma is a highly situational item. For example if the enemy team has 4 AD champions and you just need some more crit than you might buy it but otherwise it is highly unlikely to buy it on an AD carry. –  Adam Arold Jul 4 '12 at 9:45
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3 Answers

up vote 23 down vote accepted

EDIT: Updated to reflect the Atma's change to 1.5%.

I'm not sure what the true cost of a single attack damage is, but here are some points of comparison:

Long Sword: 415g, 10ad = 41.5g/ad
BF Sword: 1650g, 45ad = 36.7g/ad

So, while the reality is more complicated, you could say that one point of attack damage costs around 39g. Here are the values of the Atmas passive at different health levels:

2000 hp: 2355, 30 ad = 78.50g/ad
2250 hp: 2355, 33 ad = 69.78g/ad
2500 hp: 2355, 37 ad = 62.80g/ad
2750 hp: 2355, 41 ad = 57.09g/ad
3000 hp: 2355, 45 ad = 52.33g/ad
3250 hp: 2355, 48 ad = 48.31g/ad
3500 hp: 2355, 52 ad = 44.86g/ad
3750 hp: 2355, 56 ad = 41.87g/ad
4000 hp: 2355, 60 ad = 39.25g/ad
4250 hp: 2355, 63 ad = 36.94g/ad
4500 hp: 2355, 67 ad = 34.89g/ad

So at somewhere around 4020 hp it becomes worth it for the damage alone.

Here's a similar table considering only the cost of the combine, rather than the total cost of the item:

1000 hp: 825, 15 ad = 55.00g/ad
1250 hp: 825, 18 ad = 44.00g/ad
1500 hp: 825, 22 ad = 36.67g/ad
1750 hp: 825, 26 ad = 31.43g/ad
2000 hp: 825, 30 ad = 27.50g/ad
2250 hp: 825, 33 ad = 24.44g/ad
2500 hp: 825, 37 ad = 22.00g/ad
2750 hp: 825, 41 ad = 20.00g/ad
3000 hp: 825, 45 ad = 18.33g/ad

So if you already have the two base items, you only need around 1400 health to make the combine worthwhile.

The wiki page says:

The amount of health required to be as effective as the B. F. Sword is 1500, when taking both armor and crit hit chance into account.

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Excellent! And interesting. But what about for just the combine cost (825)? It's only the combine cost that adds attack damage, after all. The armor / crit remains exactly the same as before combination, so I think that the combine cost is the one which needs to be compared. –  Raven Dreamer Aug 12 '11 at 1:30
    
That's true, though it depends whether the armor and crit are going to be of full usefulness to the champion you're playing. If you'd buy armor and crit chance anyway, it becomes a very attractive item! I've added another table above that only considers the combine cost. –  Chron Aug 12 '11 at 1:36
    
Thanks, Chron, excellent answer! Welcome to the site! –  Raven Dreamer Aug 12 '11 at 1:42
    
It is no longer 2% please update. –  Adam Arold Jul 3 '12 at 14:09
    
Thanks for the update, but you did not change the values. :) –  Adam Arold Jul 4 '12 at 8:11
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Accurate as of May 2013

  • If you take into account all of the statistics on Atma's Impaler, you need 1083 health to make the item gold efficient.

  • If you take into account only the attack damage from Atma's Impaler, you need 3833 / 4381/ 4452 health to gain the same attack damage as if you had spent the gold on Long Swords / Pickaxes / B. F. Swords instead.

  • If you already have both a Chain Vest and Avarice Blade, and you are comparing only the amount of AD granted by the combine cost (780g) for the passive vs spending the gold on AD items, you need 1300/1486/1510 health to gain the same attack damage as if you had spent the gold on Long Swords / Pickaxes / B. F. Swords instead.

Below is the math, in terms of gold efficiency. I use basic stat items and their costs to calculate the gold value of the final item. From there I use the known values to solve the equation for the health necessary to make the item gold efficient.


