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

[Cadsuane]

Yeah, that would mean the probability is additive, thanks.

You know that's just semantics, and the change in attack rate is still linear.

I've got a linear function, 1+x=y, that graphs the line which describes the expected number of swings per attack round with x double attack added. It's non-discrete, works pretty well.

You know I can go up to any line with a constant slope in a cartesian graph, mark the increase after f(x) changes by 1, and compare delta y to total y, to get a smaller percentage every time. This is a trivial characteristic of a linear function. It's still a linear function. I know this because it's a line; the first difference is always the same number. This has nothing to do with diminishing returns.

[Redshift]

All of this arguing is breaking our friendships apart.

[Ferien]

Yeah, that would mean the probability is additive, thanks.

You know that's just semantics, and the change in attack rate is still linear.

I've got a linear function, 1+x=y, that graphs the line which describes the expected number of swings per attack round with x double attack added. It's non-discrete, works pretty well.

You know I can go up to any line with a constant slope in a cartesian graph, mark the increase after f(x) changes by 1, and compare delta y to total y, to get a smaller percentage every time. This is a trivial characteristic of a linear function. It's still a linear function. I know this because it's a line; the first difference is always the same number. This has nothing to do with diminishing returns.

I'm going to say this once more and I'm done.

The numerical increase in Attacks/time is linear. The percentage increase in Attacks diminishes with each marginal increase.
The percentage increase in total damage output due to the marginal increase in Attacks is diminishing.

Nobody gives a shit about how many more attacks you get.
The important part is "How much more damage will I do compared to what I do now," and that, my friends, diminishes with each marginal increase in Double Attack.

[Cadsuane]

That is all true, but the return is not the percentage increase, the return is the first difference, which is delta y. At least, that's the commonly accepted definition.

[Deadgye]

Yea, he can, 'cause you fail at reading. He originally made a statement with 2handers in mind. Then Monk was brought into the picture, and he is altering his definitions to accommodate this case, while keeping his logic the exact same. He hasn't changed his argument one bit (you just fail at reading and/or comprehension), just the semantics that people are -still- arguing over, for some unknown reason.

The fact that he had to change it to make it work for DW and H2H means it wasn't correctly set up. I'm sorry you fail to see that. Saying that you can't use "swings" and that you have to use "rounds" and then making a note in a later post that you have to multiply the rounds by 2 if using H2H or DW is retarded. If you use "swings" like you should in the first place then you don't run into that problem.

And back on topic with the semantics argument: Diminishing returns in respect to percentage DoT increase, Linear returns in respect to exact DoT increase.

[orinthia]

"Swings" doesn't account for haste and time does it?

[Kaylia]

Semantically, that's not what "diminishing returns" means, though you've got the basic idea right.

"Diminishing returns" by itself means that every additional unit of input leads to a smaller increase in output than the one before it did. It's one of the primary principles of economics, go look it up on Wikipedia. It's also applied often to Psychology (if you have something you like, the second satisfies you less than the first, and the third even less, and so on...)

The reason it applies to DA is simple: every increase in DA after the first gives you an increase in total output that is less than the +DA it gives you. Yes, the increase is linear with respect to the damage you would have done with 0 DA, but the fact is that 90% of the time you're not starting at 0% DA. You either have a Brutal Earring on, or you're a WAR and starting at 10% anyway. The reason is because you're not calculating it as (increase)/(base), you're calculating it as (increase)/(current).

So in the case of something easy like Brutal for WAR, it's going to be maximum 5/110 = 4.54%, and if you've already put 5 merits into DA, it's 5/115 = 4.35%. You have to compare this to other options in that slot, and the only piece better than it is Wyvern Earring, which gives a minimum increase of 5%. Of course, as redshift pointed out in his response to me, all of this has to be filtered through your current accuracy first, so it's always going to be a minimum 5% lower (i.e. 4.54% becomes 4.31% and 5% becomes 4.75%).

Edit: Sorry, just going to bring back the reason why I'm even explaining it when it's generally just a semantic issue. It's because some people (like the OP, for example) don't understand that 5 more DA doesn't always give 5 more attacks per 100 "swings".

I understand what diminishing effect is, the concept is pretty simple.

However, comparing the # of swing is rarely useful. We compare stats in term of damage increase they offer, and DA has a diminishing return on the damage it offers when you stack it.

[Cadsuane]

No you don't. The return is the difference, not the ratio. The ratio is relative. The return is constant.

[Kaylia]

Your function and your variable can be anything. You're simply defining it in a way that it's a direct relation

[Redshift]

Swings and rounds; the next semantics argument...

[Shinryuu]

DA has linear returns because only absolute damage matters and every 1% of DA yields an absolute damage increase of 1 swing per 100. 0% DA gives you 100 swings (some will be missed, yes, at least 5%). 100% DA gives you 200 swings, a 100 swing increase. Between 0% and 100% the amount of swings is linear.

"Why does only absolute damage matter?"

Because only absolute damage kills stuff.

Why are people arguing DA has decreasing returns (a phenomenom only observed in the case of say, high levels of labour intensity in factories; each worker will produce less units in a period of time the more labourers crowd the factory)? Because the percentual increase in swings decreases as the base level of DA increases. However, consider this: decreasing returns would mean 1% DA would give 1 more swing but 50% DA would give, say, 25 more swings. The opposite? Haste. 1% haste is 1 extra swing in a set timeframe, and 50% haste is 100 more swings.

"But the more DA I have the less effective adding DA is!"

