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** Warrior DPS Guide ** Version 0.28
*******************************************
----Table of Contents----
1.1 Introduction
2.1 Guide Basics
2.2 Impale
2.3 Dual Wield Specialization
2.4 2-Handed Weapon Specialization
2.5 Deep Wounds
2.6 Flurry
3.1 FAQ
*******************************************
* 1.1 Introduction *
*******************************************
This guide is a first attempt at answering the question "What talents should I
pick to dps?" The goal is to produce a list of formula by which a warrior can
properly choose his spec to maximize DPS based on his gear. I feel that this
is needed as confusion abounds on the subject.
*******************************************
* 2.1 GUIDE BASICS *
*******************************************
In order to really answer this question, we need to get the math right. I’m
going to toss out a lot of equations. The first time I write and equation
I’ll write it as **(NAME)**. From then on, if I say 2*Name what I mean is 2
times the quantity calculated by the equation Name. This is going to get a
bit technical, but I think it’s worth getting right. Please correct me if I
botched an equation, goodness knows there’s enough of them that I might have
screwed a few up.
Let’s start by trying to understand basic DPS. Here’s two equations, one for
a DW warrior, and one for a 2-Handed Warrior:
(NOTE: some times when the equation is said and done, it helps to plug in
some actual values and get a percentage. When I plug in actual values, I’m
going to use +13% hit for DW, +5% 2H, +24% crit. You can plug in your own
values and see for yourself, but these are the values I’m going to toss out
there for examples.)
Equation:
**(DW1)** (DPS(MH) + AP/14) + (DPS(OH)+AP/14)*(.5 + DWR/5*.25)
2-Hander
**(2H1)** DPS(MH) + AP/14
DPS(MH) = DPS Main Hand
DPS(OH) = DPS Off hand
AP = Attack Power
DWR = Ranks in Dual Wield Talent
DW1 should calculate the base DPS for a DW warrior’s attacks, 2H1 will
calculate base DPS for a 2 handed warrior’s DPS. Seems simple enough.
However, this is a basic measure of DPS. In reality, some swings hit, some
miss, and some crit. Misses can become very complicated as they will start
to factor in a Mob’s block/parry/dodge and will be further mitigated by armor.
To keep things a bit more simple, we’re going to work with just theoretical
DPS output. We’re not going to worry about what kind of mob we’re hitting.
In this case then, we’re going to miss a base number of 5% of the time with a
2-hander and 24% of the time when we DW.
Now, the next question is, can crits miss? This has been argued and fought
ad nauseum. Suffice is to say “maybe they miss”. To be on the safe side,
we’re going to calculate everything twice. In one case, crits can miss, in
other cases crits always hit.
Now, let’s look at dps when we add hits/misses/crits to the formula:
CRITS CAN MISS
**(DW2)** [DW1*(2+Imp/10)*Crit + DW1*(1-Crit)] * (1-.24+Hit)
**(2H2)** [2H1*(2+Imp/10)*Crit + 2H1*(1-Crit)]*(1-.05 + Hit)
Subject to (DW2) Hit <=24 , (2H2) Hit <= 5
Imp = ranks in impale
Crit = Chance to crit
Hit = extra chance to hit gear being worn
ALL CRITS HIT
**(DW3)** DW1*(1-.24+Hit - Crit) + DW1*Crit*(2+Imp/10)
**(2H3)** 2H1*(1-.05 + Hit- Crit) + 2H1*Crit*(2+Imp/10)
Subject to (DW3) Hit <=24 , (2H3) Hit <= 5
Imp = ranks in impale
Crit = Chance to crit
Hit = extra chance to hit gear being worn
*******************************************
* 2.2 Impale *
*******************************************
Impale only applies to special moves rather than white damage. As such, this
section has been removed. I will return to it when the special move damage
section is added. (See the F.A.Q. section for the old <wrong> section).
As a side note, when I come back to this section, I'm expecting Impale to be
a poor investment for two talent points from an over all PvE dps perspective.
Math will follow to support that, but at the moment, feel free to treat it as
an unsubstantiated opinion.
*******************************************
* 2.3 Dual Wield Specialization *
*******************************************
How about DW Spec? Obviously, it doesn’t do a thing for 2-H, so we can
ignore it for the moment.
Let's start with how the text reads: "Increases damage dealt by the offhand
weapon by X%" (up to 25%)
While the intuitive assumption might be "25% of base damage" some
testing on the warrior forums has indicated that this is "25% of the 50%
off-handed damage". Hence rather than the off-hand doing 75% of base
damage with 5/5, it does 62.5% damage.
