Did you know that DA has diminishing returns? (lolalla)

[Byrthnoth]

http://www.geocities.com/jheregls/jh.../HastevsDA.jpg

Compare apples to apples!
Haste line is (1/.99) to (.2/.19), or ((1-x/100)/(1-x/100-.01)).
DA line is (1.01/1) to (1.81/1.8 ), or ((1+x/100+.01)/(1+x/100)).
... and yes, I used this graphs months ago and had this same discussion!

The Y-axis should say "Number of Attacks" to reduce confusion I guess. Still, this discussion is fairly worthless due to the extremely limited situations where you might be trading Haste for DA in a TP set (are there any?)

[Furoris]

I think just about everyone is going about these calculations the wrong way, and it would be better to consider as a statistically Binomial distribution with successes being X="double attack proc" with and p="%DA" is the probability that any given swing will double attack,

Each Swing is independent and not affected in probability by the one preceding it.
Therefore the expected value of Successes (DA procs) per "n" swings with a "p' DA rate
E[X]=n*p
Thus if n=100 swings and DA%=5%
E[X]=100*.05=5
if n=100 DA%=10%
E[X]=100*.10=10
DA%=15%
E[X]=100*.15=15
Therefore the new attack rounds in the time that originally contains the 100 swings now contain n+E[X] number chances of possibility to hit, thus 105, 110 and 115 respectfully.

I sorry guys, though it is for the wrong reasons, the math illiterate people are right. You forgot the meaning of statistical independence.

Edit: However it should be noted while each swing is independent on one and other ACC, DA, Haste, and DMG per hit are not independent from each other, and would have to be factored into "p" in order to determine damage increase. Also for the purposes of this proof Zanshin and that new WHM ACC thing are ignored.
Edit 2: realized i skipped a step

[Abandon]

http://www.geocities.com/jheregls/jh.../HastevsDA.jpg

Compare apples to apples!
Haste line is (1/.99) to (.2/.19), or ((1-x/100)/(1-x/100-.01)).
DA line is (1.01/1) to (1.81/1.8 ), or ((1+x/100+.01)/(1+x/100)).
... and yes, I used this graphs months ago and had this same discussion!

The Y-axis should say "Number of Attacks" to reduce confusion I guess. Still, this discussion is fairly worthless due to the extremely limited situations where you might be trading Haste for DA in a TP set (are there any?)

These charts are the wave of the future.

[Furoris]

These charts are the wave of the future.

These charts are wrong....

[Byrthnoth]

I'm sorry, but no! If you start from 0% Trait, obviously it has a static effect. The point is that you need to calculate the percentage increase in number of attack rounds (assumed to be equal to DoT) due to an increase of 1% of any given trait.

If you have 10% Double Attack, you'll get 10% more attack rounds than you would with 0% Double Attack. If you use a Brutal + 5/5 DA merits and have 20% Double Attack, you'll get 20% more attack rounds than you would with 0% Double Attack, but only 9.1% more attack rounds than you would with 10% Double Attack. Going from 0 to 10% DA resulted in a 10% increase in attacks, while going from 10 to 20% DA results in a 9% increase in attacks. The effects are diminishing.

If you have 10% Haste, you'll get 11.1% more attacks than if you had 0% Haste. If you have 20% Haste, you'll get 25% more attacks than if you had 0% Haste, and 12.5% more attack rounds than if you had 10% Haste. Going from 0 to 10% Haste was only an 11.1% increase, while going from 10 to 20% Haste resulted in a 12.5% increase in attack rounds. The effects are increasing.

Though the static effect you get stays the same, the percentage benefit to your damage output decreases the more of it you add. This is true of all additive traits (Look at MAB,) while the opposite is true of all subtractive traits (Look at Haste or Magic Damage Down.) Magic Damage Down and Haste are similar, but not the same in their growth pattern I think.

