The Mathematics of Warlockery - Page 2

Mezelline · 03-19-2008, 11:30 PM

murphjp,

Excellent feedback, thank you! In response to your questioning of the value of spell haste, I have tried a couple different spell haste scenarios and have been surprised to find diminishing returns in effect. With 32% spell haste, a 4.5 OOCT spell drops to 3.52 OOCT, so 32% persona spellhaste is actually resulting in 0.98/4.5 = 21% actual spellhaste, which is a significant rise from my 16% listed. I think my problem was that I was using focused casting to determine my calculation, and then didn't consider the effect diminishing returns had upon the actual dps increase. So to be more accurate, I need to adjust my spellhaste ratio to:

4000 parse
32% spellhaste (cast reduction+recast reduction) is really 21% quicker casting
4000/ 1.21 = 3305 dps
695 dps from 32% persona spellhaste
21.71 dps from 1% persona spellhaste
Spellhaste is 2/3 casting speed reduction, 1/3 recast reduction
1% casting speed reduction = 14.5 dps
1% recast speed reduction = 7.25 dps

So in my formula I'd adjust spellhaste from 15 dps = 1.3% cast = 1.6% recast to 15 dps = 1.0% cast = 0.5% recast.

I find it interesting that you believe the cast:recast ratio should be 1:1. Any particular reason why? Another reason why I push the ratio closer to 2:1 is that casting speed is still very effective even when not backed up with recast. For example, if you cast a high efficiency spell such as Aura with ~5000 efficiency, if you don't have the proper recast you can throw an extra lower efficiency spell into your casting rotation, such as Cata with ~2500 efficiency. Now, if you had it backed up with equal amounts of recast instead of doing the 2.5k you could cast the 5k again for a 50% increase in dps from that spell. However you cannot do the same with recast; with recast even though you'll be able to pump out more Armageddons per minute, it also means you're going to be spending more time casting those slow, high efficiency spells, the opportunity cost being less quick/lower efficiency spells.

On crits, however, I am pretty sure that your wrong. In your formula, you are calculating crits based upon the assumption that crits are simply x1.3 damage, rather than max*1.3. And I'm not sure where you get the value "7620" from in this line:

Quote:

(11390*0.28) + (7620 *0.72) =
3190+5486 = 8676
8676* 12 =104116

It looks like you're trying to do a weighted average between crit damage and non-crit damage. Is 7620 the mean of your uncritted distortion?

Mezelline · 03-19-2008, 11:41 PM

Oh another question I have is about this part:

Quote:

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.

How do you come to the conclusion 1 crit = 20 SD? This is vastly different from my own formula. Remember that our AEs are only 1/3 affected by spell damage, some spells are cast more often than others, and that some spells such as Flames/Aura/Netherrealm/Gift are not affected by an increase spelldamage at all, but are affected by an increase in crit. (This is why I tried to reduce everything to a raw dps baseline, rather than a baseline based upon an ingame stat)

Mezelline · 03-20-2008, 12:11 AM

Oh yeah I forgot to adjust the formula for %base damage to make sure it doesn't affect SD. So changing the reverse engineering:

4000 starting dps*60=240,000 damage in one minute
(Adjusted average 13 applications of SD damage per minute) * 950 spelldamage = 12,350 damage in one minute from SD mod.
(240,000-12,350)/60 = 3794 dps can actually be affected by %damage.
3794*1.01 = 3832
1% base damage= 38 dps

I also mucked up my readjusted formula in the above post...

So my final formula now looks like:

*****
15 dps from a direct damage proc = 1% persona spell crit = 1% persona cast reduction = 2% recast reduction = 37 spell damage = 50 INT = 0.4%base damage
*****

murphjp · 03-20-2008, 12:50 AM

Quote:

Originally Posted by Mezelline

I find it interesting that you believe the cast:recast ratio should be 1:1. Any particular reason why? Another reason why I push the ratio closer to 2:1 is that casting speed is still very effective even when not backed up with recast. For example, if you cast a high efficiency spell such as Aura with ~5000 efficiency, if you don't have the proper recast you can throw an extra lower efficiency spell into your casting rotation, such as Cata with ~2500 efficiency. Now, if you had it backed up with equal amounts of recast instead of doing the 2.5k you could cast the 5k again for a 50% increase in dps from that spell. However you cannot do the same with recast; with recast even though you'll be able to pump out more Armageddons per minute, it also means you're going to be spending more time casting those slow, high efficiency spells, the opportunity cost being less quick/lower efficiency spells.

I agree I don't now what the best ratio is. I was making a spreadsheet to accualy tell me but after entering #'s for 3 hours into it I gave up. I just keep the 1:1 ratio since it works. but 2:1 or 1:2 may be better.

Quote:

Originally Posted by Mezelline

On crits, however, I am pretty sure that your wrong. In your formula, you are calculating crits based upon the assumption that crits are simply x1.3 damage, rather than max*1.3. And I'm not sure where you get the value "7620" from in this line:

It looks like you're trying to do a weighted average between crit damage and non-crit damage. Is 7620 the mean of your uncritted distortion?

I used apoc #'s with low int since that is what I had without any +spell damage on me.

Apoc does 5335-9905 max damage. 7620 mean damage

That is without crits and I used the average damage in my calc. for crits I used

Min damage = 9905 Max Damage = 12876 Mean damage = 11390

Using 11390 for the caculation with crits. Showing it was an accualy increase of 49% on average when you crit.

murphjp · 03-20-2008, 01:00 AM

Quote:

Originally Posted by Mezelline

Oh another question I have is about this part:

How do you come to the conclusion 1 crit = 20 SD? This is vastly different from my own formula. Remember that our AEs are only 1/3 affected by spell damage, some spells are cast more often than others, and that some spells such as Flames/Aura/Netherrealm/Gift are not affected by an increase spelldamage at all, but are affected by an increase in crit. (This is why I tried to reduce everything to a raw dps baseline, rather than a baseline based upon an ingame stat)

yes I know 20 BoE was based on using only single target spells, and Apoc with a cast rotation. I uded my casting order of casting more damaging spells when up<ie apoc/distortion/aura was cast 100% of the time it was up> and spells like disolve/encase was cast only as fillers.