Crits can miss:
[(2)*Crit + (1-Crit)] * (1-.24+Hit) * ((DPS(MH) + AP/14) +
(DPS(OH)+AP/14)*(.5 +.125)) )- [(2)*Crit + (1-Crit)] * (1-.24+Hit) *
((DPS(MH) + AP/14) + (DPS(OH)+AP/14)*(.5)))
[(2)*Crit + (1-Crit)] * (1-.24+Hit) *( .125*(DPS(OH)+AP/14))
[plugging values]
(2*.24+(1-.24))*(1-.24+.13)*(.125*(DPS(OH)+AP/14)) = .138* (DPS(OH)+AP/14)
or 13.8% more dps from the off hand
Crits always hit:
((DPS(MH) + AP/14) + (DPS(OH)+AP/14)*(.5 +.125)) ) *((1-.24+Hit - Crit) +
Crit*(2)) - ((DPS(MH) + AP/14) + (DPS(OH)+AP/14)*(.5)) ) *((1-.24+Hit - Crit)
+ Crit*(2)) = ((1-.24+Hit - Crit) + Crit*(2)) * (DPS(OH)+AP/14)*.125
[plugging values]
((1-.24+.13-.24)+.24*2)*.125*(DPS(OH) + AP/14)
= .141(DPS(OH)+AP/14) or 14.1% more dps from the off hand.
To summarize
Crits
Miss Hit
DW [Crit+1]*(.76+Hit)*.125*(DPS1) (.76+Hit+Crit)*.125*DPS1
Example 13.8% more OH Dps 14.1% more OH Dps
Where DPS1 = DPS(OH)+AP/14
So even from these two examples, it should be clear that DWS offers some
modest returns.
*******************************************
* 2.4 2-Handed Weapon Specialization *
*******************************************
There is a certain amount of confusion concerning if 2-Handed Weapon
Specialization enters before or after added attack power. After some field
work, I believe that it enters /after/ attack power is added in. If you
have compelling evidence to the contrary, please contact me (e-mail address
at the end of this FAQ).
The general formula for this is easy to write:
[(DPS(MH) + AP/14 )*(2HR)*2*Crit + (DPS(MH) + AP/14 )*(2HR)*(1-Crit)]
Where 2HR is ranks in 2-Handed Weapon Specialization divided by 100.
<<NOTE: We only need one equation since we have enough +hit to ignore the
crits can hit/crits can miss debate>>
It should be clear that this is a flat 5% dps increase from 5/5 Ranks.
The most common form of this equation will be:
[(DPS(MH) + AP/14 )*.05*2*Crit + (DPS(MH) + AP/14 )*.05*(1-Crit)]
Where we have selected 5/5 ranks.
Imagine we're using Tuf (since almost every warrior has one) and we're
rockin out at 1200 AP with at least +5% to hit and a 21% chance to crit
(I think all of this should be pretty reasonable).
TuF dps =61.4 http://www.thottbot.com/?i=40529
(61.4 + 1200/14)*.05*2*.21 + (61.4 + 1200/14)*.05*.79 = 3.09 + 5.81
= 8.9 dps increase
*******************************************
* 2.5 Deep Wounds *
*******************************************
>> Note: My findings here have surprised me so much that I continue to
question my own math, however so far, every "field test" I've tried has
been supporting my math. Please e-mail me if you see a mistake I have
made. <<
In order to reach impale on the tree, you need to also take Deep Wounds.
But does deep wounds contribute substantial dps or is it simply a filler
talent taken along the way?
Let's start with the text associated with Deep Wounds: "Your critical
strikes cause the opponent to bleed, dealing 20/40/60% of your melee
weapon's average damage over 12 seconds".
Some quick field work and forums prodding has yielded the consensus that
deep wounds ticks every 2 seconds for a total of 6 times over 12 seconds.
The wording here is very confusing. It sounds like a simple case of
"weapon damage * .6 / 6 = damage per tick". However, recently while dueling,
I was hit by a spinal reaper. The deep wounds applied to me ticked for 143
damage per tick. Some simple math will show the issue:
148 * 6 / .6 = ave weapon damage = 1480
This is (sadly) no where close to spinal reaper's average damage. Instead
http://www.thottbot.com/?i=38057 the average damage is 203+305/2 = 252.
Applying the 60% modifier: 252 * .6 = 152.4
That's still not exactly what deep wounds ticked for in my duel, but it's VERY
close. I'm disturbed that the two weren't equal, but I'm still not exactly
certain why. NOTE THAT THIS APPEARS TO USE WEAPON DPS ONLY AND NOT FACTOR IN
ATTACK POWER.
