Bard : Are there Diminishing Returns on the Crit Stat?

Topic title. Can't really get a feel for the actual values of increments. Would the crit stat become less efficient than det by-the-point after reaching a certain threshold?

It's probably best not to invest too heavily into it since at a certain point, having more crit rating only means you have less determination or skill speed. Not to mention that over investing will cause your dps to shift wildly depending on your luck.

Directly, no. 13-14 crit from gear or food equals +1% crit chance.

Indirectly, yes, there is a diminishing value on crit. Simply because +1% crit isn't very valuable if you have a high crit rate already. In terms of numbers:
+1% added while you have 10% crit rate means you get 10% more crits on average (from 10% to 11%)
+1% added while you have a 20% crit rate means you get 5% more crits on average (from 20% to 21%)

For more extreme measures: Let's say you have 50% crit rate. 1% isn't really going to matter here. Or the most extreme one: +1% while you have a 98% chance to crit is nearly pointless.

Quote:

---

Originally Posted by Lyrica_Ashtine

Indirectly, yes, there is a diminishing value on crit. Simply because +1% crit isn't very valuable if you have a high crit rate already. In terms of numbers:
+1% added while you have 10% crit rate means you get 10% more crits on average (from 10% to 11%)
+1% added while you have a 20% crit rate means you get 5% more crits on average (from 20% to 21%)

---

Of course, the opposite side of that math is that +1% crit is the same amount of DPS (all else being equal, of course) no matter if it's your 11th percent or your 100th.

Quote:

---

Originally Posted by Viridiana

Of course, the opposite side of that math is that +1% crit is the same amount of DPS (all else being equal, of course) no matter if it's your 11th percent or your 100th.

---

Both true as well as false, as strange as it sounds. While every single percent crit has a steady DPS increase, which theoretically +0,5% for every 1%, it does not come at a cost. Considering how gear works right now you're sacrificing stats from another category to increase one. So it's actually less than +0,5% dps increase for every 1% crit chance increase. While at start it's only marginal, at one point Determination would outweight Critical hit rate. Although, with current gear I don't think we can reach a point where crit would weigh less than det right now - For a bard anyway. In the future, perhaps.

Quote:

---

Originally Posted by Lyrica_Ashtine

While every single percent crit has a steady DPS increase, which theoretically +0,5% for every 1%, it does not come at a cost. Considering how gear works right now you're sacrificing stats from another category to increase one. So it's actually less than +0,5% dps increase for every 1% crit chance increase.

---

Right, I grant that the tradeoff may stop being worth it, but if you could maintain all other stats equal, a 14 point change in crit will always be the same (with those other stats constant). I just don't like calling what crit does "diminishing returns."

Quote:

---

Originally Posted by Viridiana

Right, I grant that the tradeoff may stop being worth it, but if you could maintain all other stats equal, a 14 point change in crit will always be the same (with those other stats constant). I just don't like calling what crit does "diminishing returns."

---

I didn't refer it as diminishing return, I mentioned it has diminishing value

Quote:

---

Originally Posted by Lyrica_Ashtine

I didn't refer it as diminishing return, I mentioned it has diminishing value

---

Fair enough. Too used to seeing everyone call it diminishing returns.

You're both right.

Crit has Marginal Diminishing Returns. Every point of Crit you stack will give you the same linear returns in damage, no matter if you have 400 Crit Rate, or 700 Crit Rate. But, the overall percentage of this damage value decreases each time your Critical Hit Rating increases.

This link has all of the Crit rate testing/theorycrafting.

585 Crit is aproximately 22-23% Crit rate from the looks of it. Unless im reading that wrong. Someone else in the comments mentioned that those numbers actually translate to a 40% Crit rate but i'm not sure.

at 605 crit all my damages(skills, auto-attacks, dots) averages around 40% or more per encounter.

Quote:

---

Originally Posted by ChriZirhC

at 605 crit all my damages(skills, auto-attacks, dots) averages around 40% or more per encounter.

---

How about some more concrete numbers, because this reeks of baloney

Quote:

---

Originally Posted by Lyrica_Ashtine

How about some more concrete numbers, because this reeks of baloney

---

I would but is it even allowed to post screenshots of parses here?

Quote:

---

Originally Posted by Lyrica_Ashtine

How about some more concrete numbers, because this reeks of baloney

---

I did some more concrete analysis today, from my fcob parses i had between 40 and 35% crit rate on the 3 fields autos, skills, and simulated outgoing dots, simulated outgoing dots were the lowest at 35-37 and skills were the highest at 39-40+ (im posting this from memory based on a conversation i had with another bard this morning on crit scaling) this is at 577 base crit + flint caviar. I didn't feel like popping a flint caviar again to see what my crit was at the time of the parses or taking the time to plug my gear into ariyala to let it calculate the total but needless to say its probably a little over 600 crit. This is mostly accounted for by the 10% flat buff from straightshot (straight shot procs explain why outgoing spells have the most crits) and by internal release.

