Elitist Jerks Item Level Mechanics

01/31/09, 10:07 PM   #1
Seratha
Von Kaiser

Blood Elf Priest

Kirin Tor
Item Level Mechanics

There’s been a number of changes to the item level formula since Hyzenthlei’s original post on the subject and the WoWWiki page on item level is similarly out of date with no discussion occurring there, so I thought it’d be a good idea to collect the current mechanics into one place. All items have an item level that give the item certain properties like armor value, weapon DPS, and a budget guideline that may or may not be followed.

Equations
The item level for all items begin calculation the same way by taking the various stats on an item and multiplying them by their corresponding stat mods. Most stats have a stat mod of 1, including Strength, Agility, Intellect, Spirit, Resistances, and all rating stats. Stamina is the only “white” stat that has a stat mod of 2/3. The table below lists the various stats and their corresponding modifiers.

 Stat Modifier Strength 1 Agility 1 Stamina 2/3 Intellect 1 Spirit 1 Ratings 1 Attack Power 1/2 Spell Power 6/7 Mana per 5 5/2 Armor 1/14 Block Value 13/40

The item value is determined by taking a stat multiplied by its modifier and raising it to the power of log(2)/log(1.5), which is approximately 1.7095, and adding it to the rest of the stats on the item each multiplied similarly. Once all stats are added up, the resulting value is raised to the 1/1.7095 power. The resulting equation is:

$itemValue= [(stat[1]*statMod[1])^{1.7095}) + ((stat[2]*statMod[2])^{1.7095}) + ... + ((stat[n]*statMod[n])^{1.7095}) ]^\frac{1}{1.7095}$

For most items this is the same item value that will go in to equation to determine the item level, but not all slots of equipment are created equal. When it comes to helms, chests, pants, and two handed weapons, their slot modifier is 1. Other slots have a different modifier.

 Slot Modifier Chest 1.00 Head 1.00 Legs 1.00 Two Handed Weapon 1.00 Shoulder 3/4 Hands 3/4 Waist 3/4 Feet 3/4 Wrist 9/16 Neck 9/16 Back 9/16 Finger 9/16 Off Hand 9/16 Shield 9/16 Wand 5/16 Trinket 17/25* One Handed Weapon 27/64 Ranged 81/256

*When it comes to trinkets, I’m not sure of the exact slot modifier. Hyzenthlei’s post listed them as a having a slot modifier of 17/25, but WoWWiki doesn’t even list a slot modifier. I haven’t done any testing to figure out the correct modifier as most trinkets have procs that are difficult to quantify in their budget.

$itemSlotValue= \frac{itemValue}{slotModifier}$

Dividing the item value by the slot modifier yields the item slot value. This is the raw value that will go into equation to determine item level and weapon DPS. Depending on the quality of the gear and the suggested item level, one of many different formulas could be used. Originally in vanilla WoW, the formula to calculate the item level was a linear formula that had three different equations depending on the quality of the item.

Uncommon:
$itemLevel= 2.0 * itemSlotValue + 8.00$
Rare:
$itemLevel= 1.8 * itemSlotValue + 0.75$
Epic:
$itemLevel= 1.2 * itemSlotValue + 26$
Starting with item level 100 epics, however, the linear formula was replaced with a logarithmic formula that allowed greater scaling as item levels increased. Similarly, in Wrath of the Lich King, rare items and uncommon items from quest rewards shifted into using a logarithmic equation as well. As of patch 3.2, rare and uncommon items with random enchants now use the listed formulas below.

Uncommon:
$itemLevel= 101.18*ln(itemSlotValue) - 292.23$
Rare:
$itemLevel= 97.632*ln(itemSlotValue) - 287.14$
Epic:
$itemLevel= 106.29*ln(itemSlotValue) - 344.36$
Sockets
Sockets take up a flat amount of an items budget. It appears that to create a socket, Blizzard sacrifices 16 points from any stat they feel like choosing and then using that to create a socket of any color. The same stat can be sacrificed multiple times to create multiple sockets. The socket bonus seems to be just that, a bonus that consumes no portion of the item’s budget.

Set Bonuses
Like socket bonuses, they’re free and consume no portion of the item’s budget.

