Diminishing Return on Stats

Hey. So talking with FC and raid mates about builds and stats, and the topic of diminishing returns came up. So I am curious to know if there are any solid numbers saying "You get diminishing returns on Determination after X amount"

I ask this because, if you reach the diminishing return number, sounds like it would be most beneficial to add stats into other slots to maximize what you can put on your character.

People throw around "diminishing returns" badly sometimes. If you start @ 100 of a figure, add 10, that's a 10% increase. Add another 10 to 110 and if you use 110 as the base #, you'll get a figure of less than 10% increase. But it's not, any increase should be compared to the original base #.

So there is such a thing as linear returns and as far as prime stats, det/crit/acc, give linear returns. Until cap. I've heard #s thrown around for a crit cap that was 520 ish I think? Haven't heard of a det cap, and acc varies by job and is easily googled.

skill/spell speed are a different ball game, and are effectively increasing returns with a cliff at the end.

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Originally Posted by Alistaire

I've heard #s thrown around for a crit cap that was 520 ish I think?

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I don't actually think there is a "cap" on crit, but there is a limited amount of crit you can get based on gear/food. "You can only buff a stat as high as the gear will allow it to go" sort of idea.

To elaborate more on the Skill/Spell Speed comment: These stats will lower the recast of your abilities by a very small amount, and it takes a lot to reduce the cooldowns by even 1/100th of a second. So instead of looking at Speed as a linear increase, you can see it as a "stairway" increase; that it rises sharply then stays flat for a long time. The other characteristic of Speed is TP/MP management. If you have high stats in Speed, your abilities execute faster, and your TP/MP drains more quickly. This can be a problem in longer fights, causing starvation where your DPS will plummet. And finally, the last point about Speed is that when you equip gear that boosts Speed, your not equipping gear that has other stats. For example you equip a ring that has +Speed and +Determination. You could equip instead a ring that has +Critical and +Determination. This matters when you factor in the above points. These ideas in combination are what Alistaire means when he says speed "returns with a cliff at the end". Too much speed is a bad thing, in general.

Yes, any "cap" is like that in this game; the stat will keep going, but stops helping after a point. Semantics. The difference is in knowing that just because your stat keeps going up, doesn't mean it keeps helping, where if you were looking for it to "cap" as in stop raising on your character screen despite you adding more into it...you won't see that here.

Yes above posts are correct, there are absolutely no caps in this game whatsoever. Every single stat has been proven by all data mined by players and all info from SE itself, to be linear. Every single point of anything is just as effective as the last point you put into it.


The only thing that slightly varies from this is speed, in that it hasn't been proven to be beneficial to have more speed. However the stat still increases your speed at a linear pace.
Accuracy would also fall under this category while increasing your accuracy will still give you an increase in accuracy at a linear level, it has no benefit once you hit 100% hit chance.

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Originally Posted by Alistaire

People throw around "diminishing returns" badly sometimes. If you start @ 100 of a figure, add 10, that's a 10% increase. Add another 10 to 110 and if you use 110 as the base #, you'll get a figure of less than 10% increase. But it's not, any increase should be compared to the original base #.

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If you go from 1% crit to 2% crit, that is a 100% increase in critical hits. However, going from 99% crit to 100% crit is a substantially lower gain. This, they told me, was diminishing returns - and it was bad.

Yet players require the same amount of statistical points to go from 1% to 2% crit as they require to go from 99% to 100% (against targets of equal level). In both instances, I am critting 1% more than before for the same price.

If that's the case, does this mean "diminishing returns" do not exist in any practical capacity until you reach 100% of a condition, or reach a cap arbitrarily set by SE? AND ALMA WAS RIGHT ALL ALONG? YOU BASTARDS?

That's not how diminishing returns works, 1% is still a helpful gain. From what I've gathered the only diminishing returns in this game in regards to starts is the middle areas for Determination and Piety. Main stats always give a boost, an equal boost at that.

Wouldnt diminishing returns to crit be like this if it existed; At 200 crit rating 14 rating increase crit with 1% and at like 500 rating you would need say 20 to increase crit with 1%. Just random numbers for an example. Like above posters have said, stats seems
linear.

