Items - Comparing Efficiencies

Explanation

The purpose of this guide is not to tell you what items to buy/build for any specific hero or game. The purpose of this guide is simply to provide insight into the comparable efficiencies of similar items. With this new insight, you can then make more educated decisions on which items to buy/build for each circumstance.

Now, because Dota is a complicated game, I am only going to compare a single stat at a time. Otherwise the math could get pretty crazy, and there would be too many variables to really be able to make sense of it. So the rest of the guide is divided into sections by which stat is being compared.

Note that while there is a bit of math shown, you don't really need to understand it. Just look at the yellow values to see how items compare. The higher the number the better (ie more stats per gold).

All items will follow this general formula:
Item Name - stat * 100 / cost = value

Changelog

4-12-13

• Added Percent Based section to Mana Regen
• Added a TODO section

4-11-13

• Finished Health Regeneration section
• Sorted Attack Speed, Health, Mana, and Health Regen sections by value
• Renamed guide from 'Items - Bang for Buck' to 'Items - Comparing Efficiencies'

4-10-13

• Finished Health section
• Finished Mana section

4-9-13

• Added Manta Style to damage section
• Fixed Daedalus, Crystalys, Desolator, and Orchid Malevolence. The calculations were showing ALL damage, when they should have only showed how much damage was added by the respective item.
• Finished Attack Speed section

TODO

• Temporary duration heals for Health Regen section
• Flat boost for Mana Regen section
• Find a better way to sort/organize the Damage section
• Do Damage Reduction section: armor, magic, block

Single Target Damage (per hit)

The yellow value is against a target with 0 armor, the orange value is against a target with 10 armor, and the red value is against a target with 20 armor. Except for on Desolator, orange is the yellow value times .625, and red is the yellow value times .455. My armor (damage reduction) calculations are based off of the information at this site: http://www.dota2wiki.com/wiki/Armor .
Red and orange are omitted when some of the damage is not affected by armor.

Damage items

Blades of Attack - 9 * 100 / 450 = 2.0, 1.25, .91
Broadsword - 18 * 100 / 1200 = 1.5, .94, .68
Quarterstaff - 10 * 100 / 900 = 1.11, .69, .5
Claymore - 21 * 100 / 1400 = 1.5, .94, .68
Javelin - (21 + .2 * 40) * 100 / 1500 = 1.93, 1.21, .89º
Mithril Hammer - 24 * 100 / 1600 = 1.5, .94, .68
Demon Edge - 46 * 100 / 2400 = 1.92, 1.21, .89
Sacred Relic - 60 * 100 / 3800 = 1.58, .95, .69

Stats items

(damage is only from main stat)
Iron Branch - 1 * 100 / 53 = 1.89, 1.18, .86
Circlet - 2 * 100 / 185 = 1.08, .64, .47
Gauntlets of Strength - 3 * 100 / 150 = 2.0, 1.25, .91 (for strength heros)
Slippers of Agility - 3 * 100 / 150 = 2.0, 1.25, .91 (for agility heros)
Mantle of Intelligence - 3 * 100 / 150 = 2.0, 1.25, .91 (for intelligence heros)
Bracer
For strength heros - 9 * 100 / 525 = 1.71, 1.07, .78
Wraith Band
For agility heros - 9 * 100 / 485 = 1.86, 1.19, .88
For other heros - 6 * 100 / 485 = 1.24, .78, .56
Null Talisman
For intelligence heros - 9 * 100 / 490 = 1.84, 1.18, .88
For other heros - 6 * 100 / 490 = 1.22, .77, .56
Belt of Strength - 6 * 100 / 450 = 1.33, .83, .61 (for strength heros)
Band of Elvenskin - 6 * 100 / 450 = 1.33, .83, .61 (for agility heros)
Robe of the Magi - 6 * 100 / 450 = 1.33, .83, .61 (for intelligence heros)
Ogre Club - 10 * 100 / 1000 = 1.0, .63, .46 (for strength heros)
Blade of Alacrity - 10 * 100 / 1000 = 1.0, .63, .46 (for agility heros)
Staff of Wizardry - 10 * 100 / 1000 = 1.0, .63, .46 (for intelligence heros)
Reaver - 25 * 100 / 3200 = .78, .49, .35 (for strength heros)
Eaglesong - 25 * 100 / 3300 = .76, .48, .34 (for agility heros)
Mystic Staff - 25 * 100 / 2700 = .93, .58, .4 (for intelligence heros)

Recipes

Only listing items with reasonable efficiency (ie > 1.0), or for the purpose of pointing out popular low efficiency items (ie over-priced).

