What is scaling?

It's quite obvious that DPS depends on the gear one has.

However for different specs this dependency is different. To measure this, we introduce a special value: scaling. Scaling with a certain stat depicts how much dps will a certain spec gain by gaining 1 unit of this stat.

So, basically, scaling of the spec at given gear level is described by a set of numbers, that tell us how useful this or that stat is for DPS. These numbers are called scalars or scaling coefficients. One can use some other words for naming these numbers, but you'll understand what people are talking about if you get the general idea.

Example: finding out scaling coefficients

Here at shadowpriest.com, we're pretty used to trusting SimulationCraft by Dedmonwakeen - an excellent software that models raid dps. The SimCraft project has a wiki page that provides simulation report for its very latest version: http://code.google.com/p/simulationcraf ... testReport. The report includes DPS ranking of various specs, mana problems information and scaling values.

The latter makes the LatestReport page an excellent resource for quickly finding out scaling coefficients that are relevant to the latest changes in WoW (SimCraft team is working hard to keep our software sync to even the most recent changes in the game, check RecentUpdates page to be sure).

Let's, for example, get scaling values for, say, level 70 shadowpriest in patch 3.0.3:
1) Use the link on mentioned page to navigate to http://code.google.com/p/simulationcraf ... tReport_70.
2) Scroll the page to hit the bottom, and use "a general cross-spec analysis" link to navigate to: http://code.google.com/p/simulationcraf ... 70_General (by the way while you scroll you might notice precision estimates for scaling values we're about to see!)
3) Scroll all the way down to the bottom of the page.
4) You'll see a big table with specs in its rows, various stats in its columns and numbers in the cells. Each number represents scaling of some player with some stat given certain gear equipped and certain raid composition (you can find out gear and raid description in the "Test Environment" section of the report).

At this very moment I'm seeing the following scaling values for a patch 3.0.3 shadowpriest that doesn't use SWD in rotations (by the time you're reading this, data might change, since LatestReport is constantly updated to be sync with the latest version of SimCraft):

spec................................sphi..spp....spc...spha..spi....int
priest_shadow_noswd_3_0_3....2.04..1.29..0.99..0.91..0.30..0.33

This means that in the raid described in "Test Environment" section with players that have rotations described in that section and have the described gear equipped, increasing spellcrit by 1 unit will increase dps of that shadowpriest by 0.99. Same for other stats, and other specs.

Are scaling coefficients useful for a plain shadowpriest that doesn't care about theorycraft?

Scaling analysis is very important for game balance and it was actively used to push buffs for shadowpriests' dps across the WotLK beta. But what's interesting is that scaling coefficients can also be used for determining what piece of gear is better for dps. And here's how:

Let's pick Ring of Ancient Knowledge and calculate how useful it is for shadowpriest mentioned above (patch 3.0.3, no SWD). Following the instruction described above, we can find out values of RoAK's stats for that shadowpriest, and then calculate value of RoAK by applying basic maths:

Ring of Ancient Knowledge
Binds when picked up
Finger
+30 Stamina --> 0 dps
+20 Intellect --> 20 units * 0.33 scaling = 6.6 dps
Requires Level 70
Equip: Improves haste rating by 31. --> 31 unit * 0.91 scaling = 28.21 dps
Equip: Increases spell power by 39. --> 39 units * 1.29 scaling = 50.31 dps
---
Total = 0 dps from stamina + 6.6 dps from intellect + 28.21 dps from haste + 50.31 dps from spellpower = 85.12 dps

By comparing dps gains for items you can actually find out what piece of gear suits your toon better. You just need scaling values (e.g. from SimCraft), and some basic maths!

Of course these calculations are quite tedious and what's more - not all gear stats are as simple as spellpower or intellect, e.g. using those numbers are you able to tell how good is T6 4pc for your dps, huh?

