The Mathematics of Warlockery

Mezelline · 03-18-2008, 01:47 PM

So I've seen alot of threads wandering around about comparing spell crits vs. spell damage vs. casting speed vs. recast speed vs. int, and I wanted to consolidate the info in a thread that wasn't a couple months old. I've been tweaking my formula all expansion and I think I've got it to a pretty stable level now. I was wrong about of lot of things. After doing some extensive controlled in-game testing in the past few days I've gained a new appreciation for crits and a lessening of interest in spellhaste.

Assumptions:
Level 80 warlock
50% actual crit rate (so in persona, need roughly 60% crit)
850 INT
32% cast speed reduction
32% recast speed reduction
950 spell damage mod
18% base spell damage (assumes WoCP proc is up 1/2 of time)
Averages around 4k dps in a raid scenario
Does not have mythical epic
Only concerned with single-target DPS
Ignoring broodlings/netherlord/acid storm for simplicity

THE BIG EQUATION:
15 dps from a direct damage proc = 1% persona spell crit = 1.3% cast reduction = 2.6% recast reduction = 37 spell damage = 50 INT

METHOD:
From playing around with Flames and lower level nukes on the badgers in KP, it looks actual damage dealt by a spell is calculated the following:
1. Start out with unmodified value of spell. This is determined by the level of the caster, and the "innate" damage of the spell (like how good the spell is/what quality it is)
2. Calculate the spell damage cap, which is 1/2 of the "unmodified value"
3. Add "unmodified value" to "spell damage", up to the spell damage cap, then check for a crit or make a "roll" if the spell has a damage range
4. Multiply that sum by your %base damage modifier
5. Multiply that product times 30% if you critted.
6. Multiply that product times an "intelligence modifier"
7. End result of spell.

In other words,
1. The only things that increase the spell damage cap are getting a higher quality spell, or gaining/losing levels.
2. %base damage, crits, and intelligence modifer are multiplicative, not additive. So if I crit for 30% more damage and I have 18% base damage, on that spell I actually gain 1.3 * 1.18 = 53.4% damage, as opposed to just 30+20=50% damage.

ON INT:
The "intelligence modifier" is a tricky thing to get ahold of. At 850 starting int, adding 1 int results in roughly 0.25 damage per second on most spells. The catch is that our level 80 spells benefit a large amount more than most of our other spells; both Armageddon and Cataclysm get about 0.5 damage per second for 1 int. Only our level 80 spells are affected like this, so I'm guessing it has something to do with EQ2's tier system. Because arma and cataclysm make up like 20% of our dps most of the time, a weighted average results in 1 int being equal to 0.3 dps. Even though int doesn't do much on most spells, the gains on cata and arma keep it interesting. As long as you are NOT at the soft cap, roughly (12*level)+25. Hard cap is (15*level)+25.

ON SPELLDAMAGE:
There are 4 factors that affect spell damage. The first, and most important element, is how many spells you are *actually* casting per minute. For a warlock at 32% cast speed reduction, the optimal adjusted number of spells per minute ranges from 23-25. (this is adjusting 3 AEs as 1 single-target dps spell, since AEs get 1/3 SD penalty, and excluding aura/gift/nether completely) I got this number by running an algorithm on our spell efficiency chart.

The second factor is the spell damage cap. As warlocks, even our weakest nukes do not cap out until we hit 1k spell damage mod. Because crits work off of maxdamage+30%, it means that for us SD is very usable all the way up into the 1.5k SD mod range. Our only spells that don't utilize gain dps at 950 mod spell damage are Netherealm, Acid Storm, Aura, Flames, and Gift. The sum total of which is usually less than 20% of our dps.

The third factor being how much crit and %base damage you have, as the spell damage you apply up to the cap can be both critted and enhanced by %base damage.