You take 1024 damage from Thunder IV unbuffed. With Shell IV on (-56/256), you take 800 damage, about a 20% decrease. With another -56/256 from gear, you take 576 damage. A 28% reduction. Because you used the same amount of trait and got an increasing amount of percentage effect, the effects are increasing!

It is an issue of semantics, but this is the only way to view it when you're trying to compare gear pieces. Maybe the terminology is wrong, but the idea isn't. For instance, say you have -45% damage down with 0 MDB and want to know if you should use Lamia Mantle +1 (MDB+4) or Hexerei Cape (Damage -3%.) From the same 1024 damage nuke, you'd take 564 damage without either (-114/256). With Hexerei (another -7/256,) you'd take 540 damage. With 4 MDB, you'd take 542 damage. Considering we started from 0 MDB, we aren't seeing the diminishing effects of stacking MDB here, we're seeing the increasing effects of Magic Damage Down. If both pieces were your first pieces of Magic Damage Down gear, Lamia Mantle +1 would be 984 damage and Hexerei would be 996 damage.


Edit:
Statistical Independence does apply here, and over time you will definitely see the assumed average for Double Attack, but that's irrelevant to its percentage growth with respect to damage. 120 attacks/110 attacks is always going to be less than a 10% increase, even though it's a 10% increase in Double Attack.

[Furoris]

The semantics argument is only when considered a percentage increase from after a previous increase. Double attack is not modeled well to represent how it function while haste on the other hand is. In fact a proper percentage increase graph would show haste linearly and DA as a step function, while a graph of strait # of attacks in a given time would show DA linearly and haste Exponentially, this is because Haste is defined as a %. Quick protip scientists try to make graphs as linear as possible to simplify calculations, thus why such thing as a % graph exists. While a strait haste % increase is linear a Damage % increase is not and Hit% increase is also not.

DA is misleading in that is is listed as a % like haste but the % for DA is actually a Probability not % increase.

TL;DR the only thing better then DA is Haste, and both should only be used if and only if you have enough ACC.

Edit to not double post:

I'm sorry, but no! If you start from 0% Trait, obviously it has a static effect. The point is that you need to calculate the percentage increase in number of attack rounds (assumed to be equal to DoT) due to an increase of 1% of any given trait.

If you have 10% Double Attack, you'll get 10% more attack rounds than you would with 0% Double Attack. If you use a Brutal + 5/5 DA merits and have 20% Double Attack, you'll get 20% more attack rounds than you would with 0% Double Attack, but only 9.1% more attack rounds than you would with 10% Double Attack. Going from 0 to 10% DA resulted in a 10% increase in attacks, while going from 10 to 20% DA results in a 9% increase in attacks. The effects are diminishing.

If you have 10% Haste, you'll get 11.1% more attacks than if you had 0% Haste. If you have 20% Haste, you'll get 25% more attacks than if you had 0% Haste, and 12.5% more attack rounds than if you had 10% Haste. Going from 0 to 10% Haste was only an 11.1% increase, while going from 10 to 20% Haste resulted in a 12.5% increase in attack rounds. The effects are increasing.

Though the static effect you get stays the same, the percentage benefit to your damage output decreases the more of it you add. This is true of all additive traits (Look at MAB,) while the opposite is true of all subtractive traits (Look at Haste or Magic Damage Down.) Magic Damage Down and Haste are similar, but not the same in their growth pattern I think.

You take 1024 damage from Thunder IV unbuffed. With Shell IV on (-56/256), you take 800 damage, about a 20% decrease. With another -56/256 from gear, you take 576 damage. A 28% reduction. Because you used the same amount of trait and got an increasing amount of percentage effect, the effects are increasing!

