The Mathematics of Warlockery - Page 3

Morkai · 03-20-2008, 09:46 AM

Also do you calculate Precision of the maestro (wich is now nonstop for everyone, thx for the mythics) and Tandem wich are again affected by crit but not by boe?

murphjp · 03-20-2008, 05:16 PM

Quote:

Originally Posted by Mezelline

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.

Yes that is the method I used.
As for your points.
1. You can proc crits but faster casting = more procs. So moot point.
2. I don't knwo what you mean
3.1% persona crit is less then 1% accualy crit. But they are close enough to assume its a 1:1 ratio. Witha 63% crit rate I crit anywhere from 61-65%.
4. Crits don't hit for the max every time so I took eth average #. The same way I did for teh non crit hits so it works.
5. I used armagedon as an example. I could have used any spell but the results would have been the same since the ratio from min damage to max damage is the same for 90% of the spells.

murphjp · 03-20-2008, 05:57 PM

Quote:

Originally Posted by Morkai

Also do you calculate Precision of the maestro (wich is now nonstop for everyone, thx for the mythics) and Tandem wich are again affected by crit but not by boe?

Quote:

Originally Posted by Morkai

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.

I did not this may lower the efictiveness of BoE. They are affected both by cast speed though.

But I know you don't see large benifits of BoE, but look at the Spell Acid. Without any BoE its a spell that does minimal damge with 700 BoE it rivals Disolve, but requires less power, and is on a faster recast.

So its like having a 100% proc, that does 200-700 more damage each spell. Depending on if its an AE or not.

As for how I calculated it, I took a 10 min timeframe. Calculated every spell I would cast in that period. I used no modification spell times as well so it would not be biased. I kept dots on the mobs at all times anad kept other high damage speels cast before low damage spells, IE aura over disolve.

I then did the same calculations again using a BoE of 21 added on to every spell that can have a BoE. And it came up to about 0.3% more damage then the precious calc.

1% crit = aproc 0.3% dps increase so
1% Crit = 21 BoE.

These calculations don't include procs, I also didn't include casting of spells like Netherrealm, Gift or acid strom. So it will be less more like 1crit = 30 BoE.

That being said the soft cap for BoE starts quite fast so after about 500-800 BoE its not nearly as efficent to have it.

Mezelline · 03-20-2008, 08:32 PM

Morkai,

If you are trying to figure out how much real damage 1 crit does per minute, I think your equation 37*60=2220 is wrong. That is how much extra damage you'll get off of BoE in a minute if you have 100% crit instead of 0% crit.

In my formula, 1% persona crit = 15 real dps. So it would be 15*60=900 damage per minute.

It is worth noting that in my formula the extra damage you get from critting SD mod is factored into the "crit" value, rather than the SD value.

I could understand someone arguing that if you increase SD mod, you don't get just the extra damage from the SD mod itself, you get more than the SD mod because it can crit. However, in my equation crits operate off of a 4000 dps base, and that 4000 already assumes 950 SD mod. So I cannot adjust my SD mod value to compensate for crits, because that would make the two variables codependent, which would make any comparison of the two irrelevent. The only way to genuinely compare them to each other is to calculate the actual dps produced by altering one variable completely independent of the other.

I suppose if you want to nitpick and ignore codependancy you could argue that SD mod is a little bit more powerful because it can be critted. But it's not going to move SD mod much more than maybe ~4 SD mod down, and moving this damage from the crit column will drop crits ~10%.

But personally, I'd much rather have a robust formula than introducing all sorts of errors like codependency. Because eventually it'll come to the point where you set up the equation according to what you "feel" is right, rather than what the numbers would suggest.

murphjp,
Are you saying that for SD you found an optimal spell casting order for a 10 minute fight? That's crazy, you probably had to look at 400 spells, and if you did it by hand probably have all sorts of errors creep into the analysis. What I did is construct an algorithm to calculate optimal casting order, and I found that there ranged 29-32 spells per minute no matter how long the fight lasted. And then I adjusted that value to remove the auras and dock the AEs by 1/3 to come up with an adjusted SD mod application value of 24.

Mezelline · 03-20-2008, 08:39 PM

Morkai,

Procs such as PoM and Tandem are easy to compare in this equation. Just open up ACT, look at how much dps those procs are doing, and compare accordingly from that 15 dps figure if you're curious to see if you'd prefer having Tandem+TC to something like DKtM+PoM+Aria+Allegro.

If you're wondering if PoM and Tandem are included in the formula I would respond yes, of course. Because in my crit calculations I started with a base dps number that included the effects of all procs, and yeah it was assuming traditional PoM+Tandem. Likewise in my spellhaste calculations I also worked off a base dps number that included the effect of procs of well. I calculated SD mod totally independent of starting dps, so it correctly does not effect procs at all.

hennyo · 03-20-2008, 10:29 PM

murphjp · 03-21-2008, 02:22 PM

Quote:

Originally Posted by Mezelline

murphjp,
Are you saying that for SD you found an optimal spell casting order for a 10 minute fight? That's crazy, you probably had to look at 400 spells, and if you did it by hand probably have all sorts of errors creep into the analysis. What I did is construct an algorithm to calculate optimal casting order, and I found that there ranged 29-32 spells per minute no matter how long the fight lasted. And then I adjusted that value to remove the auras and dock the AEs by 1/3 to come up with an adjusted SD mod application value of 24.

I did it in excell, optimal casting and what accualy happens are different.I used 10 mins due to spells like apoc only hitting once in a min or 12x in 10 mins.

I was able to just enter a BoE # and it automaticaly adjusted the damage. Although with more spell haste the BoE vs crit rate should go down.

Dehah · 03-30-2008, 03:29 AM

First, nice posts Mezelline. I like to see people reverse engineer how things work.