To simplify item comparison we use Best Raiding Gear Available thread that takes SimCraft's scaling values for stats and unique item bonuses, plugs them into a huge gear spreadsheet and then assigns certain ratings for available gear. However, when the BRGA thread is outdated because Mef has some other stuff to do, you can evaluate most of the items by your own. Just as we evaluated the RoAK.

Pretty simple, isn't it?

This post features more or less detailed theorycraft that explains how scaling works, what are common scaling problems and why they appear.

Why is scaling so important for balancing the game?

It's not a rare situation in WoW that Spec A and Spec B are doing similar dps in a certain tier of content, but as new content patches arrive, Spec A starts doing more and more dps and the further - the bigger becomes the difference.

Why this happens? Because of rather obvious fact - DPS depends on the gear one has, but for different specs this dependency is different. To measure this, we can introduce a special value: scaling. Scaling with a certain stat depicts how many dps will a certain spec gain by gaining 1 unit of this stat. Using this term we can concisely describe a situation from a previous paragraph: Spec A scales better than Spec B.

If some specs are supposed to deal roughly the same dps, then we must make sure that they not only start with comparable values of dps, but also have pretty close scaling values. This will ensure game balance throughout the entire expansion.

By design different specs scale differently. For example, a 1-nuke spec inherently scales well with criticals and haste, however a dot spec has troubles with leveraging those to the fullest. This means that each spec needs personal treatment in order to be balanced across multiple tiers of content.

An important note: DoTs analyzed here do NOT benefit from crit or haste directly. In fact, a very dull picture of scaling troubles with DoT specs made Blizzard to introduce such talents as Pandemic (Each time you deal damage with Corruption or Unstable Affliction, you have a chance equal to your spell critical strike chance to deal 100% additional damage), and additional effect for Shadowform (Your Shadow Word: Pain, Devouring Plague, and Vampiric Touch abilities deal increased percentage damage equal to your spell critical strike chance).

Theorycraft summary

* Scaling values are interdependent, so poor scaling with certain stat decays scaling with other stats, and vice versa - awesome scaling with certain stat improved scaling with other stats.

* Current itemization system highly favors specs that can scale well with multitude of stats, that's why it's important for a competitive raiding spec not to have scaling pitfalls.

* Scaling of a DoT/CD spec with spellhaste and spellcrit becomes increasingly worse as better gear is acquired.

* By themselves neither DoTs, nor nukes on CDs get benefits from spellhaste. They rather allow to fit more filler spells as caster gets more haste. This adversely affects scaling with spellhaste, since filler nukes have lower DPC values.

Table of Contents

1. Examples on scaling.
1.1. Example: why specs should scale with all stats in a balanced fashion.
1.2. Example: how scaling issues can be completely hidden in a certain tier of content.

2. Why different specs have different scaling patterns?
2.1. Scaling pattern: 1-nuke.
2.2. Scaling pattern: damage over time + nuke filler.
2.3. Scaling pattern: nuke on cooldown + nuke filler.
2.4. A bigger picture of scaling.

----------------------

1.1. Example: why specs should scale with all stats in a balanced fashion.

Every single item in the game has so-called item budget that governs its potential for being powerful. After item budget is determined game designers assign exact values for certain stats on the gear according to the special formula. What we need to know in regards to scaling is that this formula dislikes items with 3-4 stats and highly favors a multitude of stats being distributed on an item.

For example, lets design two epic chest pieces without sockets that have an equal item level. First of those, Shroud of Instant Annihilation will have its budget spread around 6 stats, while its counterpart, Chestpiece of Awesome Destruction will have only four. Below are the stats that fit such scheme and have the same budget:

Stat_____________________________sta__int__spi__crit__hit__spellpower
Shroud of Instant Annihilation________25__28__28__34___18___60
Chestpiece of Awesome Destruction___42__40__0___0____18___77

As we see, Chestpiece of Awesome Destruction has comparably higher values of a small amount of stats it has, however, Shroud of Instant Annihilation, while having less spellpower, features two additional stats with quite considerable values.

