Double Attack - Triple Attack

[CDF]

Okay, so this discussion is a complete non-starter, but I already finished this so I'll run with it. Karmically speaking, I already chipped in my 2 cents of non-trivial observation on the... first page.

First, attempting to make a distinction between attack round frequency and attack frequency is pretty retarded. "Attack frequency" is obviously attacks per unit "time." Derp, I didn't know you couldn't convert attacks/round to attacks/time to damage/time!

Regarding the crop yield example, changing the "input" of consideration merely is a change of reference, dollars in effect "yielding" a crop because dollars can be converted to seed (with the dollar-to-seed conversion being variable). From either the point of view of dollars added or seed added, you still have a rate, crop/dollar or crop/seed, so you can refer to how those rates change (increasing, decreasing, negative).

A percent change is not a rate of a change but a percent change of output (additional DA merely has a 1:1 correspondence with damage per unit "time"... because it is additional rate of damage) that is unitless.

Talking about a trend in percent change per unit of DA (in a vacuum) is peculiar because in effect, you're holding "fixed" the marginal output from 1 unit of input while varying the initial output, so the interpretation of how output ("crop") changes with input (dollars or seeds) doesn't really apply. But, if you want to fixate on this "trend," it's actually a case of negative marginal return, not decreasing marginal return.

The moment you get into trade-offs and opportunity costs, you're out of the vacuum. No more glib talk about overarching trends but specifics (even though the specifics depend on "DoT" per unit whatever). Trade-offs != talk of rates of return. Comparing percent gain/loss in damage per unit "time" is convenient and useful because it abstracts away "all else being fixed." But no one ever said otherwise.

For a FFXI example, yes, with percent changes you could determine when +X amount of INT is better than +Y amount of MAB after some critical value of base MAB, but that is not a "property" of how the percent change varies or "diminishing returns." To say so is really not understanding the situation. Actually, it's a consequence of +X amount of INT being more (absolutely) efficient in the presence of high amounts of MAB while the (absolute) efficiency of MAB remains fixed.

Partial differentiation of the magic damage formula should make this obvious. Changes in INT depend in part on MAB. The more MAB you have, the more efficient additional INT is. On the other hand, the efficiency of additional MAB is fixed. That is why INT can overtake MAB (and vice versa), not because of "diminishing returns."

[Cream Soda]

Again, the technicalities, I don't care for them
"it's actually a case of negative marginal return, not decreasing marginal return."

I just care that adding more DA = less % increase in damage.

[CDF]

All that is being argued is technicalities and in-a-vacuum observations that don't actually matter to decision-making in FFXI, so at least own up to that. I have.

[Shamaya]

It matters when calculating it the correct way means one item is better, and calculating the incorrect way means a different item is better,

Wikipedia ya ya

In FFXI, diminishing returns (also called diminishing marginal returns) refers to how the marginal production of a factor of production, in contrast to the increase that would otherwise be normally expected, actually starts to progressively decrease the more of the factor are added.

Quoted from wiki, only I changed 'economics' to say FFXI. This is a pretty universal and practical concept applying to anyone who wants to make everyday decisions, and they will act on the principle whether or not they are conscious of it. So the concept should be well known independent of economics. I'm studying Japanese right at this moment. I also was studying it last Saturday before going out to a dinner party with my JP coworkers. I already know a bit of Japanese. I didn't "need" to study; I was just brushing up. The marginal increase in my vocabulary from studying that afternoon was relatively small. In comparison, if I'd just arrived in Japan and went out to such a party, time spent studying would have been extremely valuable, since each bit of vocabulary memorized would have meant vast marginal increases with respect to my knowledge of the language. I'm an alcy. Right now I have over a 6pack in my fridge. So there's no impending need to go to the store. The addition of another six pack immediately means little. But, if I had 1 beer in the fridge, I might be much more inclined to drop by the convenience store, as the adding a six pack to my reserve would be a great marginal increase. Marginal gain is an inherent factor in essentially all decision making. If we're talking about decision-making, who care's about net increase. Give me marginal increase. If we're not talking about decision-making, then feel free to plea to whatever other concepts you like.

[Miraun]

Math is not this thread's problem... the problem is English. I can't tell whether or not people aren't understanding the concept of Marginal versus Absolute returns, or whether or not they are arguing which is a better evaluation method in FFXI.

Marginal Change: Change from Point A to Point B
Absolute Change: Change from Point A to Point B based upon an absolute reference.

Marginal returns are decreasing.
Absolute changes are constant.

