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Not to be overly arrogant
I would say in light of this disclaimer that I'd hate to see you actually being overly arrogant, but I've been playing this game and the forums a long time so I've seen it before.
The way critical hits work at the top end is misunderstood by pretty much everyone that wasn't a coder or me, because a coder told me how it worked 10-15 years ago and I've kept that knowledge under wraps until this thread. Shecks is very data driven and did figure it out on his own, but no one else has spent the time to do it.
This is a big yikes. Plenty of people have run the numbers over and over again on crits over hundreds of thousands of attacks. What you're claiming as the Colonel's secret herbs and spices that only you know and Shecks managed to stumble across has been pretty common knowledge since the mid-2000s at least. Just because you needed to be spoon fed info by Clementius doesn't mean it's beyond everybody else's comprehension.
You disagreed with that basic info and provided an example that ignores critical hits so we're at an impass. If you had bashed at the top end on any characters you'd understand, but that's hard to show someone.
I disagreed with your wonky logic regarding time wasted after killing a denizen. I told you why, and your answer has been 'excuse me sir but I have more arties than you, you clearly don't understand'.
I don't disagree that faster attacks are better; I stated multiple times that they are. I don't disagree that each % of crit chance is increasingly more valuable; anyone with a calculator or a spreadsheet can figure that out. All this has also been common knowledge since you were still at Hogwarts, where apparently they don't teach reading comprehension.
edit: This is not to mention that you even posted this info yourself back in 2016.
i love it when self-righteous people get caught up in their own bullshit. like that episode of south park where all the people in San Francisco smell their own farts.
@Kshavatra No, @Cooper is right. People in Achaea have an aversion to actual numbers. Almost everything is based on feel. There are huge spreadsheets Cooper has at least seen, if not posted himself, that show that once you get to high crit the balance time to move is the biggest downtime. It gets mitigated by using queuing and with areas with high density, but the last hit is always de-valued due to overkill (less so if you have Maya) and the balance just after the last hit where you are moving to the next denizen is 0. The amount of devaulation might be overestimated, but once you are fully artied it is the only place where you can improve efficiency so I can see why.
People can have their aversions all they want, a simple thought experiment shows that 160 seconds of wasted time is faulty logic. Agree to disagree, I'm done arguing it
Most of these formulas have been public for some time, yes. Most of the numbers I've given are from scripts I've had since I was a player, actually, with minor tweaks to account for plane-razing when that was requested (since I never had nor bothered with that crit level in them). I'll throw out a few more numbers relevant to the discussion, since I also had scripts to work out dps differences across different levels of critical chance, and different attack speeds, and hopefully clarify some things and either verify or dispel a lot of assumptions being made here, without breaking down exactly how every crit bonus works and some of the more behind the scenes mechanics.
Using 65% as a maximum realistic critical chance:
Every 1% of crit past 43% is between 4-5% dps increase
Every 1% of crit past 31 is between 3-4%
Every 1% of crit past 20 is between 2-3%
Every 1% of crit below 20 is between 1-2%
To address the discrepancy between faster and shorter attacks, at the high end, there's a few scenarios to address here. The biggest discrepancies are at the high end of crit chance, the lower ends tend to stay pretty competitive. Using the example of 1.4s serpent balance vs 3s gut balance (which covers the far ends of most bashing use cases, showing the most extreme discrepancy outside of a few niche strategies, I believe), you've got three scenarios. These are all calculated using real crit and damage values against UW-level mob health for a 145-hour session, and should all be accurate within a percent or so (assuming the same dps across both attacks). Percentages are truncated for readability.
If you have neither plane-razing crits nor maya figurine, there's a baseline discrepancy:
At 42% critical chance, the faster attack has a 6% faster clear rate.
At 65% critical chance, the faster attack has a 14% faster clear rate.
If you have plane-razing crits, but not maya figurine, the discrepancy very clearly increases in favour of the faster attack:
At 42% critical chance, the faster attack has a 11% faster clear rate.
At 65% critical chance, the faster attack has a 26% faster clear rate.
However, if you have both plane-razing crits and a maya figurine, the discrepancy all but vanishes:
At 42% critical chance, the faster attack is less than 0.2% faster clear rate.
At 65% critical chance, the faster attack is 2% faster clear rate.