It is an issue of semantics, but this is the only way to view it when you're trying to compare gear pieces. Maybe the terminology is wrong, but the idea isn't. For instance, say you have -45% damage down with 0 MDB and want to know if you should use Lamia Mantle +1 (MDB+4) or Hexerei Cape (Damage -3%.) From the same 1024 damage nuke, you'd take 564 damage without either (-114/256). With Hexerei (another -7/256,) you'd take 540 damage. With 4 MDB, you'd take 542 damage. Considering we started from 0 MDB, we aren't seeing the diminishing effects of stacking MDB here, we're seeing the increasing effects of Magic Damage Down. If both pieces were your first pieces of Magic Damage Down gear, Lamia Mantle +1 would be 984 damage and Hexerei would be 996 damage.


Edit:
Statistical Independence does apply here, and over time you will definitely see the assumed average for Double Attack, but that's irrelevant to its percentage growth with respect to damage. 120 attacks/110 attacks is always going to be less than a 10% increase, even though it's a 10% increase in Double Attack.

Yes this is the semantics argument, it comes down to using a percentage growth to represent differences in damage and the terms associate with such a model, however it that model only proves that haste has a greater effect then DA which we all already knew, but it doesn't prove that when stacking more (unless the case of giving up ACC and possibly large amounts of STR and ATK) wouldn't be effective.

My 1st post was addressing a different model where people where calculating DA rate for 100 round as 5 DA = 105 with then next calculation being 95 round etc. which is strait wrong.

[Abandon]

These charts are wrong....

Not referring to the info. Just the graph itself.

[Liquidedust]

I think just about everyone is going about these calculations the wrong way, and it would be better to consider as a statistically Binomial distribution with successes being X="double attack proc" with and p="%DA" is the probability that any given swing will double attack,

Each Swing is independent and not affected in probability by the one preceding it.
Therefore the expected value of Successes (DA procs) per "n" swings with a "p' DA rate
E[X]=n*p
Thus if n=100 swings and DA%=5%
E[X]=100*.05=5
if n=100 DA%=10%
E[X]=100*.10=10
DA%=15%
E[X]=100*.15=15
Therefore the new attack rounds in the time that originally contains the 100 swings now contain n+E[X] number chances of possibility to hit, thus 105, 110 and 115 respectfully.

I sorry guys, though it is for the wrong reasons, the math illiterate people are right. You forgot the meaning of statistical independence.

Edit: However it should be noted while each swing is independent on one and other ACC, DA, Haste, and DMG per hit are not independent from each other, and would have to be factored into "p" in order to determine damage increase. Also for the purposes of this proof Zanshin and that new WHM ACC thing are ignored.
Edit 2: realized i skipped a step

For me it is for example more of measure the gain from a specific DA% piece (and its gain) relative to other pieces with other stats in same slot. If I already have lets say 20% DA (WAR, Brutal and 5 DA merits), will the gain from 2% more DA in grip slot outweight the relative gains from an Axe, Mythril+1 or Platinum Grip for example.

Here the relative return of 2% DA must be weight against the acc/STR gains in same slot. In this case we have a relative gain of 1.67~ vs. a possible +1 fSTR and 1-2% hitrate. Will the actual gain from 2% DA be better then the other choices in this case.

But yes you are correct that on its own it doesn't really matter, but when weight against other stats in same slots the relative gain must be weighted against other relative gains to get the complete picture.

[Yugl]

Here is how one player mentioned the diminishing returns of DA:

100 Swings + 5% DA = 105 Swings

Since you can neither DA those 5 extra swings nor the 5 DAed regular swings, you're left with 95 DAable swings. Adding 5% to your current 5% DA would mean you DA 5% of those 95 DAable swings. Now here is my question: Are the DA percents on equipment grouped or are they independent of each other? For example: If I use Brutal Earring with 5% DA, would it be 5% of my 100 swings DAed or would it be 1% of my 100 DAed then 1% of the 99 and so forth?

To make this question easier to read:

5% of 100 Swings DAed

v

1% of 100 Swings DAed + 1% of 99 Swings DAed and so forth until 5% is reached

[Furoris]

Not referring to the info. Just the graph itself.