It is not viable to measure FFXI purely on either marginal or absolute return evaluation. There are a myriad of factors in every comparison. Look at the Turban versus Askar debate. Its only better under X conditions.

[SassiAsura]

Wasn't it a diminishing return when you were stacking the double attack rate which would overwrite the triple attack of a weapon that would have otherwise had a higher frequency? I believe I remember reading about a certain trophy item that starts with the letter R back in the day concerning this. ;P

[Cadsuane]

Wrong. This is precisely why you fail.

With respect to attack round frequency (which is not the same thing as attack frequency), 2A returns are constant. With respect to attack frequency, they are diminishing.

If I have 2A+0% and I add +1%, for every 100 attacks (read: swings of weapon), I have 1 swing added. If I have 2A+99% and I add +1%, for every 100 swings of my weapon (which happens in ~50 rounds), I get 0.5 extra swings of my weapon. (Feel free to try to save what's left of your face by arguing over the decimal places in that 0.5 number.)

Thanks for providing such a clearly worded example of why you don't know WTF you are talking about.

Yeah, but those 100 swings in the second example happen in roughly half the time, so the difference comes from the fact that you're not actually evaluating frequency. 99 DA nearly doubles attack frequency which means 100 swings with 99DA happen in almost half the time that it does with 0DA. Since half the time has elapsed, of course only half the extra attacks from DA have occured. This is exactly what we'd expect, since DA gives you the same number of extra attacks, per unit time.

Frequency is 1/p. It's measured in hertz or, the number of cycles per second. For us it's good enough that it's the number of attacks per unit time. I hope this explains where your problem is coming from.

Thank you for once again replying only to the part of the post I didn't want a reply to. Please reply to the seed/crop example.

Also, diminishing returns is basically 100% economics, so don't be offended as a math major (I too majored in math).

Your point is basically that the return can change based what the dependent variable is, I guess?

[Byrthnoth]

This is the last time this idea was bickered about, and based off my post I assume that there was another time a few months before that I'm not finding.
http://www.bluegartr.com/forum/73096...s-lolalla.html

My chart died when lolGeocities went down (nuuuuuuuuuuuuuuu) but it was just the two equations I listed plotted for 0 to 80% Haste/Double Attack or something. I don't know if I made the economics argument in this thread or the one before it, but it essentially boiled down to the same argument we're having here except there were fewer people on my side.

If you want to compare gear pieces in FFXI, you have to account for all the variables that you're changing when you swap them and come up with units that encompass all of them. It's rarely necessary to go all the way to "Damage per minute" or something, but you can if it's a compete enough simulation (see Shamaya's link posted earlier in this thread). Because of this, and because stats rarely start from 0 when comparing gear swaps, it's important to calculate the marginal benefit you get from pieces. That said, there are two ways to look at it:

For instance, 3 Acc from Platinum Grip +1 vs. 2% DA from Pole Strap:
3 Acc = 1.5% Hit rate under uncapped conditions.
20% DA base + 2% DA from Pole Strap = 1.67% increase in Attacks per DA
These stats affect each other, obviously. Your hit rate determines the efficiency of your DAs. You want to find out where the point is where 3 Accuracy becomes better than 2% DAs, so you can switch if you need to.

Way #1 to do the math:
(XX% [Hit rate] + 1.5%) * 1.20 [DA rate] = XX% [Hit rate] * 1.22 [DA rate w/Pole]
Makes sense, right? You take the number of attacks you'll get on average per attack round (1.20 for 20% DA) and multiply them by the chance that the attacks will hit to estimate the value of the DA and Hit rate combination.

Prepare to has magic trick

Way #2 to do the math:
(XX% [Hit rate] + 1.5%) / XX% [Hit rate] = 1.22 [DA rate w/ Pole] / 1.20 [DA rate]

Crazy division trick turns a logical equation into the marginal benefit of each piece.
THE CROWD GOES WILD KHHHHHAAAAAAAHHHHH~!

Spoiler: show

For those of you actually interested:
1.0167*XX% = 1.5% Hit rate + XX% <-- Multiplied both sides by XX%
0.0167*XX% = 1.5% Hit rate <-- Subtracted XX% from both sides
XX% = 0.015/0.0167 = ~90% Hit rate, so Platinum +1 isn't such a bad option if you've got uncapped Acc on WAR main with 5/5 DA and Brutal.