Quote:

---

Originally Posted by PROBOUND

Someone else in the comments mentioned that those numbers actually translate to a 40% Crit rate but i'm not sure.

---

Quote:

---

Originally Posted by MrYaah

I did some more concrete analysis today, from my fcob parses i had between 40 and 35% crit rate on the 3 fields autos, skills, and simulated outgoing dots, simulated outgoing dots were the lowest at 35-37 and skills were the highest at 39-40+ (im posting this from memory based on a conversation i had with another bard this morning on crit scaling) this is at 577 base crit + flint caviar. I didn't feel like popping a flint caviar again to see what my crit was at the time of the parses or taking the time to plug my gear into ariyala to let it calculate the total but needless to say its probably a little over 600 crit. This is mostly accounted for by the 10% flat buff from straightshot (straight shot procs explain why outgoing spells have the most crits) and by internal release.

---

40%+ every encounter is a bit sketchy, unless you're blessed with god-like luck, but yeah, that Crit% range is beyond reasonable.

At 577 base Crit, +5% is 28.85, giving you 605.9 Crt.

605.9*0.0697-18.437 = 23.79423

23.79423 /100+10%*15/60 = 26.29423+10 = 36.29423% IR adjusted Crit% with Straight Shot uptime at 100%

There's no such thing as "Bard crit scaling". That's just the standard Crit formula, but the Crit% is stacked up higher due to Straight Shot uptime.

flint caviar is 4% and it ends up being 599 crit that i had for the encounters. 36% sounds just about right, you have to remember that the 40% number was outgoing skills which includes autocrits on straightshot. also I think im probably squeezing out more than the standard number of crits from internal release since im making sure to always line it up so i refresh my dots during it being up, which ends up making it so i think more than ((15/60)*100)% of my dot's tick time is buffed, not super positive.

Thanks for all the input. I assume the 40% crit from 550~600 value is before buffs such as straight shot and IR? Having my crit rate float around there seems to be reasonable.

No... It would be after buffs such as IR and Straight shot. 575 CRT is inbetween 550-600, so:

575*0.0697-18.437 = 21.6405% Crit Rating unbuffed.

Next time I'll ask for screenshot and remove the names so no one gets in trouble. The numbers seem right though. Between 35% and 40% for bards. It is believed that 550 crit gives you give.you about a 20% chance to crit. Straight shot is believed to give you 10% to 15% on top of your base crit.

I'll try to remember to post some ss when I get home. I'm going to paste this here, i did some testing which i posted in a reddit thread

So i did a test run myself with the highest crit rate chance i could achieve, i had 668 crit points, I ran the test for 1hr 17minutes (approximately two apkallu omelettes) and just auto attacked a dummy non stop, autos only no crit buffs or anything.
My results were that out of 1,431 attacks I landed 413 critical hits. This comes out to 28.86%, the expected number of crits based on valk's linear fit line is 27.81%.

Continued on next page

Continued

Now by my own admission earlier 1.4k attacks is not really enough to establish a really high confidence test, this could explain why mine was a full 3.6% higher crit chance than expected, but I mean either way it falls reasonably close and the fact that the error happened on the high side strongly refutes the idea that crit % gains per crit point start deminishing in the 500's, this is a solid 150 points higher than you claim it started to be less valueable and it continues to be well fit by a linear equation. I'll probably try grabbing all the crit % chance data from valk's stuff and from the bluegartr post and put those into numpy and attempt to recalculate the constants from valk's equation for a longer fit line, but im fairly confident a linear equation will continue to be the best fit up into the 700+ range

I feel like this thread got distracted by the whole how much crit does straightshot and internal release add question, which is rather off topic. For bards does is there a diminishing value for higher crit chance? Yes, but its marginal and so far it doesnt look like det will outweigh crit any time soon.

