The Ultimate Black Mage Resources with Damage Calculator

[Kenji1134]

*Incoming Wall-o-Text*

For those of you who have access to MATLAB, or probably any decent code compiler, here is the code I have been using to estimate rotation potency.
Keep in mind this is not dps, this is simply the overall potency output over a period of time, going off the assumption that all spells have "roughly" the same % scaling from stats (ie. Fire 1 goes up by 2%, Blizz 3 goes up by 2%), and that all spells have the same crit rate.

*MATLAB code* - Note: The Firestarter proc use logic is still a bit rough. Feel free to improve upon it.

clc;
F1 = 270;
F3 = 396;
F3UI = 154;
B3AF = 154;
T2 = 14; %Estimating at 14 pps
SMana = 5; %Starting Mana: 4 for under 251 pie, 5 for over
rng('shuffle');
Time = 0; %Total Time Elapsed
TPot = 0; %Total Potency
Loops = 1000000; %Number of iterations <- Important!!!
STPot = 0; %Short Potency for this loop
STime = 0; %Short Time spend in this loop
Z = zeros(1, Loops); %Array to hold resulting PPS values for each loop
Next = 0; %Are we casting the next Fire 1?
Firestarter = 0; %Do we have a Firestarter proc up?

for s = 0: 1: Loops
STPot = 0; %Reset short potency
STime = 0; % Reset short time
TPot = TPot + 308; %Regen Phase (Thunder counted later)
STPot = STPot + 308; %Regen Phase
Time = Time + 8; %Time for Regen Phase
STime = STime + 8; %Time for Regen Phase
Mana = SMana; %Reset Mana to full
Next = 0;
while Mana > 0
TPot = TPot + F1; %Cast Fire 1
STPot = STPot + F1; %Cast Fire 1
Time = Time + 2.5; %1 GCD for Fire 1
STime = STime + 2.5; %1 GCD for Fire 1
Mana = Mana - 1; %Cast 1 spell
if rand(1) <= 0.6
Firestarter = 1;
end
if (Firestarter == 1 && Next == 1) %Have proc AND casted next Fire1
TPot = TPot + F3; %Cast Fire 3
STPot = STPot + F3; %Cast Fire 3
Time = Time + 2.5; %1 GCD for Instant Fire 3
STime = STime + 2.5; %1 GCD for Instant Fire 3
Next = 0;
Firestarter = 0;
else
Next = 1;
end
end
%Now we calculate the effect of Thunder 2
if STime >= 21
TPot = TPot + 295; %Full Thunder 2 Duration
STPot = STPot + 295; %Full Thunder 2 Duration
else
TPot = TPot + 14*STime; %Partial Thunder 2 Duration
STPot = STPot + 14*STime; %Partial Thunder 2 Duration
end
Z(s+1)=STPot/STime; %Update array with PPS for this loop
end
disp('5 Fire 1 Method')
fprintf('PPS = %f , STD = %f, Min = %f, Max = %f\n',TPot/Time,std(Z),min(Z),max(Z))

Time = 0;
TPot = 0;

for s = 0: 1: Loops
STPot = 0; %Reset short potency
STime = 0; % Reset short time
TPot = TPot + 308; %Regen Phase
STPot = STPot + 308; %Regen Phase
Time = Time + 8; %Time for Regen Phase
STime = STime + 8; %Time for Regen Phase
Mana = SMana; %Reset Mana to full
TPot = TPot + F3; %Quick-Cast Fire 3
STPot = STPot + F3; %Quick-Cast Fire 3
Time = Time + 2.5; %1 GCD for Quick-Cast Fire 3
STime = STime + 2.5; %1 GCD for Quick-Cast Fire 3
Mana = Mana - 2; %Cast equivalent of 2 spells
while Mana > 0
TPot = TPot + F1; %Cast Fire 1
STPot = STPot + F1; %Cast Fire 1
Time = Time + 2.5; %1 GCD for Fire 1
STime = STime + 2.5; %1 GCD for Fire 1
Mana = Mana - 1; %Cast 1 spell
if rand(1) <= 0.6
Firestarter = 1;
end
if (Firestarter == 1 && Next == 1) %Have proc AND casted next Fire1
TPot = TPot + F3; %Cast Fire 3
STPot = STPot + F3; %Cast Fire 3
Time = Time + 2.5; %1 GCD for Instant Fire 3
STime = STime + 2.5; %1 GCD for Instant Fire 3
Next = 0;
Firestarter = 0;
else
Next = 1;
end
end
%Now we calculate the effect of Thunder 2
if STime >= 21
TPot = TPot + 295; %Full Thunder 2 Duration
STPot = STPot + 295; %Full Thunder 2 Duration
else
TPot = TPot + 14*STime; %Partial Thunder 2 Duration
STPot = STPot + 14*STime; %Partial Thunder 2 Duration
end
Z(s+1)=STPot/STime; %Update array with PPS for this loop
end
format COMPACT
disp('F3 + 3 Fire 1 Method')
fprintf('PPS = %f , STD = %f, Min = %f, Max = %f\n\n',TPot/Time,std(Z),min(Z),max(Z))