If you started from 0% DA and were adding Pole Grip, it'd be:
0.02*XX% = 1.5% Hit rate
XX% = 0.015/0.02 = 75% hit rate required before Platinum +1 is worthwhile. So you Brutal-less DRG/SAMs should stick to Pole grip.

[pahnphoenix]

it is a semantic argument. incidentally, the side with an actual practical agenda (the side that says DA has diminishing returns) is correct, though that's at times just a fortunate coincidence. i would (probably--i get bored) never have argued about it if i didn't see why it's important to let people know that DA has diminishing returns. however, (as i ramble about below) while the motivations and the argument itself are distinct, i think the fact that my motivations themselves come from a focus on gear/food/stat comparison and practicality is actually what leads me to be right while, say, cadsuane, is wrong.

the crux of the argument is the concept of a return. people who say DA doesn't have diminishing returns have some fundamental issue about calling % DoT increases (or "stat points") "returns". this is because, for all their chest beating, *they don't understand what returns are*.

if you dig enough on alla, you can find some really self-indulgently philosophical posts about this by me, which could be of interest to people who don't cower in fear when they hear the word "semantics". they're not particularly wise or interesting or anything, but i do think i bring out some of what's going on in the discourse. in a nutshell, the topic was: things have value, and this isn't something you can take for granted and leave unexamined. to illustrate, how is a factory producing, say, cars, different from a MNK equipping some double attack? obviously they're different in many ways, but an important one is that DA gets converted directly into DoT. it's not like, "i have 100 cars, i'll get paid $1,000,000, but if i have 200 cars, i get $1,500,000."

what i'm saying is that the DoT is like the cars, not the dollars. the returns you get on your investment are the DoT, with no middle ground. "uhhhh, no dummy, there's additional attacks, and they're worth less b/c of X,Y,Z (or they're not worth less, cue diminishing returns argument)." actually, no. obviously, DA causes additional attacks. however, that isn't any more salient to the value of DA than what the animation looks like, or trivial mathematical facts about your number of attack rounds (maybe with the brutal earring you attacked a prime number of times, but wouldn't have without it). you buy 1 thing with a brutal earring: damage over time. period. that is the value, that is all we're talking about. you invest in the DA gear, it returns DoT. the input to the function is DA, the output is DoT--full stop.

value can't be abstracted out of the system in which it makes sense... the system determines what value means. it's not arbitrary that we look at DoT instead of rate of attack round increase. we lookers are looking with a purpose: maximizing damage. we have a system for doing this; a system for analyzing it and a system for achieving it. we acquire ATT/ACC/DA/whatever gear, throw it into the mix, and the mix spits out DoT.

does anyone understand what i'm on about here? i don't think i'm explaining it very well, but honestly i think the heart of the problem is that people are decontextualizing concepts like "returns". ...and of course that's the heart of the problem, b/c i and people like me know that 1 more % DA still gets you 1 more attack, and "DA doesn't have diminishing returns" people know 1% DA is less valuable when stacked on top of a lot of DA than on top of a little. the latter people may think the heart of the argument has to do with not understanding math or economics... but i would argue that people like me are just better philosophy students than people like cadsuane(:, because i am capable of keeping track of what's salient in a discussion. this apparently generalizes to being better at understanding concepts in economics.

to summarize, the only way economic principles even apply to discussions about DA (and therefore, the only way anything is "a return" in the first place) is insofar as we're discussing how much DoT we get from DA. saying DA doesn't have diminishing returns is *the same type of error* as accusing someone of paying you less than they owe b/c the dollar bills they give you are dirtier than you'd like them to be. figure that out and you'll see how obviously right the "diminishing returns" camp is.

[pahnphoenix]

hmm. here's a separate short post that might speak to people who come into this disagreeing with me but have the potential to agree (ie they aren't experiencing the psychological state known as "butthurt" and are entering into an actual conversation).

say you produce silent oil. suppose you buy 1 slime oil, 1 beeswax, start your synth, and get 1 silent oil (yes, those aren't the actual numbers in the game; this is an example). the first time you do this, you sell the oil for 100g. maybe you make 50 oils, and you get 100g each. what if you make 100 oils, but at that point certain factors (competitors, lower demand, whatever) make it so that you get 100g for the first 50, but only 80g for the last 50. is this a case of "diminishing returns"?

of course not. you throw in 1 slime oil, 1 beeswax, you produce 1 silent oil. the value of the slime oil might change, but you're investing those ingredients and getting back slime oil at a constant rate. you're getting a constant return of slime oil. that's the production system, and then there's a bunch of further considerations that affect how much you get paid for your silent oils.

but is DA, additional attack rounds, and DoT a system like that? no. there's no market saturation or anything external to the system influencing the value of your additional attack rounds. in this system, you're producing DoT. the DA is the slime oil and beeswax, and the DoT is the silent oils. if 1 slime oil and 1 beeswax produced 1 silent oil, but 10 slime oils and 10 beeswax produced 8 silent oils, that would be diminishing returns. that's what happens with DA and DoT. that's the whole system.