Diminishing returns of crit come from the increased chance of procing bloodletters twice (or more if you're multidoting) on the same dot tick. worst case scenario is that you're at 100% crit rate and critting every dot tick on every dot, which gives you a 50% chance of procing for each dot you have out, for single target dps theres a 25% chance you will proc 2 bloodletters, multidotting makes the math more complicated than i want to deal with.

stupid 1000 character limit

Either way when you're losing 25% of your procs the value that bloodletter adds to crit is decreased by 25%. If we assume, without the rivers of blood trait, that crit would have approximately the same value for bard that it does for other physical dps then we can assume bloodletter adds .1 dex weight per crit point to the value of crit, at 100% crit you'd be at .305 instead of .33, this is slightly less than det, but the problem with det is that it caps at a much lower number, even in a worst case scenario you're probably going to end up prefering crit heavy items because they offer so much more crit and will still have a higher stat weight. We're well short of this worst case scenario and with the way the scaling works (only proc 50% of your dot crits) you're not going to be anywhere near the point where double proced bloodletters are a problem let alone anywhere close enough to making them worse than det.

#1 napkin math

You'll start encountering diminishing returns of crit when the baseline of gear on a bard allows the bard to reach an average of 50% crit. Off the top of my head, that should be around 800 CRT.

But, you have to remember that the weighting of CRT is directly affected by Strength. So yes, even if there are diminishing returns for Bards due to Bloodletter procs and naturally the weighting should decrease due to this sole reason, CRT weighting will still increase because of DEX and WD increases.

Also if the bard never had bloodletter procs, then its weighting would be in the 0.23X range.

Yea, .23x effective dex for the non rivers of blood crit weight is what i assumed in my calculations. Also what makes you say 50% crit is a break point for diminishing returns? As far as i can tell the returns scale down as you increase crit rate but theres no break point for this and what i was argueing was that even at 100% crit you're still going to build det over crit.

Just to redo the napkin math with 50% crit rate, lets simplify this to single target dps because I dont wanna have to bust out my statistics book to figure out how to calculate the chance of more than 2 procs happening out of 4 possible events because theres a bunch of different distinct events that could cause this. Either way

Is there any way to remove the 1000 character limit?

chance of procing both bloodletters is (critchance*procrate)^2 or (.5*.5)^2 = 6.25%. essentially at 50% crit you will be wasting a bloodletter proc on 6.25% of your dot ticks. I think the way to do the math is to compare a perfect world where you can get a double proc and it counts as two bloodletters and give that a weight of .1 dex, then figure out how many bloodletters you'll get in the real world where its either none procs or some procs. Either way we're getting into that math that I cant exactly remember how to do off the top of my head. I'm gonna go discuss this with a buddy of mine who hopefully hasn't forgotten or possibly ill google it, either way ill come back with the lost effective stat weight from bloodletter at 50% crit.

So, im pretty sure, when you're allowing for overlapping bloodletter procs you just double the number of bloodletter procs you'd expect from a single dot at 50% crit, so

Perfect World
(.5*.5)*2 = .5, so half a bloodletter every dot tick

Vs Real world the equation for bloodletter procs is
chanceboth proc + 2*(chance one procs and one doesnt)
=(critrate*procrate)^2 + 2*(critrate*procrate*(1-(critrate*procrate))

https://docs.google.com/spreadsheets...it?usp=sharing

so at 50% crit chance you should get .4375 bloodletters per dot tick

continuing math

.4375/.5 = adjustedbloodletterdexweight/.1

adjustedbloodletterdexweight = .0875 so adjusted crit is now .3275, still more than det, and even if it was less than det its closer than the difference in stat caps (where you get 2 det for every 3 crit, look at materia to see this most clearly)

And this number is actually lower than the actual adjusted number would be since the current statweight for crit, is .339 and its safe to assume that that was calculated with a fair amount of critrate. One of the assumptions is that the current statweight was calculated in a perfect world where you never lose any bloodletter procs, but the stat weight was likely calculated at a lower crit % where you still lost some bloodletters.

If you edit your post you can get by the 1000 character limit, and continue to add to it.

You're calculating the effective weight on CRT just through BLprocs, without factoring DEX/WD/DET values, or how CRT naturally works on the jobs rotation. At 50% CRT, that may well be the weighting when accounting for BLprocs alone, but that effect is greater when you take into consideration the rotation itself. When factoring the rotation, keeping the same stats I used to calculate the original weights, CRT weighting falls down to 0.281.

This is natural and applies to more jobs. More Crt = Decrease in weighting.

Also, the weights were calculated with 556 DET, which is a good baseline to work with the Bards Stat-Weights, when looking at the current tier of gear. We're not calculating weights due to bloodletter procs. We're taking into account other stats, as well as the normal rotation of the bard. That is something you're forgetting.

And yes, they are calculated in a "perfect world scenario", as it'll be impossible to calculate RNG, latency or a persons twitch reflexes into a model. Therefore, CRT and BLprocs have been averaged out.