Weapon DPS
Weapon DPS is an interesting property of items as there seems to be multiple ways of calculating it. The recently introduced Heirloom items managed to answer and raise questions. Prior to level 57, making them equivalent to rare items from vanilla WoW, the Heirloom weapons do not scale linearly, but instead seem to alternate between linear and polynomial increases. From levels 58 to 67, the Heirloom weapons increase DPS exponentially as item level increases. From 68 to 80, the weapon DPS also increases exponentially, but at a different rate. Epic items from item level 100 to item level 226 all hold the same exponential scaling.

The equation for item level from item slot is a logarithmic equation and the equation from item level to weapon DPS would require an exponential equation, therefore an equation from item slot value, the value prior to item level, to weapon DPS would be a linear equation.

For rare items past item level 134, the following equation can determine one handed weapon DPS:

$dps= 0.568 * itemSlotValue + 47.204$

To calculate two handed weapon DPS, just multiply the result by 1.3, as a two handed weapon will have 30% more weapon DPS than a one handed weapon.

For epic items from item level 100 onward, the following equations determine weapon DPS:

One Handed Weapon:
$dps= 0.5922 * itemSlotValue + 43.388$

Two Handed Weapon:
$dps= 0.7714 * itemSlotValue + 56.129$

Ranged Weapons until item level 219:
$dps= 0.5423 * itemSlotValue + 38.32$

Wand:
$dps= 1.0657 * itemSlotValue + 82.251$

The fact that epic items from TBC and WotLK share the same formula for weapon DPS leads me to believe that the formula for rare items in TBC may not be the same as the formula for rare items in WotLK.

A caveat about using the item slot value to calculate weapon DPS is that certain weapons, like [Cataclysm's Edge], are under budget according to their item level and will display a lower weapon DPS than properly budgeted items at the same level.

DPS Sacrifice
For caster weapons the inherent DPS in a weapon is mostly useless. To overcome this problem, Blizzard began sacrificing some of the DPS on a weapon in order to allow it to be traded for Spell Power at a rate of 4 Spell Power to 1 Weapon DPS. From Molten Core to Sunwell, Blizzard had been sacrificing enough DPS to bring a one handed weapon down to approximately 41.4 DPS.

In WotLK sacrificing DPS works differently than previously. It appears that Blizzard is intending to make Spell Power intrinsic to a weapon in much the same way that weapons have a natural DPS. The calculation to determine a weapon's Spell Power is similar to the calculation for a weapon's DPS.

Rare Spell Power:
$spellPower= 2.217 * itemSlotValue + 29.842$

Epic Spell Power:
$spellPower= 2.435 * itemSlotValue - 1.123$

The only exception to this that I’ve found is the [Netherbreath Spellblade] that has a higher than expected DPS. Unlike their melee counterparts, Heirloom items do not use the same Spell Power equation as rare quality items. They have a higher coefficient which explains their higher Spell Power compared to an equal item level rare.

Legendary Items
With the exception of Thori'dal and the Tempest Keep legendaries, legendary items use the same calculation for stats and weapon DPS as an epic weapon of equivalent item level. Both Warglaives come out as being equivalent to being 156 epics and the stats on Val'anyr that appeared on the Armory put it at the equivalent as a 239 epic. What sets a legendary apart from an epic is the proc associated with it.

Procs
Items that have chance on hit mechanics or other special effects will have those counted towards the item’s budget. These fall under the same problem that trinkets have in that they are hard to quantify with a number and most likely have an assumed cost based on their theoretical benefit.