*end code*

So we set the potency of our abilities as a reference. Start with a regen phase of Blizz 3, Thunder 2, and Fire 3, taking 8 seconds, and outputting 308 potency while setting up Thunder 2.
Then we start spamcasting Fire1.
After every Fire1, we try to get a Firestarter proc. If we did get a proc, we note that we have one. Regardless of whether we got a proc, we cast the next Fire1, and note that we are casting the next one.
Then we return to the actual casting sequence of Fire1, retry for Firestarter, but now since we cast a 2nd Fire 1, and have a Firestarter proc banked, we can cast Fire 3.

Once we're out of mana for Fire 1's, we look at hold long it's been since we cast Thunder 2, averaging it to 14 PPS, and factoring in the 8 second regen period beforehand... Then back to the top.

This sequence is run 1 million times to have reliable averaging.

[Sleigh]

*Incoming Wall-o-Text*

What does your code have to say about Thunder I and Thunder III when applied?

[Kenji1134]

Mmm... nothing.
The code uses Thunder 2 because... I generally use Thunder 2. =)
Thunder 3 isnt really worth it...
With 5 Fire1's, your longest rotation will be F1-F1-F3-F1-F1-F3-F1-B3-T3-F3, which is a total of 26 seconds, versus Thunder 3's 24 second duration.
Your shortest rotation is 5-F1s with no Firestarter procs, + B3-T3-F3 which is 21 seconds. So at best you exceed T3's dot by 2s, at worst you lose 3s of the dot.
With T2, your longest cycle is 25.5s, and shortest is 20.5s, so you will almost always get the full duration of T2.

[PuroStrider]

Gear Page Updated with Turn 5 gear comparison

DPS Calculator is also updated and ready to rock!

--

@Kuroyasha - I know that feel bud. Hopefully they'll release the item fusing feature soon where you could fuse gear to keep stats/appearance of one another.

@Kenji1134 - I wish I'd gone with computer science route in college. I was born for these kind of things for sure. Maybe I'll get into it once I retire in ~40 years xD. How does MATLAB compare to my raw data by the way? (That is if you can adjust it to match my awesome data) ^^

[Kenji1134]

PuroStrider,

Hmm... guess Ill poke around in your formulas for a bit, see what I can come up with.
Though I imagine your results are averaged over a large set, so your formulas dont have any variance in them... though I suppose that with 1,000,000 cycles, variance is moot...

Hmm... excel formulas look like holy hell man!
Have you tried looking at the value of 1 potency... or maybe 100 potency? Perhaps the entire reason the game uses potency in the first place is to do 1 generic calculation, get a "potency value", and then apply it to whatever you happen to be doing?
If nothing else it would greatly simplify the calculations.

Poking around in your math some more, namely for Fire 1 vs Fire 3... 396/270 is ~1.466. For various values of WD/int/det, the ratio between your calcs of F3/F1 is within 1% of the potency ratio. That may be sufficient justification to reduce your F3 equation... cause I like big numbers and bigger explosions... down into a baseline potency calculation... then multiply my results by it. =)

[Kenji1134]

*Dropping The Math-Text Bomb*

Code Printouts: (Using my stats)
Intelligence = 423
Determination = 258
Weapon Damage = 66
Critical Hit Rate = 395
Spell Speed = 463
Potency =
2.4730
5 Fire 1 Method
PPS = 107.111960 , STD = 1.851122, Min = 94.878049, Max = 107.647059
DPS = 264.887842 , STD = 4.577825, Min = 234.633384, Max = 266.211142
F3 + 3 Fire 1 Method
PPS = 109.178302 , STD = 3.700309, Min = 98.111111, Max = 113.086957
DPS = 269.997905 , STD = 9.150862, Min = 242.628746, Max = 279.664007