Hence despite the wording, deep wounds applies .6*(average weapon damage) EACH
TICK.
Hence with a tick every 2 seconds, added damage would become:
AWD = Average Weapon Damage
(AWD) * .6 * 6(ticks) = total added damage per crit
(Crit)* (AWD) * 3.6 = total expected added damage per swing
or in DPS, take the total damage and divide by the weapon speed:
(Crit)* (AWD) * 3.6 /(weapon speed) = expected added dps
which condenses to:
(Crit)* (DPS) * 3.6 = expected added dps
adding in misses, we'll get:
DW Crits Can Miss
(1-.24+Hit)*(Crit)*(DPS)*3.6
DW Crits Always Hit
(Crit)*(DPS)*3.6
2-Handed Crits Always Hit
(1-.05+Hit)*(Crit)*(DPS)*3.6
2-Handed Crits Can Miss
(Crit)*(DPS)*3.6
Notice that the above formulae assume that the entire amount of added
damage will be applied. This is close to the truth, but not quite the
truth. In reality, Deep Wounds cannot stack, hence every time you crit
you will overwrite any currently active version of deep wounds.
This means that the above is a good approximation, but to get a better
estimate, I've resorted to a monte carlo simulation technique. Basically,
I've simulated 10,000 swings in an attempt to determine how often deep wounds
will be active, and what the simulated damage added will be.
To compare our formula above to my monte carlo estimation, let's give a quick
example. Use all of the assumed stats I listed at the start of this guide and
assume that we're using The Unstoppable Force http://www.thottbot.com/?i=40529
.24 * 233.5 * 3.6 = 201.744 expected added damage per swing
or a startling:
.24*61.4*3.6 = 53.1 expected added dps
The simulation returns an estimate of 40.4 dps. So you can see that deep
wounds scales badly with crit, but exceptionally well with superior weapons.
The added DPS from Deep Wounds is actually so startling, especially compared
to other talents such as impale, that it seems like a very solid choice.
*******************************************
* 2.6 Flurry *
*******************************************
Let’s start by considering a 2-hander. When flurry procs, it’s a rather
simple affair. Our weapon speed is increased by 30% (with 5/5 ranks).
Hence if we did 200 damage in a 2 second swing, now we do 200 damage
in 2 *.7 = 1.4 seconds. Hence dps shifts from 200/2 dps to (200/2)/.7.
In general, our flurry dps is just:
2H1/.70 when flurry is active.
DW is, however, somewhat of a nightmare. Previously we were able to think
of the dps from both weapons summing easily since both were happening
simultaneously. Now, however, each weapon swing consumes a flurry charge.
Further, some weapons are faster than others… hence with a slow main and a
fast off hand, the off hand is /much/ more likely to consume flurry charges.
Let’s image both weapons have an equal speed. When flurry procs we have a
50% chance of the charge being consumed by either weapon. We can weight
this, however, by weapon speed. Consider the weight:
**MHP** 1-[MHS/(MHS + OHS)] = % of times flurry is consumed by MH
**OHP** 1-[OHS/(MHS + OHS)] = % of times flurry is consumed by OH
Where MHS = Main Hand weapon Speed and OHS = Off Hand weapon Speed. Now if
the main hand has a speed of 2 and the off hand has a speed of 1, you can see
that the MH will consume the flurry charge (on average) 1/3 of the time while
the off hand will consume the charge (on average) 2/3 of the time.
When flurry procs then, we have a main hand that gets a bonus of:
(DPS(MH) + AP/14)/.7
and an off hand with:
(DPS(OH)+AP/14)*(.5 + DWR/5*.25)/.7
So, we assign that dps whenever flurry is active. Let’s say flurry is active
for FP percent of the swings. MHP*FP = % of flurry swings consumed by the
main hand, and OHP*FP = % of flurry swing consumed by the off hand. So if
flurry is active 50% of the time, and we have the weapon speeds mentioned
earlier, the main hand will have flurry active 1/3*50 = 16.67 % of the time
and the off hand will have flurry active 2/3*50 = 33.33% of the time.
