Direct Hit; how much is "enough"?

[Maero]

The thing with crit is you need such a high amount to see anything because basically it is a % chance of dmg happening were as other stats are more of a guarantee in dmg.
Now in the case of smn the better stat i guess is crit over DH because dots are involved but jobs like Red Mage DH is better

[Neela]

Now in the case of smn the better stat i guess is crit over DH because dots are involved but jobs like Red Mage DH is better

its not just the dots what makes crit interesting/needful for smns the most important reason is ruin iv since we need those procs more than ever since ruin iii and ww got nerfed imo : o

[Fannah]

In a way, flat multipliers are a diminishing returns by nature. Going from x1 to x1.1 is a gain of 10%, while going from x2 to x2.1 is a gain of 5% of your former dps. Even if you gained 0.1 in both case for the same amount of points.

Skill Speed and Spell speed are more efficient the more you put points in, in a way. Reducing 0.01 GCD from 2.50 is proportionnaly less powerful than reducing 0.01 from 2.00 GCD.
To take some obvious numbers, reducing 0.01 GCD from 0.02 GCD is an upgrade of +100% attack speed. While reducing 0.01 from 0.10 GCD is an increase of 10% attack speed.

[Shurrikhan]

None have (in themselves; see the post directly above) diminishing returns, but two double up on their gains (Crit and Speed, as the first also enhances the value of the extra chance given and the latter gives the same flat GCD reduction despite that becoming a greater and greater proportion of the remaining GCD).

As such, unless dependent on Crit or Speed, stats like Det and (as it may be overtuned for most anyways) DHit tend to be strongest at the very beginning of an expansion, but are quickly surpassed by Crit or Speed if you can get either high enough (either one a vast majority of your secondary stat total).

Edit: In general, unless you need a specific GCD (DRG, SAM, etc.) or you get procs from crits (Bard), you tend to be better off either avoiding or stacking Crit/Speed. The secondary stat options of your tier will largely make that decision for you, however. By next, we may well all be pushing for Crit and/or Speed.

[Remedi]

We are kinda already at the place where crit is overtaking dh last time I've heard

[Karshan]

its not just the dots what makes crit interesting/needful for smns the most important reason is ruin iv since we need those procs more than ever since ruin iii and ww got nerfed imo : o

Except crit has nothing to do with ruin IV procs, it's not like the SS buff from back then.

The trait reads : "Grants a 15% chance that a pet action will trigger Further Ruin, upgrading Ruin II to Ruin IV." Nothing in here involves crit, it's just 15% each time an action is used by you pet.

No the reason Crit is better is because it suits best the spiky damage profile jobs, which summoner is, (especially when the crits hit the spikes), as opposed to more linear damage profile like DRK, NIN or RDM, who benefit more from DH. Well at least when we were under 1500, now with the new caps, and with next cap in 6 months able to reach 2000 up to 2500-2800 k easily, I think crit will return as the sovereign secondary stat for most jobs.

[Kitfox]

its not just the dots what makes crit interesting/needful for smns the most important reason is ruin iv since we need those procs more than ever since ruin iii and ww got nerfed imo : o

Ruin 4 is triggered by pet actions, it has nothing to do with Crit.

No, the reason Crit is better is because it suits best the spiky damage profile jobs, which summoner is

That's also not the reason. Crit is preferred by a lot of classes because of its quadratic growth and its availability on gear, party compositions involving DRG/SCH/BRD/AST are also a factor in favor because of raid buffs that boost crit rate. Damage is compared using rotational simulators and the damage formula to find the best performing gear set. Crit scaling being quadratic in nature means that if enough of it is available on gear, it gets more powerful than the other stats with linear gains after a point. The point at which that happens depends entirely on the stat spread on the gear. If crit is paired with detrimental stats, like sks is in some cases, or if there's simply not enough crit on the gear, the gear set might not end up focusing on crit. The only jobs that have inherently crit skewed focus are the ones with class mechanics centered around crit, such as BRD or MNK.

[nand]

Hey,

I'm new to FFXIV and found this thread while searching for resources on how damage formulas work in this game. I thought it was an interesing enough question to try and answer conclusively via the power of mathematics. I used the formulas from the following website to calculate the effective DPS gain from crit / direct hit rating, respectively:

https://docs.google.com/spreadsheets...F38/edit#gid=0

The way I decided to approach the problem was by making the assumption that we have a "fixed" pool of stats to allocate from (say, 3000 rating in total) and it's up to us to decide whether we want to lean that pool more towards crit rating or more towards direct hit rating. That is, I assume that we're presented with a series of choices such as "would I rather have 40 crit rating or 40 direct hit rating?". In the context of this framework, the question is: how much should I lean towards one or the other?

