Double-Attack: Increasing Returns or Not?

[Beckwin]

Anyone care to clarify the effects of stacking Double Attack? In a discussion right now and I can't seem to explain it isn't a situation of increasing returns. The counter argument is that they do stack because increased number of attacks = more attacks for DA to proc on, or something to that effect. I'm trying to explain that DA attacks on attack rounds, not number of attacks.

[LD]

uh.... DA & TA proc on each attempted strike, that's why a MNK/WAR can attack 4 times + kick.
DA & TA don't stack, Zanshin probably stacks with DA (but not visa versa), 'occasionally attacks x to x times' weapons (with the exception of Virtue, iirc) don't stack with DA, which is why Ridill Wars prefer zerk/agg merits.

[RKenshin]

Zanshin doesn't stack with DA, and yes DA does stack with the sea weapons.

DA does not have increasing returns because you can only DA once on each swing.

Note: +DA adds the +DA percent to each swing, not each attack round. So if you're a MNK/WAR, each punch in an attack round will have a 10% chance to DA. It's not a 10% chance to DA once in an attack round.

[Suiram]

I read this question as something like, "Is the effect from adding brutal earring in a situation where one already has double attack better, worse, or the same bonus as adding it to one where you do not?" to which the answer is "slightly worse".

If you have no double attack, then 100 attempts is 100 swings. With 5% double attack it's 105, or a 5% (= 105/100) increase. However, if you already have 10% double attack, then it's the difference between 115 and 110 swings in 100 attempts, or a 4.5% (= 115/110) increase.

[Delekii]

I think people are using the word "increasing" or "decreasing" returns way too much these days.. As Suiram showed above you do get less of a RELATIVE increase in attacks when you start with more DA, but 5% DA will add the same number of attacks, damage and TP whether you start at 0%, 10%, or 40% DA - 5 attacks in 100 base attacks.

[Max™]

*pats the poor unloved Amood*

Yes, thats right, you stack with DA too, not that anyone knows or cares... stupid FQM latent.

[Beckwin]

I think the argument may have also been that 17 to 19 % DA was a large enough increase that it sped up TP gain more than 3% haste would. tbh there's some pretty simple sounding math to be done to figure it out, but it sounds tiresome. Could do a no magic haste figure, medium magic haste, and high magic haste, and also some consideration for hasso v. no hasso. Basically just figure the average time to hit 100+ tp after an average return WS or something. The haste part is easy; for double attack I guess you'd have to figure how many trips out of 100 attacks would result in an attack round less to 100tp and average that out. I'm fairly convinced the haste would win out, because 3% is a 15ish delay reduction per swing which is 90ish on a 6 hit trip to 100, so about 1.5 seconds on absolute minimal haste (just the pants). 2% double attack lets you subtract roughly 1000 delay out of 100 swings, which is 16-17 trips to 100 tp, which works out to about 60 less delay per trip. Since that sort of return on average delay reduction should be universal or slightly declining? for stacking DA and we know from all the LR/Hasso/Haste testing that Haste delay reduction returns get larger as they are stacked, I think it's a fair assumption that there isn't really any DA piece that beats a haste piece for TPing, in raw terms of speed to 100 TP.

Sorry for the wall o' text, and if anyone sees errors in my logic or sees something I overlooked in this all, let me know. And math enthusiasts, feel free to run the TP speed figures for varying haste/DA scenarios.

[Evelyn]

I think the thing thats confusing is that DA increases attacks by a set %, which doesn't change regardless of how much DA you have on, whereas 1% haste actually gets more effective the more haste you have on.

And if you're having the discussion I think you're having, then no, Ares' Flanchard is not more effective than Homam Cosciales in straight tp-gain comparisons.

[Suiram]

I think the thing thats confusing is that DA increases attacks by a set %, which doesn't change regardless of how much DA you have on, whereas 1% haste actually gets more effective the more haste you have on.

And if you're having the discussion I think you're having, then no, Ares' Flanchard is not more effective than Homam Cosciales in straight tp-gain comparisons.

I'm pretty sure DA gets less effective the more you already have, rather than being unchanging, this being due to the fact that you can't double-attack twice in the same swing. Although you are right that haste does become more effective.

[Delekii]

I think the thing thats confusing is that DA increases attacks by a set %, which doesn't change regardless of how much DA you have on, whereas 1% haste actually gets more effective the more haste you have on.