OIC, I would make some, but I already need to make 10 for one of my lab class later today...

edit also to not double post:

For me it is for example more of measure the gain from a specific DA% piece (and its gain) relative to other pieces with other stats in same slot. If I already have lets say 20% DA (WAR, Brutal and 5 DA merits), will the gain from 2% more DA in grip slot outweight the relative gains from an Axe, Mythril+1 or Platinum Grip for example.

Here the relative return of 2% DA must be weight against the acc/STR gains in same slot. In this case we have a relative gain of 1.67~ vs. a possible +1 fSTR and 1-2% hitrate. Will the actual gain from 2% DA be better then the other choices in this case.

But yes you are correct that on its own it doesn't really matter, but when weight against other stats in same slots the relative gain must be weighted against other relative gains to get the complete picture.

This is correct and returns everyone back to shit is situational, though i would like a comparision at some point of how much acc/atk will out do 1 DA and 1 haste respectully, also would like to see a strait comparison +2% DA grip and Crit+3% grip for a War with 20% DA

[Furoris]

Here is how one player mentioned the diminishing returns of DA:

100 Swings + 5% DA = 105 Swings

Since you can neither DA those 5 extra swings nor the 5 DAed regular swings, you're left with 95 DAable swings. Adding 5% to your current 5% DA would mean you DA 5% of those 95 DAable swings. Now here is my question: Are the DA percents on equipment grouped or are they independent of each other? For example: If I use Brutal Earring with 5% DA, would it be 5% of my 100 swings DAed or would it be 1% of my 100 DAed then 1% of the 99 and so forth?

To make this question easier to read:

5% of 100 Swings DAed

v

1% of 100 Swings DAed + 1% of 99 Swings DAed and so forth until 5% is reached

/sigh had to double post anyways...
Every swing is independent and there for has the same chance at DAing, this is the exact thing i was talking against.

The outcome of the previous trial has no effect in the next trial, that is the definition of independence, these calculations have been proven over many times in Statistics. No offense but I'm not here to teach you statistics so please if you still don't get it take a stats course.

[FailureMidgard]

Could people read the full thread before posting? Seriously holy shit.

Since I'm one of the main math people arguing against the "ZOMG it's only linear", I'll state this again:

IT IS 100% IRRELEVANT SEMANTICS.

If you:
a: Think DA is linear and only linear
b: Think DA is diminishing and only diminishing
c: Can't grasp that you -must- think about other stats besides DA

Then you have no grasp of the situation, and should stop arguing.

To repeat, the damage function is multi-variable (multi-dimensional) and as such needs to -always- be considered as such. It is stupid to debate the nature of 1 partial derivative of a ~4 dimensional function and ignore the fact that 3 others exist.

Furthermore, if you seriously insist on this, as I said before, depending what you compare DA to, you can get a linear OR diminishing graph.
To repeat myself:

If you compare DA to # of attack rounds, it is linear. Instead of doing the math on this, WHICH EVERY GODDAMN PERSON ACCEPTS, give a solid argument as to -why- this is the proper way to look at it? Why are attack rounds the way to go instead of actual attacks? In fact, you can't actually make this argument in good faith unless you pretend that the only thing you're trying to figure out is if 5 DA or 6 DA is better. And I'm sorry, but a 2 year old can maybe tell you if 5 or 6 is bigger.

If you want to look at some math, I did it a few posts back, when you compare DA to # of attacks (as in, every time you swing your GK or Polearm or Gaxe or w/e), then DA actually has diminishing returns. No percent based increase, DA just has pure diminishing returns.

100 swings.
Assuming 0 base DA, and adding 5 DA, you go to 105 swings, +5 swings.
100 swings, assuming 10 base DA. This means 10% of your 100 swings were DAed swings, and as such, they cannot be DAed. Thus, you had 90.9 DAable swings (or, 90.9 attack rounds), and 9.1 DAed swings. If you now add 5% DA, you add ~.05*90.9 or 4.5 more swings. Wait, you didn't add 5 swings?! NO WAY.
100 swings, assuming 20 base DA. This means you actually only had 83.3 attack rounds, adding 5% more DA will give you ~.05*83.3 or 4.2 more swings.