Quote:

---

Originally Posted by Dervy

At 50% CRT, that may well be the weighting when accounting for BLprocs alone, but that effect is greater when you take into consideration the rotation itself. When factoring the rotation, keeping the same stats I used to calculate the original weights, CRT weighting falls down to 0.281.

---

How? Please explain and include all the math you used to arrive at this .281 number. I don't see how rotation could possibly affect the effectiveness if crit, its just a damage modifier, it should not matter how you hit the boss 1500 times, crit doesnt care, it will take your crit % number of those hits and multiply them by 1.5

556 det, is that a typo? The most a bard can get at bis is around 350

And im not forgetting that other statweights affect the value of crit, im intentionally simplifying the calculations to attempt to get ballpark estimates of how increasing crit could cause the stat's value to go down, im not trying to come up with a fundamental equation that can tell you at any point the exact statweight of crit given 20 other variables, that kind of calculation is completely unrealistic. The only question I'm trying to answer is how increased crit % decreases the value of each crit point. You can basically assume that your det dex etc are all exactly the same for every value of crit in this calculation. As far as I can tell the only factor that diminishes the value of crit is a missed bloodletter proc, I don't see how comes into this at all. And from all the math I've seen and done myself I know that crit % scales linearly as crit points increase and that this pattern has continued from 341 crit up into 670 crit and so for the time being i must assume that this will continue to follow the same pattern given the lack of evidence to the contrary.

But yea I'd really love to see a good explanation for how a bards rotation can affect the value of crit, if you mean are they dropping their crit buffs or letting bloodletters go unused for long enough to miss another bloodletter proc then that bard is just playing incorrectly. Theres only one situation where a bard can unavoidably miss a bloodletter buff other than having more than one dot tick proc at the same time. Thats if you have no bloodletter procs for an entire BL cooldown and it comes off cooldown on its own RIGHT before the server calculates the dot tick. even if you're spamming bloodletter as hard as you can to put it back on cooldown theres a miniscule chance that the bloodletter proc will be calculated during the time it takes for the server to acknowledge you using bloodletter and you can get fucked, in theory. Other than that though every time you get a proc you have 3 seconds to use it before you're at risk, thats a massive amount of time and therefore can be ignored in the calculations, the assumption is that every bloodletter proc you get gets used. I am technically ignoring the fact that as crit gets higher you're getting less of those "natural" bloodletters from the 12 second cooldown so the 12 second cooldown of the spell itself becomes less valueable but once again you're already not getting many natural bloodletters so I dont see why i should further complicate the math by some likely negligible factor.

Because Critical Hit Rating has marginal diminishing returns, which is what I posted back in page 1. Everyone knows this already. Here's copypasta because I cba getting more numbers.


Going from 0% Crit to 10% Crit increases your damage by 5.00%.
Going from 10% Crit to 20% Crit increases your damage by 4.76%.
Going from 20% Crit to 30% Crit increases your damage by 4.54%.
Going from 30% Crit to 40% Crit increases your damage by 4.35%.
And of course, going from 99% Crit to 100% Crit increases your damage only by 0.33%

Each time your Critical Hit Rating is increased, the overall % damage increase will continuously decrease. That's a fact and no math can prove otherwise. Yes, the gains on Critical Hit Rating are of course, Linear, which you clearly do understand and which I can see from your math. Everyone knows Critical Hit Rating is linear. But that doesn't change the fact an increase of Critical Hit Rating will decrease it's relative value, as the overall percentage damage output is decreasing.

That IS a fact and has already been established. Also, it doesn't just "affect a Bards rotation", it affects all jobs across the board.

We've literally gone full circle here. I literally cannot break this simple down than this.

Here's your proof. http://puu.sh/fqz8h/b59e0cd1ed.png

But oh wait, we've forgotten to consider the increase of WD/DEX/DET as well once we reach 800 CRT, as those directly affect the weighting of Critical Hit Rating.

http://puu.sh/fqzv5/42dfe41a17.png

And I meant 556 Critical Hit Rating, my bad.

I'm a bit confused by the those spread sheet images and would love to have those numbers explained.

As for that copy pasta its in my opinion misleading and copied straight from krietors bard guide. I've already talked to him about it. Heres a recreation of the math followed by a correct representation https://docs.google.com/spreadsheets...it?usp=sharing

if you look at the old / new column you'll see that you get the exact numbers from the copy pasta, 5%, 4.76, 4.54, etc. This is calculated just by taking the current dps number and dividing it by the previous one. if you look at the next column its calculated by subtracting base dps from the total, giving you dps gained from crit, which is a much more relevant statistic.