Now imagine two specs. Spec A that has a DoT and a filler spell, so it strongly scales with spelldamage, but has a pitfall at crit rating: 1 sppower -> 0.9 dps, 1 spcrit -> 0.2 dps. Spec B, to the contrast, represents 1-nuke spammer and its scaling is much more balanced: 1 sppower-> 0.8 dps, 1 spcrit -> 0.8 dps. Also lets assume that casters of those specs are already hit-capped, so they dont benefit from additional spellhit on these robes.

This is how different scaling models affect benefit that different specs get from gear:

Spec_____________________________Spec A__Spec B
Shroud of Instant Annihilation________60.8____75.2
Chestpiece of Awesome Destruction___69.3____61.6

So we see that Spec A, in contrast from Spec B does not prefer generic caster gear with a multitude of stats distributed around. Instead of this, Spec A favors gear with vast amounts of spellpower. This brings us to important conclusion: gear homogenization highly favors specs that can scale well with multitude of stats, that's why it's important for a competitive raiding spec not to have scaling pitfalls.

1.2. Example: how scaling issues can be completely hidden in a certain tier of content.

Lets end this section with an important example of how a specific gear set can make or break an entire spec. Let's introduce a Spec C, so called, Dusk Disciples that have totally broken scaling: 1 sppower -> 0.6 dps, 1 spcrit -> 0.1 dps. But specially for them we'll design a chestpiece with very-very suitable distribution of stats: Icy Duskweave Robe, that will have 12 sta, 5 int, but 134 shadow spellpower and 2 sockets (2 sockets mean 2x +12 pure spellpower gems, which brings total spellpower to 158).

After comparing three designed robes, we witness the following (by the way, specs A and B deal nature damage, so Icy Duskweave Robe is useless for them):

Spec_____________________________Spec A__Spec B__Spec C
Shroud of Instant Annihilation________60.8____75.2____39.4
Chestpiece of Awesome Destruction___69.3____61.6____46.2
Icy Duskweave Robe________________0_______0_______94.8

It appears, that a spec with clearly sub-par scaling receives insane dps gains from an specially designed piece of gear. In fact, even if Icy Duskweave Robe had item level lowered by 26 (this is the difference of itemlevels between Karazhan and Black Temple!!) Spec C would still gain 77.4 dps from its chestpiece remaining the very best.

This is a clear imbalance, and one of the ways to fix it is to reduce Spec C's performance, which will in its turn weaken already sub-par scaling. After a series of nerfs, at that moment of time Spec C might gain comparable dps benefit from a chestpiece and things seems to be balanced. However, if we look into future content patches, when itemization will follow the pattern of Shroud of Instant Annihilation, and other specs will also gain access to items with sockets. Poor-poor Spec C...

This means a very important fact. Scaling of the spec cannot be judged by DPS it does at one particular level of content, since there might exist factors that completely tone down scaling shortcomings.

2. Why different specs have different scaling patterns?

In order to know how to balance specs' scaling, lets study foundations of specs' casting styles and their differences.

In World of Warcraft there exist some guidelines that rule behaviour of most spells in the game, namely:

* Direct damage spells' dps usually benefits from a certain fraction of spellpower normalized against casting time, namely: [base casting time]/3.5. This means that if a mage spams series of untalented 3.5s fireballs and a warlock spams series of untalented 3s shadowbolts, spellpower is going to benefit their dps exactly in the same fashion.

* Damage over time spells are also usually normalized, but against their duration. Bonus damage they get from spellpower is [duration]/15 fraction of spellpower. Analogue to the previous example is a comparison of v2.0 Shadow Word: Pain that lasts 24s with talents and Vampiric Touch that lasts 15s. If these dots have equal uptime, spellpower equally benefits their dps.

