Seratha

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the item level formula since Hyzenthlei’s original post on the subject and the WoWWiki page on item level is similarly out of date with no discussion occurring there, so I thought it’d be a good idea to collect the current mechanics into one place.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:



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.



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:

Rare:

Epic:

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:

Rare:

Epic:

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:



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:


Two Handed Weapon:


Ranged Weapons until item level 219:


Wand:


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 [], 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:


Epic Spell Power:


The only exception to this that I’ve found is the [] 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.

 

• Falk

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.

 

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?

http://sig.gamerdna.com/quizzes/INFL...erks/Garak.png

 

◊ songster

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.

 

• Falk

[] says nope.

There'd be way too many exceptions and different scales.

 

• Chicken

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.

buff /bʌf/ Pronunciation[buhf]
–verb (used with object)
- to reduce or deaden the force of

 

Seratha

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.

 

Mman

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.

 

Dorrinal

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

[]
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

[]
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.

 

◊ vorpalblade

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, [], 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 [] and [] (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.

 

Gorb

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.

 

◊ vorpalblade

Resilience rating statmod is 1.

Edit:

To elaborate, take [] 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.

 

Seratha

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.

[] come out to an expected item level of 212.63 matching its given 213 level. [] comes out to an expected item level of 201.7, lower than its given 213 level, but [] 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.

Which fits for that trinket, and [], but it appears that lower level trinkets use the slot mod listed. [] and [] 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.

 

Bregonn

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 [] and [] 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).

 

Dorrinal

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.

 

Mman

I went through a handful of the WotLK "on use" trinkets. All of them have the use and a static stat, so it was pretty easy to use the iLevel formula to determine what weight is being given to that use value. It seems like value of most of them is around 27% of what the on use value is. This is true for uncommon and epic items. There are a few that are closer to 26% and one that is at 28% ([]).

Most of these on use trinkets have a buff that lasts for 20 seconds with a 2 minute cooldown. There are a few exceptions. [] has a shorter buff but the same cooldown. It would make sense for it's equivalent weight to be higher than others to make up for the shorter buff. It is at around 30%, but this is only a 15% gain and the buff time is a 25% loss. There is also an item ([]) that has a shorter cooldown. This, however, does not have any effect on the equivalency weight as you can see when you compare it to []. I can only assume this is some sort of error or typo, but who knows.

 

Erdluf

[] uses spellpower as both the static stat and the on-use stat. The 30% value works for the on-use value, but you have to treat the two spellpowers as different stats, not as a single stat:

((56 * 6/7)^1.7+ (145 * 30% * 6/7)^1.7)^(1/1.7) works, but a (56 + 145*30%) formula fails.

 

Mman

Hmm, I didn't even think about the fact that the on-use and static values might be figured together if they were the same stat. But, not only does the 30% value not work, you get a much lower portion (~12% for []).

Interesting though that other trinkets that have the same use/static stat have a 30% value. Sort of leads me to believe that it is getting a boost for being the same stat instead of the shorter buff period. I'll look for some more examples.

 

◊ Wraithlin

Do everyone a favour: submit this to the TTT.

Thesis: Submitted

 

Mman

So I went back to some earlier BC items to see if those Use trinkets would have a hidden weight similar to the earlier 27%. I tested the earliest rare trinkets we get in BC, [] and []. The hidden weight was closer to 22% of the use value. So it seems like similar mechanic trinkets with similiar iLevels work in a similar manner. It is possible that these values are different do the fact that they only have a 1 minute cooldown.

Doing these tests gave me an interesting idea though. The third trinket rewarded from that quest is [Regal Protectorate]. Using the hidden weight from the other two items, what would the stat modifier need to be to get the formula to work? Turns out a value of 1/9 works perfectly. Tested some other items such as [Repelling Charge] and all the battlemaster trinkets. They all work perfectly at a 1/9 stat mod and a 27% hidden weight. It seems as though raw health then has a stat mod of 1/9.


edit: Decided to apply this same thing to trinkets that have armor to find out what sort of stat mod isgiven to bonus armor. For both [Defender's Code] and [Badge of Tenacity]. Assuming a 27% weight on the procs the stat mod works out to 1/14.

 

MatsT

Regarding sockets: I haven't done the math but just looking at items over the years i've reached some conclusions. If i get your version right, you say would remove 16 strength from a (typical warrior) level 80 item to add a socket (where you could put 16 strength). This is definitely not how it works. My theory is that it rather costs as much as putting 16 intellect on the item, a stat which didn't previously exist on the item. This means that the item would have significantly less than 16 strength more without the socket because of the diminishing nature of the item budget formula. The way this let's you stack the powerful stats without the diminishing returns is exactly what makes items with sockets so powerful (almost always preferable to socketless items of same ilvl).

If you look at number of sockets as a stat you could say it has a modifier of 16 (at lvl 80) but i'm not sure if you should look at each socket as a separate 16 of one stat or as a combined.

 

• Falk

As mentioned above, throughout TBC it's been pretty clear that the more sockets there are on an item, the better it's itemized. This definitely runs counter to removing x amount from the highest stat because of the ^1.7095 formula (which would make an item equal or worse for each gem slot by penalizing the stat you most likely want to stack in the first place)

Now that we're certain that itemization is on a logarithmatic scale (and have a much more exacting formula), it'd probably be easier to calculate accurate gem slot values, since this wasn't really feasible during 2.4/Sunwell itemization - the big assumption then was still that it was linear, and that the deviation from expected values past ilvl141 were just a poor understanding of gem socket budgeting

 

Ukerric

Do not forget that they revamped the gem slot costs during early BC. As stated in an old post (around 2.1?), originally, sockets would have a cost depending on the quality of the item. Presumably, it assumed that green quality items had green quality gems slotted, blue quality items had blue and epic had epic gems in them.

They changed that and aligned all items to the base. In other words, when you try to figure the cost of a gem slot on an item, do not assume that the gem is a blue +16 stat. Assume it is based on a green +12 stat.

 

Seratha

This was pretty easy to test. I took [Breastplate of Frozen Pain]. It has a red and a blue socket and a suggested item level of 213. Ignoring the sockets, it calculated out with an item level of 201. Adding in 16 Agility and 16 Spirit, both red and blue gems, only bumps it up to an item level of 203. However, adding 16 Strength and 24 Stamina to it gives an item level of 213.9, which is in line. I could show more, but from previous tests the method I listed seems to hold true enough.

If I remember right, sockets used to consume a percentage of the item's entire budget prior to 2.1. In 2.1, they changed it to cost a fixed value and, since the most common gem at the time were the rare gems, it was assumed that they used the cost of a rare gem as the fixed value. I wasn't doing any item level math back then, so I didn't pay much attention to it and I don't have any of the stats for items prior to 2.1, so I can't test it.

This lends credence to a 27% weight on trinket procs as WoWWiki has the armor stat mod as being 1/14. I'll update the table with that. I'll also be working on redoing the linear epic formula. The one I have listed from WoWWiki doesn't seem to fit much of anything, which makes me think it was derived as a way to get between the logarithmic 100+ epics and the vanilla epics.

 

◊ songster

Your calculations on sockets seem really odd. By the given logic, unsocketed items ought to be at least equal to, and sometimes better than socketed items, since the maximal possible benefit you get from filling the sockets is only enough to push the socketed item back up to its intended ilvl.

This seems to be at odds with itemisation in TBC and thus far in WoTLK, where socketed items tend to be significantly better than unsocketed items.