Last edited by Seratha : 08/21/09 at 12:08 PM. Reason: 3.2 updates

 01/31/09, 11:43 PM #2 Falk Soda Popinski   Falk Night Elf Druid   No WoW Account Armor value is of special interest to tanks and does not seem to follow any standardized scale (so far, I guess... we've seen 3 tiers of stuff - 200, 213, 226) as of WotLK. Extrapolating from the values in TBC gear you'd expect the WotLK stuff to have a ridiculous number, but they don't. In fact, it seems the increase in armor going from 200, to 213, to 216 is something like <3% per tier.
 02/01/09, 3:24 PM #3 PSGarak Bald Bull     Garak Undead Warlock   Hyjal On your first table, I think you meant MP/5 has a cost of 5/2, not 2/5. Do wands and other ranged weapons have the same budget?
 02/01/09, 3:41 PM #4 songster Chief Passenger   Schizzle Gnome Rogue   Earthen Ring (EU) Is there any simple formula for how vendor price is related to armor type, slot type and item level? It seems very much like there should be, but nobody's ever bothered to derive one. Which is silly, because it means you need a hefty mod like Informant to give you vendor prices on stuff, clogging up your memory with a big database of stuff. I'm sure the vast majority of such a database (anything equippable of green or higher quality, at the least, probably half the greys as well) should be derivable with an ilvl-based formula.
 02/01/09, 11:39 PM #5 Falk Soda Popinski   Falk Night Elf Druid   No WoW Account [Band of Icy Depths] says nope. There'd be way too many exceptions and different scales.
 02/02/09, 5:10 AM #6 • Chicken Mod     Upsidazi Gnome Monk   Azjol-Nerub (EU) It depends on the tier of content mostly, though even then there can be odd variations. All item level 213 rings dropping in Naxxramas for example are worth the same amount of gold, as are all item level 213 necklaces dropping in Naxxramas. This doesn't always hold true though, if you take a look at item level 115 necklaces dropping in Karazhan the price varies per item, despite all of them being the same item level. Oddly all item level 115 rings dropping in Karazhan do fetch the same price.
02/02/09, 2:11 PM   #7
Seratha
Von Kaiser

Blood Elf Priest

Kirin Tor
 Originally Posted by PSGarak On your first table, I think you meant MP/5 has a cost of 5/2, not 2/5. Do wands and other ranged weapons have the same budget?
Thanks for catching that. From what I can tell, wands and ranged weapons use the same or a very similar slot modifier. All the wands I've calculated come out two item levels lower than their expected value, while the ranged weapons come out correctly. Either wands have a different slot modifier or they're all a bit under budget. I'll play around with different modifiers and see if I can find a closer one.

The original post should be updated in a bit to include calculations for epic ranged weapon and wand DPS equations. Vendor value is an interesting topic that I hadn't thought about. There will be exceptions, but there may be a relation between item level and vendor value. It could be stats, it could be assumed amount of armor, or it could be durability. I'll keep that in mind when I tackle armor values.

02/02/09, 5:52 PM   #8
Mman
Piston Honda

Draenei Shaman

Shattered Hand
 Originally Posted by Seratha Vendor value is an interesting topic that I hadn't thought about. There will be exceptions, but there may be a relation between item level and vendor value. It could be stats, it could be assumed amount of armor, or it could be durability. I'll keep that in mind when I tackle armor values.

It is clear that armor value has some sort of relationship to sale price (at least for slots that have armor). You can use wowhead and simply sort by armor and sale price for that confirmation. But, clearly, armor is not the sole factor. There is some sort of other contributing force causing the values to differ among similar ilevel/armor/durability items. There are numerous exceptions to this, most notably with gems contributing some sort of additional weight to the value.

I also tried to find two items that had as close as possible sale values. I could not find any armor that sold for the exact same amount that wasn't something special like a ring or neck(this was not an exhaustive search by any means). This is as close as I could get though.

Item Comparison Tool - World of Warcraft

The feet with a smaller ilevel and armor amount only sells for 4c less?! The only explanation I can come up for this is that somehow spell power is valued more than armor penetration.

02/02/09, 7:08 PM   #9
Dorrinal
Von Kaiser

Draenei Mage

Terenas
 Originally Posted by Seratha *When it comes to trinkets, I’m not sure of the exact slot modifier. Hyzenthlei’s post listed them as a having a slot modifier of 17/25, but WoWWiki doesn’t even list a slot modifier. I haven’t done any testing to figure out the correct modifier as most trinkets have procs that are difficult to quantify in their budget.
There are a couple of trinkets available that are easy to calculate. Please check my math on solving for SlotModifier:

Formula:
ItemSlotValue = ItemValue / SlotModifier

The ItemLevel for both items is 59. This gives:
ItemLevel = 1.8 * ItemSlotValue + 0.75 (Rare quality)
59 = 1.8 * ItemSlotValue + 0.75
32.361 = ItemSlotValue

[Strength of the High Chief]
50 Attack Power
ItemValue is easy to calculate because there is only one stat, so the exponents are cancelled out.
ItemValue = (Stat * StatMod) = (50 * 1/2) = 25

32.361 = 25 / SlotModifier
SlotModifier = 25/32.361

[Power of the High Chief]
29 Spell Power
ItemValue = (29 * 6/7) = 24.857
SlotModifier = 24.857 / 32.361

Conclusion: SlotModifier for trinkets is 25/32.