The problem is that you're adding the first 10% to the base damage and comparing that to the addition of the next 10 crit, the correct way to calculate it is the amount of dps from base crit adds at each %, 10% adds 20 dps, 20% adds 40 (20 + 20), 30% adds 60, (20+20+20). Theres no diminishing returns, it is the definition of linear, the equation of the fit is a linear equation, y = ax+b. To say otherwise is wrong.

https://docs.google.com/spreadsheets...gid=1531556508

Everything is decreasing, isn't it? I have nothing else more to show to you.

I'm still looking into the formula you used here and i'll have to check out this EMX's hybrid model that was mentioned to get a good idea of how stat weights are calculated

Not that it really matters but you made a mistake in the formula when you used the dex value instead of det for the last portion of the expected dps calculation. Based on the written out equation (str means im guessing this ss was being used for dragoon?) the last portion ($B$8*($C$8-202)*0.00108) should be ($B$8*($D$8-202)*0.00108)

Other than that though I havn't really drawn any conclusions based off of this math. I'll dig into it and let you know what I think, thank you for the post.

http://forum.square-enix.com/ffxiv/t...Formula-Thread

Stat weights.

• First, you get a fully working rotation or sim which models out the PPS.
• Second, you find the baseline the jobs stats as per ilvl. Each time there's an ilvl increase, the baseline of stats will be changing
• Third, after you've found your baseline and the PPS, you plug it into the damage formula
• Fourth, you increase the stat increments by +5 to find the delta
• Fifth, divide the delta, or the change in dps, by the baseline dps.

There's how you calculate stat-weights.

Also, here's a link to EMX's old hybrid model/sim. It's completely out of date however (last updated like last year march lol). The current version I'm using is one that I've updated myself, which includes NIN, PLD and WAR models.

http://www.filedropper.com/ff14

EDIT: Changed that mistake I made. Thanks for pointing it out. Regardless, you'll notice the same pattern.

And yes, the formula was written out for Dragoons (hence the use of STR), but the same formula is used for jobs using DEX and INT.

Thal's Balls thats a complicated looking spreadsheet, Its going to take me a while to completely absorb all of this but sofar i can see that the basis of the rotation is ss vb wb hs hs hs hs which sounds about right, I've gotta double check when i get home that the timing lines up after the 5th hs. I figure making sure i understand how the bard rotation calculations are done is key to getting to the point where I can comment on them and, if I find that I don't agree with the methodology, refine them.

One thing to remember is that Straight Shot 10% boost is plugged into the rotation, rather than being a modifier as observed in X2. So the Actual CRT is 10%+X2.

Also in column "I", there's numbers going down. That basically displays the timer left on the Straight Shot buff. The same applies for columns "C" and "F" for Windbite and Venomous Bite. It looks complicated at first glance, but it's actually really simply to read and understand.

The main plugins from Bloodletter are all in AC - AF.

If I'm perfectly honest with you, I'm still learning how EMX set-up the bard model, especially for Bloodletter procs. I really should ask him...

One other thing, "Stupid" is the Trait that multiplies all bards outgoing damage by 1.2.

When people say "dimishing returns" really all they mean is what Dervy mentioned. 5% -> 10% crit is WAY better in terms of "Bonus Damage from Crit" than say, 25% -> 30%.

Crit just gives less "DPS-per-point" the more you stack, though an exception is made with Bard due to River of Blood. (if Crits were +100% like they are in a lot of other games, this effect would be much more noticeable)

I see, yea that doesn't actually look consistent with how I generally clip my dots. This might be a difference in skillspeed resulting in my having the augmented ironworks bow but I've always clipped my ss buff at around 4 seconds and reapply my dots right as the 1 on the timer disappears, (so im assuming somewhere around the .8 second mark).

I'm not sure this is optimal or not, I think im going to do this gcd timing thing myself based on my gcd and compare it to how things work out ingame and try to get a rotation potency number that im confident in. Also I'd want to make sure that the Bloodletter constant takes into account the opportunity cost of letting your dots drop off since you probably arnt going to be happy if the server dot tick occurs when one of your dots isnt on the boss.

EDIT:

from the ss the dps is =SUM(AB30:AC30)*(1+0.1*20/80)

is this just the sum of auto attack and rotation dps * the effect of blood for blood? If so I think it might be better to account for the blood for blood modifier in the rotation or ignore it if you're already ignoring the other buffs, at least anecdotally according to KrietoR and according to some rudimentary simulations i did using http://sim.ffxivguild.net/, its better to delay blood for blood in your rotation so that it and hawks eye completely overlap your barrage than to use it on cooldown, simulated using this (shitty) bard rotation i wrote up http://hastebin.com/cesizagika.php