* The latter means that a DoT total damage is affected by spellpower in much bigger fashion than a DD spell total damage. Let's compare Fireball (a 3.5s cast) and Vampiric Touch (a 1.5s cast, 15s duration dot). Damage per cast of both of these spells benefits from 100% of caster's spellpower, however, Vampiric Touch can be cast 2.3x times faster. So if we imagine a game without haste and a spec with 10 different dots, all of those have 1.5s cast time, then for every 1 spellpower this spec will deal additional 10 damage over the course of 15 seconds, while over the course of these 15 seconds an untalented fireball spammer will cast 4.3 fireballs that will yield 4.3 additional damage, which is exactly 2.3x times less.

* Most likely to compensate this factor DoTs usually do not crit, while DD spells usually do. Base critical damage is 150%, but all caster dps specs (except Discipline/Holy) get increases to it via talents. Usual value of critical damage for spells is 200%. Now returning to the comparison of untalented Fireball and Shadowbolt. If we mix in crit talents, Fireball will scale better with spellcrit, and will come as a winner in a spamming dps race.

2.1. Scaling pattern: 1-nuke.

Previous section brings us to a guideline of scaling for a generic caster spec that spams some direct-damage spell (exact numbers can be increased by peculiarities of the spec, e.g. "Empowered Fireball"-type talents, or "old Elemental Oath"-type talents, but bottom boundary is literally set in stone). Following numbers are for 0% crit chance and 0% haste chance (I could provide universal formulae for arbitrary values of crit and haste but its unnecessary here):
+1 spellpower -> Increases dps by 0.28
+1% crit -> Increases dps by 1%
+1% haste -> Increases dps by 1%

2.2. Scaling pattern: damage over time + nuke filler.

A spec that has some DoTs in its arsenal will have drastically different scaling pattern: it will get less benefit from crit and haste, because dots cannot crit and 1% more haste doesn't allow us to cast 1% more dots. Almost the same goes for spells on cooldowns (like Mind Blast or Shadow Word: Death) - they can crit, but similarly to dots they can't fully leverage benefits of haste.

But enough generic words, let's see an example. Imagine a spec that has an instacast DoT that deals X damage over 15 seconds and a direct-damage spell that deals Y damage per 1.5s cast. Both of those spells scale normally and a direct-damage spell crits at 200%.

Here is where the things become complicated.

Damage of such spec at 0% crit and haste:
* 1.5s of every 15s spent casting a DoT that deals X damage
* 13.5s of every 15s spent casting 9 nukes that deals Y damage each time
---
X + 9*Y damage over 15 seconds ~= 0.07*X + 0.60*Y

So what's with scaling? Following numbers are for 0% crit chance and 0% haste chance (I could provide universal formulae for arbitrary values of crit and haste but its unnecessary here):

+1 spellpower -> DoT will be dealing 1 more damage, and a nuke will be dealing 1/3.5 ~= 0.43 more damage, which will add roughly 0.07+0.26 = 0.33 dps.

This confirms our theoretical conclusion - DoT specs indeed scale better with spellpower, and the difference will be increasingly big as spec gets more DoTs or DoT duration increases

+1% crit -> DoT damage is unchanged, but a nuke will be dealing 1% more damage. This changes damage breakdown in the following way:
* 1.5s of every 15s spent casting a DoT that deals X damage
* 13.5s of every 15s spent casting a nuke that now deals 9.09*Y damage in average
---
X + 9*Y damage over 15 seconds ~= 0.070*X + 0.606*Y
This is 1/(0.12*X/Y+1) times less than +1%, and depending on X/Y ratio it can be close or far away from 1%.

+1% haste -> DoT damage is unchanged, but now we can fit more nuked between DoT refreshed. This changes damage breakdown in the following way:
* 1.485s of every 15s spent casting a DoT that deals X damage
* 13.515s of every 15s spent casting a nuke that deals 9*Y damage each time
---
X + 9.010*Y damage over 15 seconds ~= 0.07*X + 0.606*Y
Same deal here. This is 1/(0.12*X/Y+1) times less than +1%, and depending on X/Y ratio it can be close or far away from 1%.