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So instead of looking at Speed as a linear increase, you can see it as a "stairway" increase;

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It's not. That's only a reflection of the UI truncating numbers. A guy on reddit showed the detailed tests of Rez (8s base spell) and the cast time appeared to be reduced in 0.1s increments at the same ratio as a 2.5s base spell was reduced. E.g. the SS formula is probably a straight % reduction in cast time, with the game UI truncating.

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These ideas in combination are what Alistaire means when he says speed "returns with a cliff at the end".

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No. The cliff at the end of SS is because you cannot attack faster than you animate. If your animation takes 1.5 seconds, then your SS is essentially hardcapped at -1.0, whic is what, +1050?




But there seems to be a large amount of random imprecise / misinformation. Here are the facts:

1. There are two concepts. Diminishing returns and then something vaguely referred to as marginal diminishing value. Sometimes people emphasize the former by adding more words like "real DR, hard DR, formulaic DR, statistical DR". The latter is simply an economics concept of value comparison.

Formulaic diminishing returns is when the formula itself dictates that stacking a stat becomes significantly weaker. An example of this is an armor formula damage = damage / (1+armor). The damage reduction % in that formula has diminishing returns (but survivability does not, go figure).

The only real DR in this game is the value of %crit for River of blood procs. River of Blood has a %crit chance to proc every DoT tick. In a normal situation, the player has 2 or more DoTs active. All DoTs tick at the same time. Successful RoB procs on one DoT will eliminate RoB procs of the other DoTs, since you can only get RoB proc per tick. The statistical result of this is that RoB has diminishing returns from %crit. In other words, if you double your crit%, your RoB proc rate will NOT double. It will increase by an amount less than double.


Marginal diminishing value is the general result where stacking a stat becomes poorer from a value perspective. This is the basic concept of +10% crit when you have 0 base crit is worth +5% DPS. +10% crit when you have 60% base crit is worth +3.7% DPS. The more crit you stack, the less useful stacking crit is. This effect has a slow decay (each +1% decays the value by 1%).

Note: wannabe-smart people try to repeat the fact that crit rating -> crit% is linear and say it has linear returns. You know you're dealing with a pseudo-intellectual troll when they spam that every response as if it matters.

No one gives a ****. What matters is the value. Value in this case is DPS, because no one really cares what stat is giving them DPS -- they just want results. The marginal benefit in results does, in fact, diminish by stacking a single stat.


2. Spell Speed / Skill Speed has accelerating returns. Technically they're not exponential, like mathetmatically exponential. However, SS actually has accelerating (better than linear) returns. More SS makes SS more valuable. Pretty nuts.

However, the benefit of the acceleration requires a LOT of the stat to be stacked -- much more than is reasonable without killing your TP bar, or mana bar for most classes. BLMs are the only class that can meaningfully make use of stacking SS, and even for them there is some de-synergy since their UI phase has fixed ticks (mana regen ticks are not accelerated by SS, so they have to wait for the ticks regardless of how much SS they have).

For all other classes you can kiss your resource pool goodbye before you reach the SS levels where you start to really get strong DPS benefit from stacking the SS.

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Originally Posted by EasymodeX

Marginal diminishing value is the general result where stacking a stat becomes poorer from a value perspective. This is the basic concept of +10% crit when you have 0 base crit is worth +5% DPS. +10% crit when you have 60% base crit is worth +3.7% DPS. The more crit you stack, the less useful stacking crit is. This effect has a slow decay (each +1% decays the value by 1%).

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While I see how this could be construed as diminishing returns, in another sense, it isn't really. If all your other stats stayed the same and you only increased Crit, then each % increase would give you the same increase in total DPS.

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No one gives a ****. What matters is the value. Value in this case is DPS, because no one really cares what stat is giving them DPS -- they just want results. The marginal benefit in results does, in fact, diminish by stacking a single stat.

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Please, don't throw stupid statements like "diminish by stacking a single stat". Spell Speed has an increasing return.

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Note: wannabe-smart people try to repeat the fact that crit rating -> crit% is linear and say it has linear returns.

