Diminishing Return on Stats

[EasymodeX]

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

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.

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

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.

[Viridiana]

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%).

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.

[Gamemako]

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.

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.

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.

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.

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).

[EasymodeX]

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

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

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

This isn't math class.

If anything, this is economics.

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.

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).

[Gamemako]

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.

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.