*Code* - as always, may need minor tweaking... Im an electromechanical engineer, not a programmer after all =P
clc;
Int = input('Intelligence = ');
Det = input('Determination = ');
WD = input('Weapon Damage = ');
Crit = input('Critical Hit Rate = ');
SPD = input('Spell Speed = ');
%From PuroStrider's EPIC BLM spreadsheet.
F3DMG = .382*Det+1.8*Int+7.447*WD-451.36; %And thank you Wolfram Alpha!!!
AdjustedF3DMG = 0.000362*(Crit+2491)*(F3DMG+0.2769*SPD); %And TI-89!
Potency = AdjustedF3DMG/396/1.097 %3rd number is a correction factor between my results and spreadsheet.
%God your excel formulas are HUGE!!!
F1 = 270;
F3 = 396;
F3UI = 154;
B3AF = 154;
T2 = 14; %Estimating at 14 pps
SMana = 5; %Starting Mana: 4 for under 251 pie, 5 for over
rng('shuffle');
Time = 0; %Total Time Elapsed
TPot = 0; %Total Potency
Loops = 1000000; %Number of iterations <- Important!!!
STPot = 0; %Short Potency for this loop
STime = 0; %Short Time spend in this loop
Z = zeros(1, Loops); %Array to hold resulting PPS values for each loop
Next = 0; %Are we casting the next Fire 1?
Firestarter = 0; %Do we have a Firestarter proc up?

for s = 0: 1: Loops
STPot = 0; %Reset short potency
STime = 0; % Reset short time
TPot = TPot + 308; %Regen Phase (Thunder counted later)
STPot = STPot + 308; %Regen Phase
Time = Time + 8; %Time for Regen Phase
STime = STime + 8; %Time for Regen Phase
Mana = SMana; %Reset Mana to full
Next = 0;
while Mana > 0
TPot = TPot + F1; %Cast Fire 1
STPot = STPot + F1; %Cast Fire 1
Time = Time + 2.5; %1 GCD for Fire 1
STime = STime + 2.5; %1 GCD for Fire 1
Mana = Mana - 1; %Cast 1 spell
if rand(1) <= 0.6
Firestarter = 1;
end
if (Firestarter == 1 && Next == 1) %Have proc AND casted next Fire1
TPot = TPot + F3; %Cast Fire 3
STPot = STPot + F3; %Cast Fire 3
Time = Time + 2.5; %1 GCD for Instant Fire 3
STime = STime + 2.5; %1 GCD for Instant Fire 3
Next = 0;
Firestarter = 0;
else
Next = 1;
end
end
%Now we calculate the effect of Thunder 2
if STime >= 21
TPot = TPot + 295; %Full Thunder 2 Duration
STPot = STPot + 295; %Full Thunder 2 Duration
else
TPot = TPot + 14*STime; %Partial Thunder 2 Duration
STPot = STPot + 14*STime; %Partial Thunder 2 Duration
end
Z(s+1)=STPot/STime; %Update array with PPS for this loop
end
disp('5 Fire 1 Method')
fprintf('PPS = %f , STD = %f, Min = %f, Max = %f\n',TPot/Time,std(Z),min(Z),max(Z))
fprintf('DPS = %f , STD = %f, Min = %f, Max = %f\n',TPot/Time*Potency,std(Z)*Potency,min(Z)*Potency,max(Z)*Potency)

Time = 0;
TPot = 0;