Yes, that's right, when you add 5 DA at 20% DA, you only add 4.2 swings. If you add 5 DA at 0% DA, you add 5 swings. That is by nature, diminishing.

I'm sure more people will either not read this post, then respond with their amazingly useless opinions, or perhaps argue with me. Instead, read this one line: IT IS IRRELEVANT IF THEY HAVE DIMINISHING RETURNS OR NOT, AND IF YOU ARE ARGUING FOR EITHER SIDE, YOU PROBABLY HAVE NO CONCEPT AS TO THE NATURE OF THIS, AND THE FACT THAT WE AREN'T DEALING WITH DOUBLE ATTACK ALONE IN A VACUUM VS THE ALMIGHTY VACUUM MONSTER.

/sigh had to double post anyways...
Every swing is independent and there for has the same chance at DAing, this is the exact thing i was talking against.

The outcome of the previous trial has no effect in the next trial, that is the definition of independence, these calculations have been proven over many times in Statistics. No offense but I'm not here to teach you statistics so please if you still don't get it take a stats course.

Oh yea, you're wrong/etc, because DA can never cause a triple attack.

[Valyana]

When I'm considering two gear options, the "returns" I'm interested in are how much either of these options will improve my damage relative to the gear I'm using now. That is, I'm interested in the effect on this (simplified) function:

TP damage/time = (Base attacks/time)*(1/1-Haste%)*(1+DA%)*((Acc%)+(1-Acc%)*Zanshin%)*Damage/Hit

Comparing damage before and after a gear change is a matter of dividing the new damage formula by the old one to tell me how much of an increase it will be; if DA is the only statistic that changes, the other terms cancel out and you get just

New Damage/Old Damage = (1+old DA%+add DA%)/(1+old DA%)

which gives a smaller improvement than "add DA%" unless "old DA%" is 0.

In other words, my "returns" (which I define as the ratio of new damage to old damage) from adding more DA are diminished because I already had some DA.

Is there some reason other than pedantry to be interested in any other "returns"? Is there something wrong with using percentage increase in damage as a metric for effectiveness?

[Byrthnoth]

This has turned into a strange argument of how DA is evaluated. Not to use the overplayed "this is how we get FFXI players to think about probability" example, but here goes:

Warrior with 5 Double Attack merits and Brutal Earring-
Way 1 (They Stack) - If you roll a 800 or above, you Double Attack. This would be a 20% Double Attack rate, and if you attacked 100 times you'd expect to Double Attack 20 of them on average. - 20% increase in # of Attacks
Way 2 (They're Exclusive) - Roll once for your job trait, and if you get an 900 or above, then you Double Attack. If you get below a 900, roll again for your merits and if you get above a 950 then you Double Attack. If you get below a 900 on the first roll and below a 950 on the second, roll again for Brutal Earring, and if you get above a 950 then you Double Attack. - 18.75% increase in # of Attacks


In some respect I can see the argument for exclusive DA traits. For instance, think of Joyeuse. Legend goes that DA+20% while using Joyeuse results in a 10% increase in Double Attack rate instead of 20% because Joyeuse already forces DA proc on 50% of attack rounds. So, having a sword with +50% Double Attack instead of "Occasionally Attacks Twice" would actually be better than Joyeuse because it'd proc 70% of the time with +20% DA instead of only 60%.

However, there is simply nothing to indicate that all other gear/jobtraits/merits/Fighter's Roll don't stack. Principle of parsimony indicates that they do, and I don't see any evidence elsewhere in the game that would indicate SE has ever considered making traits with the same name not simply stack.
Obviously, it's much harder to tell whether or not they do stack simply due to the smaller difference it would make if they did or didn't. For instance, how can we really parse if Brutal Earring acts exclusively? Most parses done to figure out the Double Attack potency of such things are done with a job that doesn't have DA to start with, and even with 15% DA, it'd be telling the difference between 19.25% and 20% DA rate.