So, doing the numbers:
Full 950 SD being applied to 24 adjusted spells per minute = 22800 damage per min, or 380 dps.
So 1 SD = 0.4 dps
Assuming not capped on any spells not listed above, of course

ON CRITS:
We can find out what our dps would like like with no crits at all with a little reverse engineering.
4000 dps
If distortion does 3405-5473 damage, it can crit for 7115 damage or it can median hit (SD added before the “roll” to determine median) for 4439 damage, for a 7115/4439 = 60% increase
We have 50% actual crits, so its really only a 30% overall increase
So 4000 / 1.3= 3076 dps
924 dps from our 50% actual crits
18 dps = 1% actual crit
Need about 1.2% crit in persona to make 1% actual crit against yellows epics
15 dps = 1% persona crit

ON SPELLHASTE:
Again, working on our assumption of a warlock doing 4k with 32% cast+recast reduction. Because of SOE's retarded coding, this means that you'll actually cast spells roughly 16% faster. Because spellhaste effects procs in addition to everything with spells, we can find out what our dps would be without any spell haste at all: 4000 / 1.32 = 3041. Now, if we add 1% spell haste (1% cast speed reduction + 1% recast speed reduction) we get 3041 * 1.01 = 3071. Or a 30 dps gain from adding 1% spell haste.

Now, the tricky thing about spell haste is the 2 components, casting speed and recast speed. For this formula to work we really need both, and it is nearly impossible to delineate the two.

On one hand, recast reduction doesn't do you any good unless it allows you can alter your casting order to improve your dps. With some spells like Armageddon with 40sec+ recast timers, there's a chance that in quick fights you'll get 0 dps from adding 1% recast. But on the other hand, it doesn't do you much good to cast spells faster if you have to break into the poor damage efficiency spells like our non-Armageddon AEs on single targets. And recast is generally more useful on items because generally you only care about recast time on them, rather than casting time.

Likewise, casting speed reduction is great because you can apply SD more often and get more procs. However, when your spells already have a casting speed of 0.75 seconds, adding 1% spell haste isn't going to result in much; going from 0.75 to 0.74 is minuscule enough that with bad lag you won't even notice the difference.

However, I throw my weight to casting speed reduction because its useful on all spells on shorter fights. Our RoK damage efficiency chart is very tiered; on single targets there is little difference between Arma/Aura/Acid, just like there is little difference between Vacuum/Master//Flames/Encase/Distortion(I'm still using Void) and Dissolve/Cata/Abs/Upheaval and Infestation/Nebula. Recast is only good if you can re-arrange your casting order to cast one tier higher, and you need a 40sec+ fight for recast to work on the T1 spells with long recast, and 60sec+ fight for recast to work on the T2 spells. In those situations cast:recast comes closer to a 1:1 ratio, however since those are uncommon I arbitrarily put the ratio at 2:1. The only situations with a 60+sec fight is a named, and in those scenarios you usually have to interrupt your spell cycle for some reason anyway.

So, the reverse engineering again:
4000 parse
32% spellhaste (cast reduction+recast reduction) is really 16% quicker casting
4000/ 1.16 = 3448 dps
552 dps from 32% spellhaste
17.25 dps from 1% spellhaste
Spellhaste is 2/3 casting speed reduction, 1/3 recast reduction
1% casting speed reduction = 11.5 dps
1% recast speed reduction = 5.75 dps

CONCLUSION
Again, this is all from testing with flames and freehand, gear swaps, parsing against solo mobs, with the 4k baseline taken from my own raid parses. This analysis does not take into account debuffs, I'm still not sure where they factor in, as I haven't found a controlled raiding environment I can test in ^_^

And of course, there's the assumptions that can cause problems. In a raid you'll have more stats that will hit you with different diminishing returns. The “pet” spells can account for a significant portion of dps in some scenarios and while they are affected by crits they aren't by SD. And when I get my mythical I have a hunch I'll end up throwing everything out the window as I bet my casting order will change completely, I'll be fighting OJs most of the time (so will be critting less) and I'll get much more SD application, recast will be more useful in longer fights, etc, etc.

I think this guide would work well for wizards too, since we have the same type of spells really. It doesn't work for enchanters/summoners too well though because their spells tend to cast faster and SD cap sooner, which throws a huge wrench in the formula.

Anyway. Comments plz k thx bye~

Pinski · 03-18-2008, 01:57 PM

Quote:

Originally Posted by Mezelline

From playing around with Flames and lower level nukes on the badgers in KP, it looks actual damage dealt by a spell is calculated the following:
1. Start out with unmodified value of spell. This is determined by the level of the caster, and the "innate" damage of the spell (like how good the spell is/what quality it is)
2. Calculate the spell damage cap, which is 1/2 of the "unmodified value"
3. Add "beginning value" to "spell damage", up to the spell damage cap, this is when the system checks for a crit and makes a "roll" if the spell has a damage range
4. Multiply that sum by your %base damage modifier
5. Multiply that product times 30% if you crit.
6. Multiply that product times an "intelligence modifier"
7. End result of spell.