We've just revealed an important pattern. Scaling of a dot spec with spellhaste and spellcrit inversely depends on X/Y ratio, where X is dot damage and Y is nuke damage. Since DoTs scale much better with spellpower, as the gear improves X/Y will increase, which will only worsen scaling with haste and crit.

2.3. Scaling pattern: nuke on cooldown + nuke filler.

Imagine a spec with Spell A (1.5s cast, 6s cooldown) that deals 2X damage and a Spell B (3s cast, no cooldown) that deals 3X damage. Both of those spells scale normally and crit at 200%. Obviously, both spellpower and crit% affect such spec's dps in the same fashion as they do affect a plain nuke spec. However, lets analyze what's up with haste:

With zero haste our rotation is as follows: A > 2x B. Now if we hasten all spellcasting by a factor of 1.5x, it will bring B to 2s cast, 0s cd and A to 1s cast, 6s cooldown. This is not exactly what we want to scale perfectly with spellhaste (as a plain nuke spec does). Let's sompare:

Original cycle: A > B > B > .. => 8X damage over 7.5s = 1.07X dps
Hasted cycle: A > B > B > B ... => 11X damage over 7s = 1.57X dps
Ideal hasted cycle: A > B > B > ... => 8X damage over 5s = 1.6X dps (2% more damage)

What would fix hasted cycle for 1.5x haste factor (100% haste) is one of the following:
1) +2% to all damage
2) +10% to Spell A damage
3) +3% to Spell B damage

All of those fixes won't work in general case since different haste factors will yield different ratios between hasted cycle and ideal hasted cycle and different shares of particular spells DPS in total DPS. As an example lets analyze 2x haste factor (200% haste) without 1s GCD cap:

Original cycle: A > B > B > .. => 8X damage over 7.5s = 1.07X dps
Hasted cycle: A > B > B > B > B ... => 13X damage over 6.75s = 1.92X dps
Ideal hasted cycle: A > B > B > ... => 8X damage over 3.75s = 2.13X dps (11% more damage)

Now we reveal a similar pattern that is also applicable to DoT spells.

By themselves neither DoTs, nor nukes on CDs get benefits from spellhaste. They rather allow to fit more filler spells as caster gets more haste. As DoTs and nukes on cooldowns have higher [damage per cast] value than filler spells (or else, it would be unreasonable to cast them), replacing a moment of casting DoT with a moment of casting filler nuke will lead to lower total dps. This adversely affects scaling with spellhaste.

2.4. A bigger picture of scaling.

Till now we've made all calculations with the assumption of 0% base haste and 0% base crit. Even such simplified analysis allowed us to find out important patterns in spec scaling. However, in real life usually gear upgrades augment several stats simultaneously, so let's see do different scaling values synergize with each other and in what fashion.

Given we have 3 stats: P (spell power, changes from 0 to inf), C (chance to crit, changes from 0 to 1), H (haste, changes from 0 to inf).

DPS a spec can be described as a sum of 4 components:
* (Base damage) A constant
* (Spellpower component) A function of spell power
* (Crit component) A function of DPS from spell power,
* (Haste component) A function from sum of DPS from spell power and crit.

In case of 1-nuke spec (section 2.1), all components are linear functions as follows:

DPS(P, C, H) = b + p*P + c*C*(b + p*P) + H*(b + p*P + c*C*(b + p*P)), where b, p, c are spec-specific coefficients, namely: b = base dps of a nuke, p = nuke spellpower coefficient per second (0.28 for most untalented nukes), c = crit:normal damage ratio

DPS(P, C, H) =
b
+ P * p + C * (b*c) + H * b
+ P * C * (p*c) + P * H * p + C * H * (b*c)
+ C * P * H * (p*c)

Scaling_Power(P, C, H) = DPS(P+1, C, H) - DPS(P, C, H) = p + C * (p*c) + H * p + C * H * (p*c)
Scaling_Crit(P, C, H) = DPS(P, C+1, H) - DPS(P, C, H) = (b*c) + P * (p*c) + H * (b*c) + P * H * (p*c)
Scaling_Haste(P, C, H) = DPS(P, C, H+1) - DPS(P, C, H) = b + P * p + C * (b*c) + P * C * (p*c)

Back then we only analyzed the following values: Scaling_Power(0, 0, 0), Scaling_Crit(0, 0, 0), Scaling_Haste(0, 0, 0). However, for the general case we can see that scalings depend on each other, i.e. a coefficient (b*c), which is actually Scaling_Crit(0, 0, 0) participates in Scaling_Haste(P, C, H).