So, weighting them by how often they consume flurry:
MHP*FP*(DPS(MH) + AP/14)/.7
OHP*FP*( DPS(OH)+AP/14)*(.5 + DWR/5*.25)/.7
Now, when flurry /isn’t/ active, we have our normal dps for each weapon,
hence our new *expanded* dps formula is:
MHP*FP*(DPS(MH) + AP/14)/.7 + (1-MHP*FP)(DPS(MH) + AP/14) +
OHP*FP*( DPS(OH)+AP/14)*(.5 + DWR/5*.25)/.7 +
(1-OHP*FP)*( DPS(OH)+AP/14)*(.5 + DWR/5*.25)
(note: if you set FP to 0 this collapses right back down to our old formula)
Now, the terrifying prospect here is that these swings can hit, miss, or crit
as well. This means that we need to distribute that math from equations
DW2/2H2 and DW3/2H3 into this equation. Get ready for massive wall of math :P
CRITS CAN MISS:
**(DW4)**
[MHP*FP*(DPS(MH) + AP/14)/.7 + (1-MHP*FP)(DPS(MH) + AP/14) +
OHP*FP*( DPS(OH)+AP/14)*(.5 + DWR/5*.25)/.7 +
(1-OHP*FP)*( DPS(OH)+AP/14)*(.5 + DWR/5*.25)] * [(2+Imp/10)*Crit +
(1-Crit)]*(1-.24+Hit)
**(2H4)**
[2H1/.70 * FP + 2H1*(1-FP)] * [(2+Imp/10)*Crit + (1-Crit)]*(1-.24+Hit)
ALL CRITS HIT:
**(DW5)**
[MHP*FP*(DPS(MH) + AP/14)/.7 + (1-MHP*FP)(DPS(MH) + AP/14) +
OHP*FP*( DPS(OH)+AP/14)*(.5 + DWR/5*.25)/.7 + (1-OHP*FP)*( DPS(OH)+AP/14)*
(.5 + DWR/5*.25)] * [(1-.24+Hit - Crit) + Crit*(2+Imp/10)]
**(2H5)**
[2H1/.70 * FP + 2H1*(1-FP)] * [(1-.24+Hit - Crit) + Crit*(2+Imp/10)]
So, how often is flurry active?
That’s an amazingly difficult question to answer. Let’s imagine for a second
that flurry can’t proc while it’s already active. For the sake of
simplicity, image crits can’t miss and that we crit 50% of the time. Hence
each swing would be either a crit followed by 3 flurry swings, or a non crit
followed by another chance. This means that we would have flurry active 60%
of the time. However, the crits in flurry re-activate flurry. Hence the
chance of having flurry active would be /significantly/ higher. This becomes
a very difficult equation to write out or understand in a meaningful way
(especially as it contains an infinite summation). To avoid it, I’ve run
what’s called a *Monte Carlo* simulation to model the scenario. I ran the
program for a simulated 10,000 swings. In this case, it’s unavoidable to add
in %hit and %crit. Hence I’ve used 13% chance to hit and 24% critical strike.
Crits can Miss Model: 52.24% (DW) 56.10% (2H)
Crits always hit Model: 55.99% (DW) 55.65% (2H)
These values might bug you a little. First off, since in the 2H model, we’re
wearing enough +hit to negate the default 5% miss, 2H and DW should be
identical. Further, all swings are always hits in both 2H models due to the
5%. Hence those 3 numbers (55.99%, 56.10%, and 55.65%) should /all/ be equal.
The fact that they are not reflects the fact that these are estimated values.
They’re close (that’s good) but not equal... in this case, not even 10,000
swings can reduce the difference between them to less than .5%. This isn’t
huge, but it’s worth mentioning. We can average the 3 to make all parties
happy (I hope) 55.91%
This means that you’re achieving theoretical DPS:
[MHP*.5224*(DPS(MH) + AP/14)/.7 + (1-MHP*.5224)(DPS(MH) + AP/14) +
OHP*.5224*( DPS(OH)+AP/14)*(.5 + DWR/5*.25)/.7 +
(1-OHP*.5224)*( DPS(OH)+AP/14)*(.5 + DWR/5*.25)] *
[(2+Imp/10)*Crit + (1-Crit)]*(1-.24+Hit)
To get a more solid hold on this, let’s imagine our weapons have the same
speed. This allows our formula to collapse down and that would mean we have:
.5*.5224*DW2/.7 + (1-.5*.5224)*DW2 =
.3731*DW2 + .7388*DW2 = 1.1119*DW2 or an 11.19% increase in DPS.
[2H1/.70 * .5591 + 2H1*(1-.5591)] * [(2+Imp/10)*Crit + (1-Crit)]*(1-.24+Hit)
2H2*.5591/.70 + 2H2*(1-.5591) = .7987*2H2 + .4409*2H2 = 1.2396*2H2 or a
23.96% increase in DPS.
That was for the *crits can miss* model, let’s look at *crits always hit*.