Atma's Impaler

Recipie

  • Chain Vest (720g) - 40 Armor
  • Avarice Blade (800g) - 10% Critical Strike Chance, 3 gold per 10 seconds, 2 gold per kill
  • Combine Cost (780g)
  • Total Cost = 2300g

Final Stats

  • 45 Armor
  • 15% Critical Strike Chance
  • Unique: You gain attack damage equal to 1.5% of your maximum health.

Gold Efficiency

Equivalencies

  • Cloth Armor (300g) = 15 armor; 300/15 = 20g per 1 armor
  • Brawler's Gloves (400g) = 8% Critical Strike Chance; 400/8 = 50g per 1% crit
  • Long Sword (400g) = 10 Attack Damage; 400/10 = 40g per 1 attack damage
  • Passive: Attack Damage equal to 1.5% of maximum health; 1/.015 = 1 attack damage gained per 66.667 health
  • Using the two previous equivalencies: You gain 40g worth of attack damage per 66.667 health

In Terms of Total Stats Gained

Using the equivalencies established above:

  • ArmorValue = 45*20 = 900g
  • CritValue = 15*50 = 750g
  • AttackValue = 40g per 66.667 health

TotalCost = Chain Vest + Avarice Blade + Combine Cost = 820+800+780 = 2300g

TotalEfficiency = ArmorValue + CritValue + AttackValue

AttackValue = TotalEfficiency - ArmorValue - CritValue

The break even point for the item is where TotalEfficiency = TotalCost = 2300g, so we solve for AttackValue.

AttackValue = 2300-900-750 = 650g

650/40*66.667 = 1083 health to make Atma's Impaler efficient

I've used the cheapest items available for each statistic to calculate the equivalent gold value of the final item. Obviously if you're comparing against more expensive (and usually more efficient) items, the gold value will fall, which raises the amount of health necessary to make the item efficient.

Because Avarice Blade is a gold generating item, the longer you keep your Avarice Blade around without combining it into the final item, the more efficient the final item becomes. As such, the health necessary to make the item efficient falls.

In Terms of Total Cost and Attack Damage Only

  • AttackValue = 400/10 = 40g per 66.667 health for Long Sword
  • AttackValue = 875/25 = 35g per 66.667 health for Pickaxe
  • AttackValue = 1550/45 = 34.444g per 66.667 health for B. F. Sword

TotalCost = Chain Vest + Avarice Blade + Combine Cost = 820+800+780 = 2300g

2300/40*66.667 = 3833 health to make Atma's Impaler efficient vs buying Long Swords

2300/35*66.667 = 4381 health to make Atma's Impaler efficient vs buying Pickaxes

2300/34.444*66.667 = 4452 health to make Atma's Impaler efficient vs buying B. F. Swords

In Terms of Combine Cost and Attack Damage Only

  • AttackValue = 400/10 = 40g per 66.667 health for Long Sword
  • AttackValue = 875/25 = 35g per 66.667 health for Pickaxe
  • AttackValue = 1550/45 = 34.444g per 66.667 health for B. F. Sword

Combine Cost = 780g

780/40*66.667 = 1300 health to gain more attack damage than buying Long Swords

780/35*66.667 = 1486 health to gain more attack damage than buying Pickaxes

780/34.444*66.667 = 1510 health to gain more attack damage than buying B. F. Swords

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It now give 1.5% AD, so the figures in @chron's have changed somewhat

However, you should consider the 18% crit chance and the armour too.

Assuming you have the typical AD carry build of PD, IE and Frozen Mallet: you will get around 35-45 from Atmas and increase your crit change to 73% from 55%. The armour adds 45% to your effective health.

Add on another PD to give 100% crit with higher health and an on-hit slow.

For ranged AD, someone like Graves/Miss Fortune/Kayle would benefit from it, more so than a squishier Twitch/Vayne type carry.

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