Divine Rapier - 300 * 100 / 6200 = 4.83, 3.02, 2.2
Monkey King Bar - (88 + .35 * 100) * 100 / 5400 = 2.28, 1.43, 1.04º
Radiance - 60 * 100 / 5150 = 1.17, .72, .52
per second - 45 * 100 / 5150 = .87±
Butterfly
For agility heros - 60 * 100 / 6000 = 1.0, .63, .46
For other heros - 30 * 100 / 6000 = .5, .32, .23
Daedalus - (81 + .35 * 81 * 2.7) * 100 / 5750 = 2.36, 1.46, 1.06º%
hero has 200 total damage - (81 + .35 * 200 * 1.7) * 100 / 5750 = 3.48, 2.17, 1.58º
hero has 400 total damage - (81 + .35 * 400 * 1.7) * 100 / 5750 = 5.55, 3.47, 2.53º
Crystalys - (35 + .2 * 35 * 1.75) * 100 / 2150 = 2.2, 1.43, 1.04º%
hero has 200 total damage - (35 + .2 * 200 * .75) * 100 / 2150 = 3.02, 1.89, 1.37º
hero has 400 total damage - (35 + .2 * 400 * .75) * 100 / 2150 = 4.42, 2.76, 2.01º
Desolator©
60 * 1.31 * 100 / 4100 = 1.92f%¬
60 * .804 * 100 / 4100 = 1.18%¬
60 * .543 * 100 / 4100 = .79%¬
hero has 200 total damage
(60 + 200 * .31) * 100 / 4100 = 2.98¬
(60 + 200 * .181) * 100 / 4100 = 2.35¬
(60 + 200 * .088) * 100 / 4100 = 1.89¬
hero has 400 total damage
(60 + 400 * .31) * 100 / 4100 = 4.49¬
(60 + 400 * .181) * 100 / 4100 = 3.23¬
(60 + 400 * .088) * 100 / 4100 = 2.32¬
Armlet of Mordiggian = 9 * 100 / 2600 = .35, .22, .16
activated - 40 * 100 / 2600 = 1.54, .96, .7
activated (strength) - 65 * 100 / 2600 = 2.5, 1.56, 1.14
Skull Basher - 40 * 100 / 2950 = 1.36, .85, .62
for strength heros - 46 * 100 / 2950 = 1.56, .98, .71
Abyssal Blade - 100 * 100 / 6750 = 1.48, .93, .67
for strength heros - 110* 100 / 6750 = 1.63, 1.03, .75
Shadow Blade - 30 * 100 / 3000 = 1.0, .63, .46
Battle Fury - 65 * 100 / 4350 = 1.49, .93, .68
Helm of the Dominator - 20 * 100 / 1850 = 1.08, .64, .47
Sange
for strength heros - 26 * 100 / 2050 = 1.27, .79, .58
for other heros - 10 * 100 / 2050 = .49, .31, .22
Yasha - 16 * 100 / 2050 = .78, .49, .35 (for agility heros)
Sange and Yasha - 28 * 100 / 4100 = .68, .43, .31 (for strength and agility heros)
Heaven's Halberd - 45 * 100 / 3850 = 1.17, .73, .53 (for strength heros)
Maelstrom - (24 + .25 * 120) * 100 / 2700 = 2.0 º
Mjollnir - (25 + .25 * 160) * 100 / 5400 = 1.2 º
assuming its you vs. another hero, both attacking eachother once per second (for math including static charge)
(25 + .25 * 160 + .2 * 200) * 100 / 5400 = 1.94 ºº
Diffusal Blade - 42 * 100 / 3300 = 1.27 (for agility heros, including burn damage)
upgraded - 62 * 100 / 4150 = 1.49 (for agility heros, including burn damage)
Orchid Malevolence © - 55 * 100 / 5025 = 1.09, .65, .48%
hero has 200 total damage - (55 + .3 * 200) * 100 / 5025 = 2.29 (target is soul burned)
hero has 400 total damage - (55 + .3 * 400) * 100 / 5025 = 3.48 (target is soul burned)
Power Treads - 8 * 100 / 1400 = .57, .36, .21
Phase Boots - 24 * 100 / 1350 = 1.78, 1.11, .81
Manta Style - 26 * 100 / 5050 = .41, .26, .19
counting images, hero has 200 total damage
(26 + 200 * .33 * 2) * 100 / 5050 = 3.13, 1.95, 1.42·
counting images, hero has 400 total damage
(26 + 400 * .33 * 2) * 100 / 5050 = 5.74, 3.59, 2.61·