[Shinryuu]

what if you make 100 oils, but at that point certain factors (competitors, lower demand, whatever) make it so that you get 100g for the first 50, but only 80g for the last 50. is this a case of "diminishing returns"?

Well, yes, it is. Economics major here. The usual classical example is putting more laborers in a factory. Due to limited capital, each additional worker produces less than the previous one. This assumes price stability. However, you changed the equation around (with Q stable and P variable). Doesn't change a thing, though.

[Cadsuane]

I'd just like to point out again that, calling my motivation into question (like you always do) regarding this issue kinda falls flat when topics like these seem to be the only reason you ever post on BG anymore, and only after I've posted in them of course. That and the caustic language, the transparent posturing, the infuriatingly arrogant and condescending tone... all in all your trolling technique is fucking superb. I can only sincerely applaud.

I just remembered there was an argument in the midst of all that too. Well, okay, two questions.

Wouldn't it be consistent on your part to refer to the return in silent oil production as a percentage gain like you're doing with DA? Like the second silent oil is a 100% increase in total silent oils, the third is a 50% increase, the fourth 33%, etc. After all, just like with DA, each additional oil represents a smaller portion of the total that's been produced.

Isn't it a problem that the percentage benefit of DA increases varies depending on the chunk size of DA you're evaluating? Evaluating the benefit of going from zero to 5% DA gives us a 5% increase in attack rate. But if we do it by 2.5% chunks, we get a 2.5% increase and a 2.43% increase, and using even smaller chunks seems to make the 5% DA as a total look even more paltry. In fact the ordered pairs on a graph with DA vs. percent increase as a dependant variable seem to change arbitrarily based on the size of the chunks we choose to evaluate! This is slightly confusing to me particularly when I was taught to avoid non-unique results like this when evaluating elasticity in economics.

[bsphil]

1000 hits at no DA
1% 1010 hits = 1.01
2% 1020 hits = 1.00990099009901 (1020/1010)
3% 1030 hits = 1.009803921568627 (1030/1020)
4% 1040 hits = 1.009708737864078 (...)
5% 1050 hits = 1.009615384615385 (...)
6% 1060 hits = 1.00952380952381 (...)
7% 1070 hits = 1.009433962264151 (...)
8% 1080 hits = 1.009345794392523 (...)
9% 1090 hits = 1.009259259259259 (...)
10% 1100 hits = 1.009174311926606 (...)

Now yeah if you compare 10% DA 1100/base of 1000 it would be 10%. Interesting stuff. If someone would've made this chart earlier might have stopped a lot of replies.

It really wouldn't have.

Also, "diminishing returns" is just a phrase that refers to the marginal gains to DoT, not a specifically economic term.

[Cadsuane]

Ah shit, the whole gang's here.

[pahnphoenix]

I'd just like to point out again that, calling my motivation into question (like you always do) regarding this issue kinda falls flat when topics like these seem to be the only reason you ever post on BG anymore, and only after I've posted in them of course. That and the caustic language, the transparent posturing, the infuriatingly arrogant and condescending tone... all in all your trolling technique is fucking superb. I can only sincerely applaud.

I just remembered there was an argument in the midst of all that too. Well, okay, two questions.

Wouldn't it be consistent on your part to refer to the return in silent oil production as a percentage gain like you're doing with DA? Like the second silent oil is a 100% increase in total silent oils, the third is a 50% increase, the fourth 33%, etc. After all, just like with DA, each additional oil represents a smaller portion of the total that's been produced.

re: my example, no, and you're a moron. % increase is what we can compare in the whole damage maximizing system. dollars/silent oils/etc are what we can compare in the other systems.

re: trolling, to be fair, i'm not posturing and i just swear when i talk. as for the tone, yes i am a good troll. but only the tone was trolling. i'd never go so far as to intentionally write something false just to stir things up. nor do i ever lie.