DA+20% being 120 Attacks
vs.
DA+15% and DA+5%, so 100*1.15 Rounds + (85*1.05 Rounds-85) = 119.25 Attacks

There are plenty of ambiguous Double Attack things. Warrior's Cuisses, Brutal Earring, and Fighter's Calligae. However, if you notice the Double Attack gear in game, most the ones that have a clear +_% on them were put into the game later, with the exception of Rune Halbred and Scarecrow Scythe.

[Tulun]

One thing that is slightly confusing; Obviously, if a single piece added 100% DA, the total swings increase would be doubled. Is there a point where DA increases again briefly?

Because from the math people are giving it seems like DA would give less than x2 swings if you had 100% DA. It's obviously not possible with any current gear but that seems to be what is implied?

Or is it simply clearer; DA may be linear but the damage over time it adds is not linear and diminishes relative to DA it adds and starting DA.

[sleekmotorwurkz]

This thread makes my head hurt, and I was a math major in college...

[FailureMidgard]

One thing that is slightly confusing; Obviously, if a single piece added 100% DA, the total swings increase would be doubled. Is there a point where DA increases again briefly?

Because from the math people are giving it seems like DA would give less than x2 swings if you had 100% DA. It's obviously not possible with any current gear but that seems to be what is implied?

Or is it simply clearer; DA may be linear but the damage over time it adds is not linear and diminishes relative to DA it adds and starting DA.

Going from 0->100 DA doubles total swings.
100 base swings + 0 DA swings > 100 base swings + 100 DA swings.

However, going from 50->100 DA only ups swings by 33.3%.
100 base swings + 50 DA swings > 100 base swings + 100 DA swings. or 150 -> 200 swings (+50/150 swings)

The big thing is a DAed swing cannot itself proc a DA, so you don't get linear returns in reference to swings made.

[Tulun]

Ahh, 1/3 of 150 is 200. Makes sense.

[Furoris]

Oh yea, you're wrong/etc, because DA can never cause a triple attack.

What? I never said that. Take a stats course learn what Independent trials mean.

No offense but I'm not here to teach you statistics so please if you still don't get it take a stats course.

Quick pointer though, a DA is a success (defined as 1) not an additional trial, each trial has the same probability to be a 1 as the last trial. (please note failure is 0 WOOOOO BINARY!!)

edit: giving up on this argument cause most of the people who do get the math/stats know the difference is semantics have already reached an agreement, all that is left is the people who don't understand either math or statistics.

[Cadsuane]

Strictly speaking Haste is not exponential growth since the affect it has on attack rates is modelled by a rational function, not an exponential one: 1/(1-x)=y, which has a vertical asymptote at x=1. That means at x=1, f(x) is undefined, since you've divided by zero. An exponential function is modelled by f(x)=a(b)^x, and is never undefined for any real number x in its basic form. So it's a common mistake to say haste gives exponential returns.

Which brings me to the next point; a stat that gives the same percentage benefit throughout is actually the definition of exponential growth, not linear growth. This is more or less why it's ridiculous to say DA has diminishing returns for not giving you the same percentage back in damage every time you stack it.

For example, if do a hundred damage per unit time, and have a stat that gives me 5% extra damage every time I add it, the damage growth is modelled by an exponential function. In this case: f(x)=100(1.05)^x, where 100 is the initial damage, 1.05 is the value that 100 is multiplied by every time stat x is added.

It's not a semantical argument; calling a decreasing percentage increase a diminishing return is mathematical absurdity.

Another argument I see being used is that DA has diminishing returns because you cannot DA off DAs. This is actually the criteria it would need to adhere to to have a linear effect on attack rate. A DA stat that could DA off itself would confer an attack rate of infinity at 100%, which would give it rational growth like haste. This obviously isn't the case.