Keeping all other factors constant, it isn't. But if you have to calculate the returns of say, 1% extra hitrate or 2% double attack, the cutoff point at 50% hitrate is 0% double attack (if you have more than that, pick the hitrate). It's just calculating the returns per variable, which is easy. Most equipment choices are between the one and the other. 1% haste (increasing returns!) isn't better than 1% hitrate in some cases. In other cases, it is.

I don't think there is a stat in FFXI that experiences diminishing returns to scale besides on a bigger level: the amount of members a LS has, the amount of healers/support a LS has, that kind of stuff (which is way harder to measure). Increasing returns would be haste, dual wield, (magic/physical) damage taken.

[FailureMidgard]

The fact that he had to change it to make it work for DW and H2H means it wasn't correctly set up. I'm sorry you fail to see that. Saying that you can't use "swings" and that you have to use "rounds" and then making a note in a later post that you have to multiply the rounds by 2 if using H2H or DW is retarded. If you use "swings" like you should in the first place then you don't run into that problem.

And back on topic with the semantics argument: Diminishing returns in respect to percentage DoT increase, Linear returns in respect to exact DoT increase.

No, if you use swings, there is diminishing returns. If you use rounds, there is no diminishing returns, get your shit straight at least.

[Thorny]

@Shinryuu: MDB has diminishing returns. For a 1000 base damage nuke with 50 MAB, the first point of MDB(1.50 / 1.01) takes the damage from 1500 to 1485, reducing damage by 15. The 50th point(1.50 / 1.50) takes it from 1007 to 1000, giving only 7 damage reduction.

[Shinryuu]

Damage taken is different, though, measured in survival time. Each point of -damage% reduces damage by exactly the same but going from -99% to -100% increases your survival time by infinity whereas going from 0% to -50% increases it only twofold. Too tired to see if this is the case for MDB but I'd say it's linear (whereas all other -damage is increasing).

[Deadgye]

No, if you use swings, there is diminishing returns. If you use rounds, there is no diminishing returns, get your shit straight at least.

They produce the same exact results ffs, linear absolute returns, decreases relative returns. Why the hell do you think I made sure to point out it was another semantics argument?

DW: 100 attack rounds, 0%DA ⇒ 5%DA = 105 attack rounds ⇒ 10%DA = 110 attack rounds.
Absolute increase of 1 attack round per %DA, relative diminishing returns.

200 swings, 0%DA ⇒　5%DA = 210 swings ⇒ 10%DA = 220 swings.
Absolute increase of 2 swings per %DA, relative diminishing returns.

Notice how the have the same exact absolute increase and relative increase due to the fact that 1 attack round = 2 swings in DW?

Back onto the semantics this thread is about though.. take a look at haste. At .2 swings / second if you add 10% haste you get .22222repeating swings / second and if you add another 10% haste on top of that you get .25 swings / second. Notice how the absolute increase is exponential? That's why haste is considered to have an exponential gain.

Really though, it's all relative. If you're comparing two pieces of gear looking at it any which way works, as long as you stick to the same method each time and don't say.. use the relative returns of DA vs the absolute returns of haste.

/semantics

[FailureMidgard]

They produce the same exact results ffs, linear absolute returns, decreases relative returns. Why the hell do you think I made sure to point out it was another semantics argument?

DW: 100 attack rounds, 0%DA ⇒ 5%DA = 105 attack rounds ⇒ 10%DA = 110 attack rounds.
Absolute increase of 1 attack round per %DA, relative diminishing returns.

200 swings, 0%DA ⇒　5%DA = 210 swings ⇒ 10%DA = 220 swings.
Absolute increase of 2 swings per %DA, relative diminishing returns.

Notice how the have the same exact absolute increase and relative increase due to the fact that 1 attack round = 2 swings in DW?

Back onto the semantics this thread is about though.. take a look at haste. At .2 swings / second if you add 10% haste you get .22222repeating swings / second and if you add another 10% haste on top of that you get .25 swings / second. Notice how the absolute increase is exponential? That's why haste is considered to have an exponential gain.

Really though, it's all relative. If you're comparing two pieces of gear looking at it any which way works, as long as you stick to the same method each time and don't say.. use the relative returns of DA vs the absolute returns of haste.

/semantics

No.

100 rounds.
0% DA = 100 swings (with a 2h).
0>5% DA = + 5 swings.
5%>10% DA = +5 swings
10% > 20% DA = +10 swings

Linear, ok. DA MUST NOT HAVE 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.

UH OH, LOOKS LIKE DA HAS DIMINISHING RETURNS!!!

Whether or not "DA" as diminishing returns depends on what you are plotting against it on the other axes (yes, that's plural on purpose). In reality, plotting it against rounds or swings is both useless. It should only be looked at multi-dimensionally as a part of the damage formula (along with accuracy, attack, base damage[str], and haste). When you look at a multi-dimensional equation with a starting point for each of those stats, it is very obvious that if 1 stat is raised significantly more on it's own, while other stats remain constant, the value of said stat lowers relative to other stats. IT DOESN'T MATTER WHAT HAS DIMINISHING RETURNS OR DOESN'T. A stat with diminishing returns can and will beat out a stat without it in a vast number of situations (or, 1 with static returns beats out one with increasing returns). This happens all the time with accuracy vs haste.

This whole debate is semantics, and 100% useless, and anyone who is actually arguing against me in it, really has no idea how these different quantities interact.

[Shinryuu]

Hey that's odd, tonight I was talking to Thorny how graphs would be three-dimensional with time on the third axis.

[Yugl]

All of this arguing is breaking our friendships apart.

This is the most correct statement of the thread.

No.
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.

Actually this statement isn't bad either.

[Charismatic]

It has diminishing returns.
/thread

[Abandon]

While we're discussing OP's post, let's add this to the fire:


How CHR effects enmity decay..... go