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It just depends of the point of view. If your boss gives you twice an increase of 1K, should you consider the second as a "diminushing returns" just because you were earning more ? And about the stats in general, stacking one is usualy not optimal just because they are multiplicating each other. This has nothing to do with diminushing return, the product of 2 linear functions is bilinear, not linear. The optimization problem is quite simple with Lagrange.

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Originally Posted by Viridiana

While I see how this could be construed as diminishing returns, in another sense, it isn't really.

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Yeah. The confusion comes down to context: return on <insert stat> for what?

Return on crit rating for crit% is completely irrelevant. What players want to know is what their return on X stat for DPS is.

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Originally Posted by Alcyon1

Please, don't throw stupid statements like "diminish by stacking a single stat". Spell Speed has an increasing return.

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L2r before clicking the reply button.

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2. Spell Speed / Skill Speed has accelerating returns. Technically they're not exponential, like mathetmatically exponential. However, SS actually has accelerating (better than linear) returns. More SS makes SS more valuable. Pretty nuts.

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I'm curious if there is more to this that we will see with a level cap raise.

I never checked what the base stats were at level 1 and I don't have a level 1 DoW/DoM to check now but....

If the GCD is 2.5s with say 20 SKP @ Lvl 1 (base stat) and the GDC is 2.5s @ lvl 50 with 341 SKP (base stat) then
either the floor for the GCD is 2.5s and we only started to see the effect @ 341 SKP for it to start going down, or it is relative to
Base Stat + Character Level. (Greater returns the higher level we get)

Has anyone done any low level skill speed testing to see the amount of SKP required to get the GCD to budge a little?

Anecdotal evidence points to low level = doesn't need much SS to get improvement. Which means if the level cap is raised, then it would take more than 10.5ss to get 0.1s off the GCD.

EasymodeX : if you don't change the other stats, X CRIT = Y DPS. This is the definition of LINEAR in terms of DPS.
What you are talking about is X CRIT = ? %DPS. There, it depends of your base crit. Example ?

My base DPS (with 0% crit) is 100.
At 0% crit : I increase my crit by A, giving me 0+X% crit. Conclusion : my DPS increases of X/2 or X/2%.
At, let's say 50% crit (my DPS is 125 now) : I increase my crit by A, giving me 0+X% crit. Conclusion, my DPS increases of X/2 or X/2.5%.

SPS is theorically the best stat for BLM's, but many people like to see big numbers. Some statistical tests showed how full SPS > full crit. Since SPS has an increasing return .....
PS increasing return = better than linear by definition.

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EasymodeX : if you don't change the other stats, X CRIT = Y DPS. This is the definition of LINEAR in terms of DPS.

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It's not linear in terms of +% DPS, which is what you want to know. You want to know this to compare it against other alternatives, like DTR or SS or w/e.

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At, let's say 50% crit (my DPS is 125 now) : I increase my crit by A, giving me 0+X% crit. Conclusion, my DPS increases of X/2 or X/2.5%.

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Your DPS increase is [(X/2)/(125)]% which is less than [(X/2)/(100)]%.

The second increase is decayed because you already have 50% base crit.


Edit: Why am I even bothering? You either get it or you don't. This conversation has been repeated a hundred thousand times on MMO mechanics discussions across the internet.

I get it, I just say :
THE INCREASE IS LINEAR IN TERM OF FLAT DPS (DAMAGE PER SECOND) and NOT LINEAR IN TERM OF %DPS. Stop forgetting to say EXACTLY what you're cheking. If your DPs is 250 and after some changes in your stuff, your new DPs is 275, you can say about your DPS "the increase is 10%" or "the increase is 25", both are correct. When you are testing/calculating your DPS, you are just checking the final outsome and not the increase in %. You are taking the highest DPS as the BiS.

The original post for this thread was asking if there are diminishing returns on stats, the answer is no.


Skill speed/spell speed/accuracy do not apply to this conversation please do not include them. They have also been addressed.

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Originally Posted by Alcyon1

Stop forgetting to say EXACTLY what you're cheking.

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There's only one thing to check when you're changing your stats for tradeoffs -- how much your DPS is increasing relative to your prior DPS.

Edit: As a sidenote, there no need to say 'exactly' what you're checking every time, because there's only one thing that's relevant. Furthermore, in the english language and human communication in general, it's up to the reader/audience to interpret the context. No one is willing or should be liable for spelling out an essay every time they refer to something.