for s = 0: 1: Loops
STPot = 0; %Reset short potency
STime = 0; % Reset short time
TPot = TPot + 308; %Regen Phase
STPot = STPot + 308; %Regen Phase
Time = Time + 8; %Time for Regen Phase
STime = STime + 8; %Time for Regen Phase
Mana = SMana; %Reset Mana to full
TPot = TPot + F3; %Quick-Cast Fire 3
STPot = STPot + F3; %Quick-Cast Fire 3
Time = Time + 2.5; %1 GCD for Quick-Cast Fire 3
STime = STime + 2.5; %1 GCD for Quick-Cast Fire 3
Mana = Mana - 2; %Cast equivalent of 2 spells
while Mana > 0
TPot = TPot + F1; %Cast Fire 1
STPot = STPot + F1; %Cast Fire 1
Time = Time + 2.5; %1 GCD for Fire 1
STime = STime + 2.5; %1 GCD for Fire 1
Mana = Mana - 1; %Cast 1 spell
if rand(1) <= 0.6
Firestarter = 1;
end
if (Firestarter == 1 && Next == 1) %Have proc AND casted next Fire1
TPot = TPot + F3; %Cast Fire 3
STPot = STPot + F3; %Cast Fire 3
Time = Time + 2.5; %1 GCD for Instant Fire 3
STime = STime + 2.5; %1 GCD for Instant Fire 3
Next = 0;
Firestarter = 0;
else
Next = 1;
end
end
%Now we calculate the effect of Thunder 2
if STime >= 21
TPot = TPot + 295; %Full Thunder 2 Duration
STPot = STPot + 295; %Full Thunder 2 Duration
else
TPot = TPot + 14*STime; %Partial Thunder 2 Duration
STPot = STPot + 14*STime; %Partial Thunder 2 Duration
end
Z(s+1)=STPot/STime; %Update array with PPS for this loop
end
format COMPACT
disp('F3 + 3 Fire 1 Method')
fprintf('PPS = %f , STD = %f, Min = %f, Max = %f\n\n',TPot/Time,std(Z),min(Z),max(Z))
fprintf('DPS = %f , STD = %f, Min = %f, Max = %f\n\n',TPot/Time*Potency,std(Z)*Potency,min(Z)*Potency,max(Z)*Potency)
*end code*

Um... so that's that... Though I am pretty sure I am not doing 264 dps. Really closer to 210... dunno, math is a fickle mistress.

[EasymodeX]

*Dropping The Math-Text Bomb*

5 Fire 1 Method
PPS = 107.111960 , STD = 1.851122, Min = 94.878049, Max = 107.647059
DPS = 264.887842 , STD = 4.577825, Min = 234.633384, Max = 266.211142

F3 + 3 Fire 1 Method
PPS = 109.178302 , STD = 3.700309, Min = 98.111111, Max = 113.086957
DPS = 269.997905 , STD = 9.150862, Min = 242.628746, Max = 279.664007

How confident are you in these results and your simulation?

I ask because I did a similar investigation in the other thread: http://forum.square-enix.com/ffxiv/t...=1#post1501774

With similar results from lightweight modeling.

Curious before I go harass our BLM who doesn't read the forums .

[Kenji1134]

How confident are you in these results and your simulation?

I ask because I did a similar investigation in the other thread: http://forum.square-enix.com/ffxiv/t...=1#post1501774

With similar results from lightweight modeling.

Curious before I go harass our BLM who doesn't read the forums .

On that thread, your potency/gcd using the first method (no double F3 trick) was 266.6 potency/gcd.
My numbers for the first method are typically around 107 potency/sec, on a 2.5s gcd, so 107*2.5=267.5, pretty much matches your numbers. So, it looks good.

Overall I am pretty sure of the potency calcs/simulation/method. Though the newest addition based on Puro's spreadsheet does not "feel" quite right... yet.

I suppose the next question becomes, IF the double F3 method is more potency... though surprisingly also more unstable (higher STD), then what is now the minimum Piety you need for the 2nd method?
Speaking for myself, as a Highlander, I needed to put 12 points into Piety to get to 251, which obviously lowered my damage per cast by a kinda noticeable amount, ~2.5%. Offhand I believe it is 9 MP per Piety for BLM... lol, or is it 7? =P

I guess I should also test the following situation...
Using the 2nd method, if we wait say... 0.5, or 0.75 sec for the Fire1 to land... adding 0.75s to the cycle time, and catching that last potential Firestarter proc, would it again be a dps gain in the long run, or is it better to just queue up B3 once the last F1 goes off?

[PuroStrider]

Though the newest addition based on Puro's spreadsheet does not "feel" quite right... yet.

-.-

I'll be happy to answer any questions regarding methodology for every single value and test on my spreadsheet. I get all my data raw from the game for my calculations to get real world result instead of throwing around potency values. You can think of me as an interpreter who translates potency into real damage. ^^

Also, when you guys are doing calculations with anything concerning subsequent casts, you have to consider casting animation delay. For instance, If you cast two Fire III in a row (3.5 sec each), your total cast time for 2 spells will actually a tad bit longer than 7.0 sec total. I have not tested the exact time for casting animation, but it's something worth mentioning.

The Fire III + 3 Fire I method is also something I will investigate in the future after I'm done tinkering with the current Fire I x5 rotation values.