And if you're having the discussion I think you're having, then no, Ares' Flanchard is not more effective than Homam Cosciales in straight tp-gain comparisons.

I'm pretty sure DA gets less effective the more you already have, rather than being unchanging, this being due to the fact that you can't double-attack twice in the same swing. Although you are right that haste does become more effective.

You can't double attack twice in the same swing, but you are more likely to double attack on each particular swing. As I said, the amount of attacks relative to your current total attacks changes depending on how much double attack you started with, but in terms of absolutes 5% double attack adds 5 attacks per 100 base attacks.

100 attacks at 0% DA, add 5% DA, you get 105 attacks, 5% increase in total attacks, and 5 extra attacks
100 attacks at 50% DA, add 5% DA, you get 155 attacks, ~3.33% increase in total attacks, but you still get 5 extra attacks, so in terms of damage/tp gain, 5% DA is still adding exactly the same damage and TP as if you had no DA to start with.

The only time I would consider DA to have "diminishing returns" as such would be if you managed to get to 100% DA, in which case of course the return on extra DA is zero. But until then, 5% DA will always add the same number of attacks in a period of time, regardless of how much DA you have otherwise.

[VZX]

x/y
if x increases/decreases, it's a linear one. (atk, DA, accuracy, anything related to base damage)
if y increases/decreases, it's an exponential one (1/x graph, whatever you call in english mathematics). (defense, haste)

diminishing or increasing return is depend how you define "what is increasing return" and "what is diminishing return"

[Suiram]

Perhaps faster TP relative to their TP gain sans any double attack whatsoever, but when people typically want to know how much adding X amount of stat will affect them relative to what they are already getting. Say you are swinging with a Del180 weapon. You're getting 5% TP per hit, so (assuming perfect accuracy) with no DA you are achieving 100 TP every 3600 frames. Add 10% double attack and you're getting it on average in 3272 frames, which is a 9.1% increase in your time to 100 TP. Go from 10% to 20% double attack and you average in 3000 frames, which is only an 8.3% increase in your speed to 100% relative to what you had been getting with 10% DA.


I think (hope) I did the math right there.

[Yutuyu]

Actually all of the answers presented thus far are incorrect. Certain types of double attack + have diminishing returns, and certain types have constant returns.

Consider the case of brutal earring vs. /war DA.

The two proc independantly in such a way that on one weapon skill both can fire (assuming it has sufficient hits to allow this). Thus one only "fires" if the previous one fails. Because they are independant in that way, there is a diminishing gain.

The math:

10% chance of DA from trait, 5% from Earring. Thus there is a 90% chance that the first will not fire. The 5% is only relevant if the first failed to fire, therefore the 5% only "saves" the failed double attack 90% of the time, reducing its effectiveness to 90%*5% or 4.5%.

It's not very noticable there, but if you consider something like Joyuese and Brutal Earring, it makes a bigger difference, where 50%*5% = 2.5%.

Conclusion:

There are different types of +double attack. Those that come from weapons and those that come from the trait are independant. As far as I can tell those that come from any "enhances the effect of" function like brutal, but those that are double attack + n simply add n% directly to the Double Attack trait, working as a direction addition (thus no diminishing returns).

I'm not entirely sure on how each individual piece of equipment functions in all honesty. Maybe someone else can elaborate on this.

[Delekii]

Well yeah, that is another layer to the argument, I was just talking about trait based double attack. I guess it really just depends on how you define increasing/diminishing returns, as Vry said.

But if we look at the OP again, the question is

Anyone care to clarify the effects of stacking Double Attack? In a discussion right now and I can't seem to explain it isn't a situation of increasing returns. The counter argument is that they do stack because increased number of attacks = more attacks for DA to proc on, or something to that effect. I'm trying to explain that DA attacks on attack rounds, not number of attacks.

The simple answer is that DA cannot proc on an attack given by DA. Consider them as two totally different sets of attacks (or if you include multihit weapons/non trait DA, three sets). Double attack can only proc on the first set, which increases not through DA but only through haste/delay reduction. So DA is only applied to a static number of attacks, and increasing DA does not increase this number, hence regardless of how much DA+ you add, it still only applies to the same number of attacks.

[Capo]

simple answer: DA will never have increasing returns. and haste will always be the better choice for tp gain unless its the only piece of haste gear you are wearing and arent getting any form of spell haste (but if this is happening then you have more to worry about than haste vs DA)