Here's what I've come up with for how spell damage is calculated.

1. Calculate the base damage ranges of the spell.

I won't get into the details of how the INT calculation works. But I will say that the INT cap is the level of the spell, not your level. Quick note: (Spell Level) * 15 + 20 is the cap.

[Min Base Damage] = INT_FUNCTION( [Min Dmg At Capped INT], [Spell Level], [Your INT] );
[Max Base Damage] = INT_FUNCTION( [Max Dmg At Capped INT], [Spell Level], [Your INT] );

2. Calculate the base damage of the spell. This will be a random number in that range.

[Base Damage] = RANDOM_INT_FOR_RANGE([Min Base Damage], [Max Base Damage])

3. If it is a crit, multiply the base damage by 130%. If the result is less than the INT-Based Max Damage + 1., then it is raised to that amount In other words, which ever is higher.

[Critted Base Damage] = MAX([Base Damage] * 1.3, [Max Base Damage] + 1)

This is a tricky part to generalize in any spreadsheet approximation. To calculate an average, you have to calculate two different averages and then merge those. Calculate what percent of the time the crit will be [Max Base Damage] + 1. For example, if a spell has a min damage of 500, and a max damage of 1000, then 54% of the time the crit will be for 1001, and the other 64% of the time it will be in the range of 1001 to 1300, or 64% of the time the average would be 1150.5. Combine those two averages together to get the average crit damage of (1001*0.54+1150.5*0.64) 1276.86.

So, coming out of this step, if it was a crit, the result is the critted base damage, if it wasn't a crit, the result is still the base damage.

[Step 3 Result] = crit ? [Critted Base Damage] : [Base Damage]

4. Multiple the Step 3 Result by 0.5 to get the Spell Damage cap. If Spell Damage is less than this ammount then you hit no cap.

[Spell Damage Cap] = [Step 3 Result] * 0.5;

[Spell Damage] = MIN([Your Spell Damage], [Spell Damage Cap])

5. Now multiple the result from step 3 with the base damage multiplier.

[Step 5 Result] = [Step 3 Result] * (1 + [Base Damage Modifier])

6. Finally, add the Spell Damage to the result from step 5

[Final Damage] = [Step 5 Result] + [Spell Damage]

One final note, the above calculations is not how the tooltips work. Tooltips take into account the base damage modifier before the Spell Damage cap is calculated.

Cici · 03-30-2008, 06:59 PM

Quote:

Originally Posted by Dehah

First, nice posts Mezelline. I like to see people reverse engineer how things work.

Here's what I've come up with for how spell damage is calculated.

1. Calculate the base damage ranges of the spell.

I won't get into the details of how the INT calculation works. But I will say that the INT cap is the level of the spell, not your level. Quick note: (Spell Level) * 15 + 20 is the cap.

[Min Base Damage] = INT_FUNCTION( [Min Dmg At Capped INT], [Spell Level], [Your INT] );
[Max Base Damage] = INT_FUNCTION( [Max Dmg At Capped INT], [Spell Level], [Your INT] );

2. Calculate the base damage of the spell. This will be a random number in that range.

[Base Damage] = RANDOM_INT_FOR_RANGE([Min Base Damage], [Max Base Damage])

3. If it is a crit, multiply the base damage by 130%. If the result is less than the INT-Based Max Damage + 1., then it is raised to that amount In other words, which ever is higher.

[Critted Base Damage] = MAX([Base Damage] * 1.3, [Max Base Damage] + 1)

This is a tricky part to generalize in any spreadsheet approximation. To calculate an average, you have to calculate two different averages and then merge those. Calculate what percent of the time the crit will be [Max Base Damage] + 1. For example, if a spell has a min damage of 500, and a max damage of 1000, then 54% of the time the crit will be for 1001, and the other 64% of the time it will be in the range of 1001 to 1300, or 64% of the time the average would be 1150.5. Combine those two averages together to get the average crit damage of (1001*0.54+1150.5*0.64) 1276.86.

So, coming out of this step, if it was a crit, the result is the critted base damage, if it wasn't a crit, the result is still the base damage.

[Step 3 Result] = crit ? [Critted Base Damage] : [Base Damage]

4. Multiple the Step 3 Result by 0.5 to get the Spell Damage cap. If Spell Damage is less than this ammount then you hit no cap.

[Spell Damage Cap] = [Step 3 Result] * 0.5;

[Spell Damage] = MIN([Your Spell Damage], [Spell Damage Cap])

5. Now multiple the result from step 3 with the base damage multiplier.

[Step 5 Result] = [Step 3 Result] * (1 + [Base Damage Modifier])

6. Finally, add the Spell Damage to the result from step 5

[Final Damage] = [Step 5 Result] + [Spell Damage]

One final note, the above calculations is not how the tooltips work. Tooltips take into account the base damage modifier before the Spell Damage cap is calculated.

thats the way spell works

Mezelline · 03-30-2008, 09:52 PM

Dehah,

Your insights into INT are very interesting. If returns on INT are indeed tied to spell level that would explain why our level 80 spells get a larger return from INT than our sub-80 spells! But I haven't noticed any diminishing returns with regards to spell level; %age wise, INT gives the same return on level 71-79...it's only when we hit 80 that there's a big bump up. Is the INT function based upon the *teir* of the spell? (I'm guessing that eq2 teir function is kinda funky and multiples of 10 count as the next tier up, like transmuting and shield avoidance)

Another thing about your function I'm curious about is that you add spell damage *after* the crit and base damage calculation. However, as murphjp pointed out a couple pages back (and I verified) base damage modifiers have no impact whatsoever on actual spelldamage amount/cap, however crits will increase the amount of damage you get from spelldamage irregardless if you're at the SD cap or not.