Bard : Are there Diminishing Returns on the Crit Stat?

[MrYaah]

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

[MrYaah]

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

[MrYaah]

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

[Dervy]

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.

[MrYaah]

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?

[MrYaah]

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.

[MrYaah]

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

[MrYaah]

.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.

[Ricdeau]

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

[Dervy]

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.