@shinryuu,

blarg. do you see my point in the above example? forget money at all... suppose you're just looking at the slime oil/beeswax silent oil system. you can talk about constant/diminishing/increasing returns. now suppose you know that you'll make less money once you produce too much. now you can talk about constant/diminishing/increasing returns again. obviously you're right that what i wrote was misleading/wrong.

hmm. let me put it another way (i also gave an example like this in the old DA thread, but no one replied to it... i suspect no one even read it, and since i systematically skim/ignore all ffxi posts that are anywhere near as long as mine, i can't blame them).

suppose there's a box. i walk up to the box. i put a carrot in the box. the box spits out a gold coin. i get another carrot. i put it in the box. it spits out another gold coin.

is this constant or diminishing returns? can you answer that question without presupposing certain things about the situation that aren't specified?

do you think it's possible that people who say DA has constant returns might be presupposing different things than people who say it has diminishing returns? does there not need to be some overarching principles and systems to even use the word returns?

is this constant returns:
1+1=2
1+2=3
1+3=4
1+4=5
1+5=6

if so, what the fuck is a return? the output of any function? surely the word has more semantic content than that.

edit: @cadsuane, it is obvious that i don't think much of you, but your motivations to argue and post are obviously emotional. do you understand? my emotions are obvious, but it's not obvious that i post for emotional reasons. what makes your motivations obvious is that many people besides me have explained your error to you, and you evade and cry instead of addressing their points. petty people like you are easily spotted by people as attentive and intelligent as myself.

[CDF]

Marginal utility--e.g., water vs. diamonds--is a distinct concept from marginal return--e.g., workers in a factory (holding other inputs fixed). Actually, I should've known people really meant diminishing marginal utility. Just don't go out of your way to argue one is the same as the other. That's just weak.

[pahnphoenix]

Marginal utility--e.g., water vs. diamonds--is a distinct concept from marginal return--e.g., workers in a factory (holding other inputs fixed). Actually, I should've known people really meant diminishing marginal utility. Just don't go out of your way to argue one is the same as the other. That's just weak.

what is a return, and in the whole "i could use haste or DA, hmmm..." decision making process, are there any returns involved?

[CDF]

Uh, return is the additional output and utility could be considered the "value" you ascribe to that. A percent change is, in FFXI, a quantification of marginal utility of X compared to Y. You know better than that.

[Cadsuane]

re: trolling, to be fair, i'm not posturing and i just swear when i talk. as for the tone, yes i am a good troll. but only the tone was trolling. i'd never go so far as to intentionally write something false just to stir things up. nor do i ever lie.

edit: @cadsuane, it is obvious that i don't think much of you, but your motivations to argue and post are obviously emotional. do you understand? my emotions are obvious, but it's not obvious that i post for emotional reasons. what makes your motivations obvious is that many people besides me have explained your error to you, and you evade and cry instead of addressing their points. petty people like you are easily spotted by people as attentive and intelligent as myself.

Over at alla what you guys refer to as trolls translates roughly to "people who disagree with me" so maybe it bears some explanation; in this case I mean that you've totally lost composure and objectivity in a debate because you've got a personal stake in it which is kiiinda what you're accusing me of, and that the utter foamy-mouthed tastelessness of your posts is so much so that it's actually artfully bad. From a professional standpoint, one troll to another, I can honestly appreciate that last bit. Recall that I haven't even bothered to call you a moron yet which at least means I'm making a token effort to discuss something besides how much of a filthy cocksucker you are.

As far as that goes though...

re: my example, no, and you're a moron. % increase is what we can compare in the whole damage maximizing system. dollars/silent oils/etc are what we can compare in the other systems.

Right, the rules change to suit you in other words. I don't know how to make that congruency any more clear and you left the other question totally unanswered, so alright, nevermind.

CDF and Shinryuu can take it from here with you though really, I wouldn't blame them if they aren't inclined.

[Shamaya]

We don't have to use return in the same way that economists or others use it...

But yes.. I say increasing/decreasing marginal utility all the time. I find it too vague though for this, though it applies. Usually I've (seen) utility used in ways that are not quantifiable or have not been quantified. It's often kind of a catch-all term. Return makes you think of numbers that you'll see in practice. Gain makes you think of numbers you'll see in general (I frequently use it). *shrug* But yeah, the dictionary is not the bible. We're not idiots; it shouldn't be (and it's not) difficult for us to understand what one-another means.

In my studying/beer examples, utility would have been a better word surely. It's probably the best word we can use to understand things such as human action and decision. There are quantifiable elements at work (or so I believe), but in the absence of a way to describe them, we should use utility.