Feel free to crunch numbers on similar trinkets to corroborate.

02/03/09, 12:00 PM   #10
Don Flamenco

Human Warrior

Bronzebeard
BLOCK RATING in the Item budget

Originally Posted by Seratha
Most stats have a stat mod of 1, including Strength, Agility, Intellect, Spirit, Resistances, and all rating stats. Stamina is the only “white” stat that has a stat mod of 2/3. The table below lists the various stats and their corresponding modifiers.

 Stat Modifier Strength 1 Stamina 2/3 Block Value 13/20
Ok, for a while now I've tried to wrap my head around why tanking items with block rating seem to be way under their budget, based on my understanding of the stat weights at the time. The description of stat weights given above would seem to imply that block rating would have a StatMod of 1, but attempting to use that StatMod in the itemlevel formula results in items that appear woefully underbudget. For example, [Wall of Terror], assuming otherwise undefined statmods to be 1:

((63^(log2/log1.5))+(42^(log2/log1.5))+(42^(log2/log1.5))+(24^(log2/log1.5))+(31^(log2/log1.5)))^(1/(log2/log1.5)) = 107.414115 ItemValue

(107.414115 ItemValue) / (0.5625 SlotMod) = 190.9584267 ItemSlotValue

(105.92 * ln(190.9584267)) - 342.12 = ITEMLEVEL of 214.177 instead of it's actual ilvl226.

Is it underbudget? Probably not.

Assuming the block rating StatMod to be variable, and replacing the 31 block rating in the top formula above with 31X, and solving for X, using the actual ilvl226 of this shield, we come out with block rating having a StatMod of 1.811.

For shits and giggles, I threw a couple more items at this formula while I had it up in excel, and plugging in stats and itemlevel values for [Shadow of the Ghoul] and [Inexorable Sabatons] (assuming the gem slot is budgeted for 16points of it's primary stat, STR) while solving for block rating's StatMod, I came up with block rating statmods of 1.738 and 1.661, respectively. For what it's worth, if you define your block rating statmod as 1, the cloak is ilvl 201.4, and the boots are ilvl 205.5, when both should be ilvl213.

So, averaging these items at least, it seems fairly clear that [b]Block Rating currently has a StatMod of around 1.75/[b]. I'll continue checking items to try and find a counter example. This can at least least hopefully ease the minds of those tanks like me who wondered why their block sets sacrificed so much: Your items aren't under budget, it's just that block rating consumes a LOT of itemization points.

EDIT: Caution when applying the itemization formula, I came out with pretty different results when I replaced 1.7095 with (log2/log1.5). While 1.7095 is a close approximation, when small differences are applied exponentially it can have a pretty significant outcome. It caused the apparent stat mod of Block Rating to drop to 1.75 from 2. Post has been updated with what ought to be the more accurate numbers.

Last edited by vorpalblade : 02/03/09 at 1:43 PM.

 Originally Posted by XI- You see, the petty rules and regulations for the general forums don't apply here. If you're a fuckwad you will systematically be mocked and embarassed to the fullest extent of our abilities. In short, take your 12 bucks, shove it up your fucking ass, and don't come back until your IQ reaches double digits.

 02/03/09, 1:17 PM #11 Gorb Von Kaiser     Gorbachev Tauren Shaman   Bonechewer Do you know what the stat mod for resilience is? EDIT - That was a dumb question. Resil, crit, etc all are 1. It wasn't immediately apparent when I read the first post. Last edited by Gorb : 02/05/09 at 10:47 PM.
02/03/09, 1:57 PM   #12
Don Flamenco

Human Warrior

Bronzebeard
 Originally Posted by Gorb Do you know what the stat mod for resilience is?
Resilience rating statmod is 1.

Edit:

To elaborate, take [Deadly Gladiator's Plate Chestpiece] for instance. Assume the two sockets are budgeted according to the highest white stat, in this case Stamina:

((85^(log2/log1.5)) + (121.33^(log2/log1.5)) + (51^(log2/log1.5)) + (66^(log2/log1.5))) ^ (1/(log2/log1.5)) = 188.5503104 ItemValue

Chest Slot Modifer is 1, so the item level is: (105.92 * ln(188.5503104)) - 342.12 = ilvl 212.8, or pretty much exactly budgeted for ilvl213, as we would expect. The only caveat is that the itemvalue determination for Sockets are still kind of up in the air. My assumption in these calculations is that you ought to take 16 (the value of a blue quality gem for anything except stamina) of the highest stat on the piece of armor for each socket.