One thing that we can see quite clearly is that for the upper end of what we can realistically achieve with current gear, critical hit rating alone completely dominates direct hit rating. But this is not always the case - there's a phase reversal somewhere at around 3000 shared total stat between the two. More fascinatingly, in a result that I didn't expect at all, in this "transition" region, it's worse to have a mixture (say 50% crit and 50% direct hit) than it is to stack 100% of either, even though they multiply each other! (This is a direct consequence of the fact that crit rating is essentially useless if you don't stack enough of it)

To best visualize these results, I decided that we should use "50% of each" as the baseline - under the assumption that on average, we'll always be able to balance the two stats as a baseline, and the question is how much we want to "lean" towards one or the other as a function of how much stat we have available. That formula looks like this:

https://www.wolframalpha.com/input/?...000,+0%3Cy%3C1



The short summary is that for <3000 total stat, you want to stack direct hit rating as much as possible. For >3000 total stat, you want to stack critical hit rating as much as possible. For ~3000 total stat, it doesn't really matter which one you go for - but always try to get as much as possible of the same stat, never mix the two.

The formula was generated using this haskell program: https://0x0.st/zz6d.hs

[nand]

The formula was generated using this haskell program: https://0x0.st/zz6d.hs

Reproduced here (too long for the original post):

import Data.Number.Symbolic

type Rate = Sym Double
type Chance = Sym Double
type Multiplier = Sym Double
type Distribution = Sym Double

baseRate :: Rate
baseRate = 364

critMultiplier :: Rate -> Multiplier
critMultiplier r = 1 + chance * bonusDamage
    where chance = (((r - baseRate) / 108.5) + 4.9511233) / 100
          bonusDamage = 0.4 + ((r - baseRate) / 108.5) / 100

directMultiplier :: Rate -> Multiplier
directMultiplier r = 1 + chance * bonusDamage
    where chance = ((r - baseRate) / 39.1) / 100
          bonusDamage = 0.25

statGain :: Rate -> Rate -> (Rate -> Multiplier) -> Multiplier
statGain cur inc f = f (cur + inc) / f cur

distGain :: Rate -> Distribution -> Multiplier
distGain pool dist = critMultiplier critRate * directMultiplier directRate
    where critRate = baseRate + pool * dist
          directRate = baseRate + pool * (1 - dist)

relGain :: Rate -> Distribution -> Multiplier
relGain pool dist = distGain pool dist / distGain pool 0.5

[nand]

Also, sorry for the triple post, but I wanted to dispel some of the claims made in this thread about the existence or nonexistence of "diminishing returns". While it's true that (assuming you haven't hit the 100% hard cap) Direct Hit rating is a "linear" stat, in a system of linear multipliers (which is pretty typical for games like these), it's generally better to balance your stats than it is to stack one. For example, if each stat "weighs" about the same on average, then instead of a 10% increase to one multiplier (=10% more damage), I could instead split them up to get two 5% increases (=10.25% more damage) instead. Mathematically, if stacking every stat into one linear multiplier results in a linear curve, then evenly distributing them across n linear multipliers results in an nth-order polynomial curve. Eventually, this will outscale the linear increase - it's just a question of how big your stat "pool" is. This phenomenon is what people often mean when they use the term "diminishing returns", but I think a better term for it is "opportunity cost". Or really, what's happening under the hood is sort of the "opposite" of diminishing returns - stats grow more powerful the less of a stat you have. So after a certain point, a badly scaling stat B will outvalue the well scaling stat A if the two become too imbalanced.

Incidentally, this can be generalized from linear stat systems to all systems of polynomials, including critical and direct hit rate. Indeed, once we go to absurdly high stat values (>50k and above) in the above graph, it again becomes better to mix your stats - because now you have a cubic scaling curve (quadratic scaling * linear scaling). So even though locally, critical hit rating seems strictly better than direct hit rating, we can still observe "opportunity cost" once going high enough. Of course, at that point, we hit the 100% hard caps anyway so this argument is moot - but it demonstrates a general concept, so I though I'd point it out.

That being said, the real question in practice is more complicated to answer (and depends strongly on the game), because the constant factor on each stat plays an important role in determining the stat weights within a bounded region (say, from 0 to 3000). The previous image illustrates that perfectly - the only reason direct hit rating outscales critical hit rating for low stat amounts is because the constant factor on it is better. So in some games it's still best to ignore all stats except the best one, if that stat is so good that it's better than the rest even after the "opportunity cost"; and it seems like this might be the case for FFXIV.