º Damage of random proc is averaged into the value.
± If your hero is attacking once per second, you can add the 2 values together and get a meaningful value. Otherwise, they should be factored separately. Also, this damage is magical and not affected by armor.
% Though the item effect is multiplicative, this calculation only factors the damage given by that item into the value. Any additional damage (ie base + other items) that you have is also multiplied by the item effect, but is an unknown and therefore can't be added into the value. In laymans terms, the more damage you have, the higher the value is, the more efficient this item is.
¬ Because target is assumed to have 0/10/20 armor, and this item reduces target armor by 6, the damage amplification/reduction is different for this item.
© Also increases damage from all other sources (ie teammates).
· To get the average value, multiply these values times .4 (because images are only active at most 40% of the time).

Attack Speed

Mask of Madness (activated) - 100 * 100 / 1900 = 5.26
Gloves of Haste - 15 * 100 / 500 = 3.00
Power Treads (as agility) - 38 * 100 / 1400 = 2.71
Hyperstone - 55 * 100 / 2100 = 2.62
Mask of Madness (average) - 48 * 100 / 1900 = 2.53
Power Treads - 30 * 100 / 1400 = 2.14
Slippers of Agility - 3 * 100 / 150 = 2.00
Iron Branch - 1 * 100 / 53 = 1.89
Hand of Midas - 30 * 100 / 1900 = 1.58
Yasha - 31 * 100 / 2050 = 1.51
Mjollnir - 80 * 100 / 5400 = 1.48
Drum of Endurance (activated) - 24 * 100 / 1725 = 1.39
Band of Elvenskin - 6 * 100 / 450 = 1.33
Wraith Band - 6 * 100 / 485 = 1.24
Poor Man's Shield - 6 * 100 / 550 = 1.09
Circlet - 2 * 100 / 185 = 1.08
Assault Cuirass - 55 * 100 / 5350 = 1.03
Blade of Alacrity - 10 * 100 / 1000 = 1.00
Shadow Blade - 30 * 100 / 3000 = 1.00
Butterfly - 60 * 100 / 6000 = 1.00
Armlet of Mordiggian (activated) - 25 * 100 / 2600 = 0.96
Maelstrom - 25 * 100 / 2700 = 0.93
Ethereal Blade - 40 * 100 / 4900 = 0.82
Manta Style - 41 * 100 / 5050 = 0.81
Drum of Endurance - 14 * 100 / 1725 = 0.81
Eaglesong - 25 * 100 / 3300 = 0.76
Sange and Yasha - 31 * 100 / 4100 = 0.76
Diffusal Blade - 22 * 100 / 3300 = 0.67
Diffusal Blade (Upgraded) - 26 * 100 / 4150 = 0.63
Ring of Aquila - 6 * 100 / 985 = 0.61
Orchid Malevolence - 30 * 100 / 5025 = 0.60
Armlet of Mordiggian - 15 * 100 / 2600 = 0.58
Monkey King Bar - 15 * 100 / 4500 = 0.33