This is slightly wrong. You have BV(Base Value) * IM (Intelligence Modifier) * 0.5 = SDCNC(Spell Damage Cap No Crit). BV * IM * 0.5 * 1.3 = SDCC(Spell Damage Cap Crit). BV * IM * (1 + BDM (Base Damage Modifier)) * 1.3 (Crit) + SDCC = Crit Damage Total. Is the correct formula, while what you're using is: (BV + SDC) * (1 + BDM) * 1.3 * IM = Damage. Which is wrong.

Intelligence is the first modifier applied. Levels do not matter, at all for damage output. You are close, but not exactly right, just for simplicity I'll explain it like you have it.

1. You have your Base Value, and multiply that by your Intelligent Modifier.
2. Next, your Spell Damage Cap is based on the above value.
3. Multiply the BV*IM value by 1.BaseDamageModifier to find out your damage.
4. If you do not crit, add on your spell damage. This is your total damage if you do not crit.
5. If you do crit, your spell damage cap is raised by 30%, so you can now gain even more damage from +Spell Damage, thus you get an even higher damage output.

Mezelline · 03-18-2008, 02:27 PM

Ahh yes I forgot about %base damage. Easy to calculate.

4000 starting dps
4000*1.01 = 4040 dps
1% base damage = 40 dps

or to fit it into the formula,
0.38 %base = 15 dps from a direct damage proc = 1% persona spell crit = 1.3% cast reduction = 2.6% recast reduction = 37 spell damage = 50 INT

Mezelline · 03-18-2008, 02:35 PM

Pinski,

I think our formulas are identical if I understand your notation correctly. From here:

Quote:

(BV + SDC) * (1 + BDM) * 1.3 * IM = Damage

I think you're under the impression that have 100% crits in my formula, when if you read #5 it says multiply by 1.3 *IF* you crit, not all the time. And the whole SDC isn't always added to BV, if the spell is overcapped you only add the cap per #3.

The reason why I did not put my explanation of the method in a similar format to yours is because that format only works if you have a 50/50 crit/nocrit ratio. And after messing around typing variables I wanted a more generalized explanation that was easy to read and would apply to any situation. ^_^

Mezelline · 03-18-2008, 02:38 PM

Another thing, critting does not increase the SD cap. Thats one piece of info I've seen on the boards quite often, but run on out to KP and Freehand+Lower level nuke some mobs....you'll see that base damage no longer increases SD caps. (Of course, the SD amount can and is still affected by crits/%base...however there is a fundamental difference between raising the SD cap and the amount at the cap being modified by crit/%base)

Pinski · 03-18-2008, 02:40 PM

Quote:

Originally Posted by Mezelline

Another thing, critting does not increase the SD cap. Thats one piece of info I've seen on the boards quite often, but run on out to KP and Freehand+Lower level nuke some mobs....you'll see that base damage no longer increases SD caps.

Crits are supposed to increase the spell damage cap and they do, as I've tested. Base Damage, however does not, but Crits do.

Pinski · 03-18-2008, 02:41 PM

Quote:

Originally Posted by Mezelline

Pinski,

I think our formulas are identical if I understand your notation correctly. From here:

I think you're under the impression that have 100% crits in my formula, when if you read #5 it says multiply by 1.3 *IF* you crit, not all the time. And the whole SDC isn't always added to BV, if the spell is overcapped you only add the cap per #3.

The reason why I did not put my explanation of the method in a similar format to yours is because that format only works if you have a 50/50 crit/nocrit ratio. And after messing around typing variables I wanted a more generalized explanation that was easy to read and would apply to any situation. ^_^

You're still using the Intelligence Modifier at the end, when it should be at the very beginning because it is very key in determining the spell damage cap.