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When you are testing/calculating your DPS, you are just checking the final outsome and not the increase in %.

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When you compare incremental changes in gear or food or changes in rotation you are checking the increase in %.

There's almost no case off the top of my head where you check the absolute value. Edit: Well, there's no case when you're actually trying to have a meaningful discussion. The only case where you use absolute values is when you're comparing to extremely specific configurations. Otherwise, the absolute values lose context and relevance.

It's like talking about total damage on a parse. Useful if you're comparing two players of the same party in the same attempt, but pretty irrelevant for discussion.

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Originally Posted by MythToken

The original post for this thread was asking if there are diminishing returns on stats, the answer is no.

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Crit has DR for Bards. Sod off.

It does not/ prove it. Every point of crit increases your Crit by the same amount. That = linear returns.

How that affects your DPS in conjunction with other stats is not what you call "diminishing returns" thats called stat weights and it is very different.

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Originally Posted by MythToken

It does not/ prove it. Every point of crit increases your Crit by the same amount. That = linear returns.

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Hahahaha.

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How that affects your DPS in conjunction with other stats is not what you call "diminishing returns" thats called stat weights and it is very different.

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Diminishing returns applies to whatever you consider the input and output.

I think most Bards care about their DPS, not their exact %crit.

It really doesn't, and so far no data supports anything you are saying. Every point of crit that they put in will increase their crit the same amount. Every increase in crit% is an increase in dps.

There is nothing to prove otherwise.

Do you even River of Blood?

I lift bro, all the time.

In Math, if you say "DPS isn't linear in crit rate (the correct term should be affine, but let's forget about it)" is wrong. You specified a variable (crit) and a function (DPS) and the last formula is (for the part affected by crit, but you add a constant for the part not affected by crit) DPS = baseDPS * (2+0.0697*crit–18.437)/2 and this is a line, i.e an affine function (linear if you want). Now, since you specified CRIT ad the variable and DPS as the result, no we shouldn't understand "increase of DPS in %". In this case, the situation is a little more complicated : you have 2 variables (old crit O and increase in crit I) and the formula is : %DPS = DPS(O+I)/DPS(O) - 1. this function is of course affine in I but not in O, and that's what you are calling "diminushing return" : for a same increase I, the answer is a decreasing function of O.

If I ask you, durng an exam "is DPS linear in crit" and your answer is no, you failed the question.

One thing oddly absent from this discussion: abilities also diminish the relative returns of certain stats. Automatic critical hits and other flat critical hit bonuses (Internal Release, for example) reduce the relative returns from the critical hit rate stat. Also worth noting that Determination appears to also suffer diminishing relative returns to strength; i.e. it is at least partially additive with strength rather than multiplicative.

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Originally Posted by EasymodeX

It's not. That's only a reflection of the UI truncating numbers. A guy on reddit showed the detailed tests of Rez (8s base spell) and the cast time appeared to be reduced in 0.1s increments at the same ratio as a 2.5s base spell was reduced. E.g. the SS formula is probably a straight % reduction in cast time, with the game UI truncating.

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As a note, this reduction is applied after most other bonuses and is additive with them; for example, Greased Lightning reduces your GCD natively to 2.125s, and skill speed still reduces by 0.00069s per point thereafter (rather than 0.00059, which it would do if it were applied beforehand and then reduced by the 85% factor from GL3). I believe Fey Light at the very least is an exception, acting directly on the Skill Speed stat itself.

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Originally Posted by EasymodeX

However, the benefit of the acceleration requires a LOT of the stat to be stacked -- much more than is reasonable without killing your TP bar, or mana bar for most classes.

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This is true, though not really the reason everyone hates skill speed. The damning thing about skill speed is that it fails to affect autoattacks, off-GCDs, and DoTs (barring situations where reapplication is naturally delayed by things like Jump), which in total comprise upwards of half of total DPS for all DPS jobs but BLM. Accelerating returns can't touch that one way or the other. Until they fix it so the stat affects autoattacks at least, the only job deliberately taking it will continue to be a tank. If it did affect at least autoattacks, it would be nearly as valuable as any other stat for many jobs (especially MNK).