However, it's been proposed that you should take a blue-quality gem's worth of an "expected" stat of the particular color socket you're creating, so in the case of this chest, a red and a yellow socket. If you assume that the sockets are budgeted for 16str and 16crit, the itemlevel comes out to 213.995. If you assume 16str and 16res, the itemlevel comes out to 214.667. The only real deviation is if you use the highest white stat (Stam), and add 24 for each socket as opposed to 16. In that scenario, the itemlevel works out to be ilvl222, and solving to determine what stat mod value of resilience rating would make the piece ilvl213 yields a StatMod of around .17, which is pretty much unfeasibly low.

So it seems safe to say that the sockets are either budgeted according to color, or to a flat 16 points of the highest stat (even if it's stamina). It's pretty close either way, so in either situation it is still safe to say that resilience rating's statmod is 1. Of course, the EASY way to see that resilience rating has a stat mod of 1 is to look at how much they're willing to put on a blue quality gem. You get 16res on a gem just like you'd get 16agi or 16str, so it stands to reason that they're given the same weight in the item budget.

Last edited by vorpalblade : 02/03/09 at 2:49 PM.

 Originally Posted by XI- You see, the petty rules and regulations for the general forums don't apply here. If you're a fuckwad you will systematically be mocked and embarassed to the fullest extent of our abilities. In short, take your 12 bucks, shove it up your fucking ass, and don't come back until your IQ reaches double digits.

02/04/09, 3:42 AM   #13
Seratha
Von Kaiser

Blood Elf Priest

Kirin Tor
 Originally Posted by vorpalblade Is it underbudget? Probably not.
Actually, I think it is under budget. There are a couple of examples of items that look to be a tier lower than their expected values. I remember reporting a chest piece back in beta when it completely threw off my average. I imagine that Blizzard itemized too many drops for Naxx-10 and when they realized that they had too many items, they moved some of them up to Naxx-25, but just changed the item level and didn't fix the stats.

[Gauntlets of the Disobedient] come out to an expected item level of 212.63 matching its given 213 level. [Fleshless Girdle] comes out to an expected item level of 201.7, lower than its given 213 level, but [Burdened Shoulderplates] come out to 212.96 when they're supposed to be 213. I tried changing the stat mod on either Block Rating or Block Value and it threw off the calculations of too many items that I don't think the problem lies there.

 Originally Posted by Dorrinal:1084678 Conclusion: SlotModifier for trinkets is 25/32.
Which fits for that trinket, and [Mindtap Talisman], but it appears that lower level trinkets use the slot mod listed. [Rune of the Guard Captain] and [Rune of Duty] come out under budget with a 25/32 slot mod, but fit closer with a 17/25 slot mod. The Dire Maul trinkets don't help any, either. Some of them seem woefully under budget while others fit just fine with the 17/25 slot mod.

 02/04/09, 8:30 AM #14 Bregonn Von Kaiser   Bregonn Dwarf Warrior   Anachronos (EU) The design philosophy for trinkets has changed considerably with TBC (2.0). In Classic trinkets either had very long cooldown or just plain stats (with the former being mostly ignored by players). In 2.0 that was changed to a fixed stat and either a proc or an use-effect with a short cooldown. They may very well have changed the slot value at that point. Note that [Strength of the High Chief] and [Power of the High Chief] were implemented in 2.3 and thus use the new slot value. The Dire Maul trinkets are most likely affected by various itemization changes since they were implemented. I remember looking at them back when they were hot and concluding that they were correctly budgetted (although not all of equal desirability).
 02/04/09, 11:31 AM #15 Dorrinal Von Kaiser   Taeus Draenei Mage   Terenas Good catch Seratha and Bregonn. Since I started with TBC I had no idea those trinkets were added later so just assumed they would be a good example. I'm sure if we applied the "new" 25/32 slot value to BC and later trinkets we can get an estimate of how much Blizzard values all these weird procs and on-use effects.

 Elitist Jerks Item Level Mechanics