Due to the way the problems simplify, our 2 hander will still end up with a
bonus of 23.96% dps increase. For DW (again, assuming equal speed weapons):
.5*.5591*DW3/.7 + (1-.5*.5591)*DW3 = .3994*DW3 + .7205*DW3
= 1.1199DW or an 11.99% increase in DPS.
More to come...
*******************************************
* 3.1 F.A.Q. *
*******************************************
************
Q:Should I use faster weapons for unbridled wrath even if it means taking
a hit to my dps?
************
Probably not... Immagine we have two weapons, a quick 1.5 speed sword
and a slower 2.5 speed sword:
[chance to hit] * [1 rage per second w 1.5 speed sword] *
[chance to get that 1 rage on a hit] = expected rage/second
.89*(2/3)*.40 = .2373 expected rage per second
[chance to hit] * [1 rage per second w 2.5 speed sword] *
[chance to get that 1 rage on a hit] = expected rage/second
.89*.4*.4 = .1424 expected rage per second
In a 10 second span, you'd expect to gain 1 extra rage with your faster
weapon. In a 2 minute long fight, that's an extra 12 rage... not even
enough for an extra WW or BT.
*******************
Q: Why would you endorse either of those specs? They're both terrible.
*******************
I'm not trying to endorse any spec, I was trying to answer the specific
question that was sent to me. The goal of this guide is to help people
pick specs that are best for them and make an informed decision on the
matter, not for me to tell people what spec to play.
*******************
Q: What happened to the impale section?
*******************
My prior impale section operated on the belief that impale improved white
damage. It currently does not, hence it was incorrect. For the sake of
posterity, the final equations are preserved below. If impale is ever
change this will become relevant again.
[START OLD SECTION]
This is a good first stopping point. Here we can add up just how much of an
effect Impale and DW specialization are having.
Start with impale, subtract us having 2 ranks from us having no ranks:
[DW1*(2+.2)*Crit + DW1*(1-Crit)] * (1-.24+Hit) -
[DW1*(2)*Crit + DW1*(1-Crit)] * (1-.24+Hit) = DW1*.2*crit*(1-.24+hit)
Is that a big number? Let’s use my example stats for a moment:
DW1*.2*.24*(1-.24+.13) = .04272DW1 = 4.272% dps upgrade
Now 2-Handed with crits missing:
[2H1*(2+.2)*Crit + 2H1*(1-Crit)]*(1-.05 + Hit) -
[2H1*(2)*Crit + 2H1*(1-Crit)]*(1-.05 + Hit) = 2H1*.2*Crit*(1-.05+hit) =
[plugging values] 2H1*.048 or 4.8% dps upgrade
Now DW crits always hit:
DW1*(1-.24+Hit - Crit) + DW1*Crit*(2+.2) - (DW1*(1-.24+Hit - Crit) +
DW1*Crit*(2)) = DW1*Crit*.2 = <plugging values> DW1*.048 or a 4.8% dps upgrade
Now 2-Handed with crits always hit:
2H1*(1-.05 + Hit- Crit) + 2H1*Crit*(2+.2) -
(2H1*(1-.05 + Hit- Crit) + 2H1*Crit*(2)) = 2H1*Crit*.2 =
[plugging values] 2H1*.048 or a 4.8% dps upgrade.
To summarize
Crits
Miss Hit
DW
Formula DW1*.2*crit*(1-.24+hit) DW1*Crit*.2
Example 4.272% 4.8%
2-H
Formula 2H1*.2*Crit*(1-.05+hit) 2H1*Crit*.2
Example 4.8% 4.8%
>>>>> FURTHER EXAMPLE <<<<<
Imagine we're using Tuf (since almost every warrior has one) and we're
rockin out at 1200 AP with at least +5% to hit and a 21% chance to crit
(I think all of this should be pretty reasonable).
TuF dps =61.4 http://www.thottbot.com/?i=40529
Impale
(61.4 + 1200/14 )*.21*.2 = 6.18 dps increase
So our DPS increase is rather modest. Given this example, I would consider
impale to be a stronger PvP talent than a PvE talent.
[END OLD SECTION]
Questions, comments? Please e-mail me at DiomedesSOTydeus@gmail.com
Revisions:
.26 Added Deep Wounds Section, Table of Contents, started added in
"further examples" to give concrete numbers at the request of several
readers (10/10/2006)
.27 Changed the Dual Wield Specialization calculations after testing
and research indicated that the +25% was from the modified 50%
oh weapon damage rather than base damage (11/08/2006)
.28 Removed the impale section as I was applying it to white damage, removed
a question from the FAQ that included an incorrect FAQ calculation.
Included section on 2-Handed Weapon Specialization.