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Originally Posted by Alcyon1

no we shouldn't understand "increase of DPS in %".

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That's the context of the discussion of MMORPG damage optimization with incremental stats/gear. So yeah.

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If I ask you, durng an exam "is DPS linear in crit" and your answer is no, you failed the question.

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This isn't math class.

If anything, this is economics.

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Originally Posted by Gamemako

The damning thing about skill speed is that it fails to affect autoattacks, off-GCDs, and DoTs [...] Accelerating returns can't touch that one way or the other.

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Well, the fact that it doesn't affect AAs and oGCDs simply sinks the initial value of SS for classes that have those. The acceleration still happens and is still relevant. Specifically, Monks, due to the GL stacking as you noted earlier (increasing the initial value for SS), get just about / almost as much value from SS as they get from crit (crit gets chunked down with diminishing marginal returns on normalized value due to the BS autocrits and traited IR that you also mentioned).

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Originally Posted by EasymodeX

Anecdotal evidence points to low level = doesn't need much SS to get improvement. Which means if the level cap is raised, then it would take more than 10.5ss to get 0.1s off the GCD.

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Ouch. Does that hold true for the 5% base Crit @ 341 as well?

So higher levels = less potency per point on all secondary stats but DET?

Probably. I guess we'll find out ifwhen they raise the level cap. DTR may have a player level coefficient as well, dunno.

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Originally Posted by EasymodeX

Well, the fact that it doesn't affect AAs and oGCDs simply sinks the initial value of SS for classes that have those. The acceleration still happens and is still relevant.

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I'm just saying that the TP really isn't too much of an issue in practice, but the other disadvantages pretty well relegate the stat to niche status. Adding autoattacks would at least give MNK another stat to consider; right now, DTR is twice as valuable as either alternative.

DTR isn't twice as valuable from an item budget perspective. It's only 40-50%-ish, or something.

If SS applied to AAs/DoTs that would be nifty but it would be overpowered / the direct effect of SS would need to be toned down. On the flip side SS works fine for BLMs, so implementation would require SE to split the way SS is applied between abilities and AAs -- toned down for DoW classes and normal for DoM. Probably not worth the complexity to manage from their end.

Basically the current argument is as follows:

1+1 = 2. 1 is merely half of 2, so it's a great return on that 1.
2+1 = 3. 2 is over half of 3, so that 1 was not a 1 well spent.

VS.

A+B=C. But B+C=D. So A is worthless.

VS.

1 = 1.

I thought determination, critical hit rate and skill speed all improved per-point as you stacked more of them? as in X amount is > than Y amount of the same stat, then an individual point of X is more effective than an individual point of Y.

Just do your job well, and it won't matter unless you gotta put on your lifting belt for bad teammates. >.>;

Pretty much people will be at the whim of RNG for a while so may as well just not think too deeply about it. Like if you got a token to upgrade a weathered item, but you got drg coil hands (not "BiS supposedly) you probably aren't going to go upgrade the weathered hands. Logical thing would to be upgrade another piece of armor with the token.(Cause main stat > all)

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Originally Posted by Arklyte

I thought determination, critical hit rate and skill speed all improved per-point as you stacked more of them? as in X amount is > than Y amount of the same stat, then an individual point of X is more effective than an individual point of Y.

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Crit, accuracy and det have a linear rate of return. One point of crit/det/acc is as valuable as another, regardless of whether you have 50 of them or 500 of them. This is true until you hit a logical cap (100% accuracy, 100% crit rate) or an arbitrary cap set by SE (something below 100% crit rate, something below infinite determination).

Skill speed has an increasing return; the more speed you have, the more valuable the next point is. This continues until you attack so quickly you travel back in time to 1.23 when the battle system was good, or your attack speed gets artificially limited by your combat animation.

Unless you're a Bard. Then crit has diminishing returns for DPS.

Well, I'm certainly not a math guru like some people here... I can however share some RL testing I did on my bard with a parser.

At 520 Crit, I auto atk a dummy for 15 minutes and my crit rate was 20%.
At 575 Crit, for the same time on the dummy, my crit rate was also at 20%...

So all I can tell you, for me anyways, after 520 crit, I don't find any increase.