Mezelline · 03-18-2008, 03:01 PM

Pinski,

Again, yeah I've heard that crits are supposed to increase to increase the SD cap, but that is simply not the case. From earlier today, playing with flames, the uncritted, unfreehand flames hit for 2113 damage on each of the 2 shots on the badgers in KP. The critted, unfreehand flames hit for 2747. 2747/2113 = 1.30 exactly. I reproduced this 10 times with both uncrit/unfreehand and crit/unfreehand.

Run out to KP and try flaming some mobs real quick, you'll see what I mean. =)

The same thing goes for intelligence modifer. It has no influence on the spell damage cap; I'm pretty sure its an urban legend-y thing much like the crits boosting caps. Try unequipping your gear that doesn't have SD mod or %base mod on it and you'll see what I mean there too ^_^

Mezelline · 03-18-2008, 03:32 PM

I wonder if perhaps we have miscommunication between raising the SD cap and how the crit mod is applied. For example, theoretical nuke does 1000 damage, has a SD cap of 500. The caster has 1000 SD mod. He casts the nuke and crits. We both say he does 1500 damage on his nuke. It's just that you say its (1000*1.3+500*1.3) and I say its (1000+500)*1.3.

You are correct though in that %base is applied before SD cap is calculated, thanks for pointing that out =) I have here in my notes uncrit unfreehand 2113, uncrit freehand 2371, for 2371/2113=1.129, which is not 1.20 because SD isn't affected by %base....so I'll change my method to:

1. Start out with unmodified value of spell. This is determined by the level of the caster, and the "innate" damage of the spell (like how good the spell is/what quality it is)
2. Multiply the unmodified value by %base damage mod to get modified value
3. Calculate the spell damage, which can go up to 1/2 of the "unmodified value"
4. Add #2 to #3 then check for a crit or make a "roll" if the spell has a damage range
5. Multiply that product times 30% *if* you critted.
6. Multiply that product times an "intelligence modifier"
7. End result of spell.

The end formula remains the same.

BTW, thanks for the comments ^_^

murphjp · 03-18-2008, 09:53 PM

Quote:

So, the reverse engineering again:
4000 parse
32% spellhaste (cast reduction+recast reduction) is really 16% quicker casting
4000/ 1.16 = 3448 dps
552 dps from 32% spellhaste
17.25 dps from 1% spellhaste
Spellhaste is 2/3 casting speed reduction, 1/3 recast reduction
1% casting speed reduction = 11.5 dps
1% recast speed reduction = 5.75 dps

There are a few probs with your calculations, I don't have the eact #'s that u have but here are the closest I have come to for spell haste / recast.

At 28% casting speed haste your accual haste is 22%. (A 4 second spell turns into a 3.12 sec spell)
At 28% recast haste your recast haste is 22%. (A 45 sec recast turns into a 35.1 sec recast)
Apoc does 5335 min / 9905 max damage. 7620 mean damage
So in a 10 min fight with no spell haste you can cast apoc every
4.0+0.5+45 = 49.5 secs
600 / 49.5 = 12 casts
12* 7620 = 91440 Total damage
With 28% recast & casting
3.12+0.5+35.1 =38.72
600/38.72 = 15 casts
15*7620 = 114300 Total Damage
114300/91440 = 1.25% damage increase
---------
So 28%Casting speed+recast speed = a 25% increase in DPS.

for a 28% crit at regular casting speed
Min damage = 9905 Max Damage = 12876 Mean damage = 11390
(11390*0.28) + (7620 *0.72) =
3190+5486 = 8676
8676* 12 =104116
104116/91440 = 13.8% increase in DPS

A 56% Crit using the exact same calc = 27.7% increase

This shows 2% crit = 1%Casting + 1% recast.

But this will vary on the spell Apoc has the largest difference from Max to min making crits much more effective, Disolve is only a 20.5% increase with 56% crits. When casting speed + recast increase will not be affected by any change in spells.

So in fact 1% Recast + 1% Casting speed > 2% crit.

Adding up every spell with recast speed and casting speed also shows 1% crit = 20 BoE, since BoE will vary will spells.

So 20 BoE = 1% crit = 1% cast = 1%recast.

Where determining cast vs recast its well a huge pain in the ass to determine what is better. Cast speed imo > recast but if you have to much of one without the other then the effect is mitigated. So I would sugest try to keep them closer togeather.