These are all paper calculations so accual #'s may be slightly higher but not much. 30 BoE for 1 Crit is to high.

Also I did take into account some spells like vacum chambers max mod is only aproc 250min-300max <depending on int>, and spells like acid are much higher aprox 500-1200.

Although I do think after 700ish BoE its effectiveness goes down alot as alot of spells start to hit there caps.

murphjp · 03-20-2008, 01:16 AM

Quote:

Originally Posted by Mezelline

So my final formula now looks like:

*****
15 dps from a direct damage proc = 1% persona spell crit = 1% persona cast reduction = 2% recast reduction = 37 spell damage = 50 INT = 0.4%base damage
*****

But As I proved 2% crit = 1% recast + 1 % Cast. So keeping a 2:1 ratio like you did have it should be

1% Crit = 1.3% Cast = 0.7% Recast

And for the Procs, I did 40DPS from my BCG in PR. So your calculations would show the Diviner's Sash of Alacrity is a better belt. <Although I do agree with this more warlocks would think your crazy.>

Oh and one more thing casting speed does have dimishishing returns. I wasn't able to find out when the retuens arn't worth it since I did my testing without TC. But its more then 38%. <38% gives you a 29% haste>

Morkai · 03-20-2008, 08:24 AM

1% cirt = 30 boe is an awful comparsion, from my statement, it dosnt stand any critic from common sense. You dont get any boe on some spells, you get 1/3 on apocalypse, how the hell would you calculate boe for our spells?
Once a dissortion does it crit, I can see a 14k hit quite clearly... how would boe make dissortion hit so much? How you can even compare them (boe and crit)?

Tell me your method, I dont understand you.

Mezelline · 03-20-2008, 08:35 AM

murphjp,

I'm sorry but I still can't understand your "proof" that 2% crit = 1% cast + 1% recast at all. Let me see if I understand you correctly:

(1) Are you trying to say that on your tooltip the sum of the first hit + all the ticks of the dot results in a *total* range of 5335-9905, for a mean of 7620?
(2) And then when you crit the tooltip range turns into 9905-12876, for a mean of 11390?
(3) And then you try to calculate the average amount of damage done by the spell by taking a weighted average of the two means?
(4) And then you multiply this times 12 for some reason? (I'm guessing that you get it from casting 12 apocs in a 10 minute fight)
(5) And then you divide the result by how much the spell did at 0% crit to see how much of a damage gain you got from including crits?

Now, if all that is the case...I see many different things wrong with this method of calculating dps gain from crits.

#1: crits do not *only* increase spell dps. It also increase dps you get from procs, which is not figured into your equation.
#2: Your formula does not allow for %base damage and SD to compound with crits, when in reality they do.
#3: You are also assuming that 1% persona crit = 1% actual crit in the game, which is flawed if you look at any ACT parse you have.
#4: Your (2) is flawed because when you crit you get max damage x1.3. You say its a range 9905-12876, I would say that it is simply 12876.
#5: Your (4) is flawed because Armageddon is not the only spell you cast in a fight. In order for this mehod to be accurate, you would have to do a separate calculation for *every* spell you cast in a 10 minute fight, and then do a weighted average of ALL your spells. Which is a pretty much impossible task.

And yeah, I would say the Diviner Sash is better than the BCG. But some of that is you only getting 40dps from the BCG; other people with more crit/%base/fighting multiple targets longer might get more than 40dps out of it, which makes it worthwhile for them. However, the two are really close so its not a huge deal if you use one over the other.

Mezelline · 03-20-2008, 09:06 AM

Morkai,

I'm not sure if that's directed at either murphjp or myself, but if you're curious how I get a "catchall" crit:SD comparison, in the block "on spell damage" I explain how I adjust for spells that get 0, 1/3, or full SD.

The reason why we see distortion doing 14k on our screens is largely because of debuffs, as well as the innate magical resistance of the mob. It's not that crits are just that super-awesome that they do 300% of the damage on the tooltip, if you'll look at your logs you will also see your non-crits doing substantially more damage than tooltip as well.

And bahh...I found out I messed up my %base calculation again, I figured my adjustment assuming 12 adjusted applications of SD per min when there's really 24. So new %base calculation:
4000 starting dps*60=240,000 damage in one minute
(Adjusted average 24 applications of SD damage per minute) * 950 spelldamage = 22,800 damage in one minute from SD mod.
(240,000-22,800)/60 = 3620 dps can actually be affected by %damage.
3620*1.01 = 3656
1% base damage= 36 dps

So slight final formula tweak:
****
15 dps from a direct damage proc = 1% persona spell crit = 1% persona cast reduction = 2% recast reduction = 37 spell damage = 50 INT = 0.42%base damage
****

Morkai · 03-20-2008, 09:27 AM

22,800 damage in one minute from SD mod isnt that bad in the abstract model, you've created, when there is 24 boe applications per minute (thats quite questionable from what I see, crit will apply where boe wont, again), but how much you'll get from crits?
If ill accept you system of coordinates and do math as you do: 37*60=2220 thats the damage one crit will do in a minute? Probably if one disortion will crit that will be more than that value considering all debufs, again. The biggest problems that thouse nubmers... do they exist in game at all?