Health

Gauntlets of Strength - 57 * 100 / 150 = 38.00
Iron Branch - 19 * 100 / 53 = 35.85
Belt of Strength - 114 * 100 / 450 = 25.33
Vitality Booster - 250 * 100 / 1100 = 22.73
Bracer - 114 * 100 / 525 = 21.71
Circlet - 38 * 100 / 185 = 20.54
Heart of Tarrasque - 1060 * 100 / 5500 = 19.27
Ogre Club - 190 * 100 / 1000 = 19.00
Armlet of Mordiggian (activated) - 475 * 100 / 2600 = 18.27
Point Booster - 200 * 100 / 1200 = 16.67
Reaver - 475 * 100 / 3200 = 14.84
Sange - 304 * 100 / 2050 = 14.83
Soul Booster - 450 * 100 / 3300 = 13.64
Urn of Shadows - 114 * 100 / 875 = 13.03
Eye of Skadi - 725 * 100 / 5675 = 12.78
Vanguard - 250 * 100 / 2225 = 11.24
Rod of Atos - 325 * 100 / 3100 = 10.48
Bloodstone - 500 * 100 / 5050 = 9.90
Heaven's Halberd - 380 * 100 / 3850 = 9.87
Aghanim's Scepter - 390 * 100 / 4200 = 9.29
Satanic - 475 * 100 / 6150 = 7.72
Sange and Yasha - 304 * 100 / 4100 = 7.41

Mana

Mantle of Intelligence - 39 * 100 / 150 = 26.00
Energy Booster - 250 * 100 / 1000 = 25.00
Iron Branch - 13 * 100 / 53 = 24.53
Robe of the Magi - 78 * 100 / 450 = 17.33
Arcane Boots - 250 * 100 / 1450 = 17.24
Null Talisman - 78 * 100 / 480 = 16.25
Circlet - 26 * 100 / 185 = 14.05
Staff of Wizardry - 130 * 100 / 1000 = 13.00
Point Booster - 150 * 100 / 1200 = 12.50
Soul Booster - 400 * 100 / 3300 = 12.12
Mystic Staff - 325 * 100 / 2700 = 12.04
Eye of Skadi - 575 * 100 / 5675 = 10.13
Shiva's Guard - 390 * 100 / 4700 = 8.30
Scythe of Vyse - 455 * 100 / 5675 = 8.02
Bloodstone - 400 * 100 / 5050 = 7.92
Aghanim's Scepter - 280 * 100 / 4200 = 6.67
Orchid Malevolence - 325 * 100 / 5025 = 6.47

Damage Reduction

Coming Soon!

Health Regeneration

Constant Flat Regen
Ring of Regen - 2.00 * 100 / 350 = 0.57
Ring of Health - 5.00 * 100 / 875 = 0.57
Headdress - 3.00 * 100 / 603 = 0.50
Hood of Defiance - 8.00 * 100 / 2125 = 0.38
Soul Ring - 3.00 * 100 / 800 = 0.38
Helm of Iron Will - 3.00 * 100 / 950 = 0.32
Tranquil Boots - 3.00 * 100 / 975 = 0.31
Pipe of Insight - 11.00 * 100 / 3628 = 0.30
Gauntlets of Strength - 0.43 * 100 / 150 = 0.29
Perseverance - 5.00 * 100 / 1750 = 0.29
Vanguard - 6.00 * 100 / 2225 = 0.27
Iron Branch - 0.14 * 100 / 53 = 0.27
Veil of Discord - 6.00 * 100 / 2650 = 0.23
Bloodstone - 9.00 * 100 / 5050 = 0.18
Mekansm - 4.00 * 100 / 2306 = 0.17
Battle Fury - 6.00 * 100 / 4350 = 0.14
Soul Booster - 4.00 * 100 / 3300 = 0.12
Linken's Sphere - 6.00 * 100 / 5175 = 0.12

Mana Regeneration

Percent Boost
Sage's Mask - 50 * 100 / 325 = 15.38
Void Stone - 100 * 100 / 875 = 11.43
Perseverance - 125 * 100 / 1750 = 7.14
Soul Ring - 50 * 100 / 800 = 6.25
Urn of Shadows - 50 * 100 / 875 = 5.71
Eul's Scepter of Divinity - 150 * 100 / 2800 = 5.36
Medallion of Courage - 50 * 100 / 1075 = 4.65
Oblivion Staff - 75 * 100 / 1675 = 4.48
Bloodstone - 200 * 100 / 5050 = 3.96
Refresher Orb - 200 * 100 / 5300 = 3.77
Battle Fury - 150 * 100 / 4350 = 3.45
Soul Booster - 100 * 100 / 3300 = 3.03
Orchid Malevolence - 150 * 100 / 5025 = 2.99
Linken's Sphere - 150 * 100 / 5175 = 2.90
Scythe of Vyse - 150 * 100 / 5675 = 2.64

Flat Boost