This means that scaling values are interdependent, so poor scaling with certain stat decays scaling with other stats, and vice versa - awesome scaling with certain stat improved scaling with other stats.

This is also true for dot and CD specs - for example their base scaling with haste is sub-par to 1-nuke specs, and this also affects scaling with lcrit and spellpower. However, exact calculations would not fit even this filled with theorycraft post.

*clap*

Please Link this to a feedback thread in the PTR. Love the *ahem* "Icy Duskweave", lol.

Best thread I have ever read on shadowpriest.com and one fo the most useful I've ever read about wow PERIOD!

Exceptional...

Nice seeing some numbers to what i have known for a long time.

Pre-bc as a spriest i was always able to top dmg meters in MC and then in BWL but always slowly getting lower and lower as others geared up more and i struggled to get enough of the stats that suited me (ie +dmg).

TBC comes along and spriests are way more popular, we finally get some gear that suits our spec and we skip 2 tiers of upgrades while we top meters. Until the inevitable happens as we all knew it would.

I have not played in about 6 months as i was sick of not having a chance at beating any half decent geared guildie on the dmg meter against brutallus etc. I love my shadowpriest, I would have quit pre-bc if i didnt find this class which suits me so much. Although it was cool being one of two spriests on the server who actually raided (as shadow, not shadow spec healing).

I have just been reading about all these scaling changes, picked up my interest a little, might have to renew my account

Nice post.

Though I wonder how this can be explained...
http://www.shadowpriest.com/viewtopic.php?f=14&t=16847
All theoritical reports show haste being better (or similar) to crit in terms of scaling at both 70 or 80 and in both 302 or 303 patch (bigger diff in 302), yet peeps in there mention of a significant increase in dps with using more crit stuff and dropping haste.

Granted that theoritical numbers are just theoritical, and practical/real world always takes precendence, but generally they should be relatively similar. If in theory A > B, in practical sense A > B...by how much, thats a diff story. But in the case above theory says A > B while practical use shows B > A, just seems wierd.

Also granted that that thread doesnt really have practical use since its not a raid scenerio but rather hitting dummies (though I think couple have posted with real raid scenerio)...but still i thought A > B on paper would be A > B in practice...

so i am slightly confused, and prolly will try myself soon whenever I get the chance...

Hi,

I noticed a small typo in the ring of knowledge example:

it should be 50.31 dps from spell dmg bringing the effective dps to 85.12

Keep up the good work guys

edit: also you still use the 175% crit example in the 2nd post instead of the 200% as of now.

Thank you for typos.


Could you please say where? I searched a bit, and didn't find it. Maybe I just fail


I'll try to look at the resource you referenced.

Could you please say where? I searched a bit, and didn't find it. Maybe I just fail

It's at the end of 2.0

"Shadow Power = 175% for most of Shadow spells"

Fix't

I tried to enter the data from above into a Wowhead stat weighting......I think its correct....let me know if it doesn't represent the data correctly.

http://www.wowhead.com/?items&filter=ma ... 1:0.33:0.3

The filter numbers seems fine to me, tho you could force bind-to-account items to be evaluated for level 70, and later split 1h and 2h weapon lists, so you don't get misguided.

Thanks much for taking the time to post this clearly.

It has helped me understand my class and gear requirements much better.

Battle for president, holy shit man good job. Thanks alot for this, I'm sure many many people will find this hella useful.