So, yes, there's a definite benefit to the faster attack speeds, though that benefit isn't as big as most people make it out to be (at the low end and high end specifically), and also has to be weighed against the increased clear speed that comes from more time spent off balance from killing blows and beefier attack kills, which leads to less damage taken and more time to heal outside of combat (neither of which I've accounted for in these numbers). There's a difference, but it's not quite as absurd a difference as people make it out to be, in most cases.
I really appreciate the solid and current data Phaestus, thank you for taking the time to put that together!
The discrepancy of the equal clear rates for PRC/Maya is that the mob he tested on couldn't be one shot with a world shattering critical hit by the serpent, meaning the plane-razing critical hits weren't an automatic one shot. I should have qualified my earlier post by saying that was a requirement while noting that the vast majority of mobs in the game are one shottable that way, but some of the high end dragon areas have a number of them.
Hey cool, thanks for finding that! I forgot I posted that on the forums 5 years ago, and that makes sense why it's common knowledge now! I've played for 22ish years and it is sometimes hard to remember what I have or haven't done.
@Kshavatra I am saying that the spreadsheets take into account your thought experiment and prove the assumptions behind it incorrect. @Phaestus's numbers prove it if you believe him. I think the reasoning is that any attack that can kill has a lower expected DPS, so you have to weight that accordingly. When you do that, faster attacks have more time in the not-overkill section of the curve and come out with more DPS.
I wrote what I think is an accurate simile of the game's crit function and ran a bunch of simulations with various factors (base crit chance, bonus crit chance from range 0% to 8%) with various combinations of auspicious paragon (20% chance to upgrade) and crit gambling paragon, as well as Maya. Expected matched extremely accurately in every single test case (also measured 0% to 8%). All testing was done as dragon, needless to say.
I still have a few things I really want to fine tune (namely the crit gambling constants), and it's noted that the game code/logic may be written in a different way than as described below, but the results come out pretty much perfectly so seems negligible to me if this is the case.
Auspicious: If you get a crit, you have a 20% chance to skip a crit level
Gambling: If you get a crit, you have a 20% chance to critical fail (no crit), a 60% chance to skip a crit level, and a 20% chance that it will just give you a regular crit.
These "skip a crit level" effects combine so if both succeed, you skip straight to Obliterating Critical instantly.
After these effects are rolled (which happen as soon as it's determined that you've rolled a critical hit), and these "skips" are applied, you continue rolling as usual with your normal crit chance stat for further increases to crit level. Obviously if you have gambling, PRC is enabled. Real-world test data suggests that Auspicious can raise you to PRC despite saying that it cannot, however data points at this level are sparse so margin of error is wide.
Maya: Technically reduces your overall crit rate, if you count the followup hit - which cannot critically hit (but gets overkill damage added to it). For the purposes of data analysis, I don't count these hits at all towards crit tracking, as they cannot crit and are basically special attacks in this context.
The previously described logic for how basic crit escalation works is absolutely confirmed. You just keep rolling your crit chance until it fails, then that's what your result is. Nothing new here, but we can definitely put any doubts to rest there.
Point of Interest: I can't promise this simulation is 100% perfect, but it's notable that at high crit chance (50%+) you actually get a higher average damage multiplier by just using Auspicious Paragon without crit gambling. You don't get PRCs at all, but on average, you'll hit a lot harder by just not gambling. Yet to be determined (mathematically at least) how that really plays out in real DPS / overall bashing speed. "average damage multiplier" is not a great metric really because it doesn't account for overkill at all. Once Maya is counted in, your overkill wasted dps drops dramatically, which would significantly increase real DPS when using crit gambling. I'm quite sure "real DPS" metrics will show this when looking at gambling, clear as day.
I think the math kinda speaks for itself, but here are some sample scenarios for people to get a feel for how these effects work out, in practice:
I'll whip up a PvE sim and plug this in after I polish off some of the questions I have about base crit chance and confirm the gambling constants are exactly right.
I'll also see what I can do about displaying this info in graph form with some more practically useful information.
What a bunch of nerds.
Realistically though, mathing this stuff out is amazing.
Question: Crit Gambling paragon says that on critical fail, you will deal no damage. Has anyone ever tested/confirmed this? You can't see when it happens so you'd have to use big data to check it (on real NPCs who can die) and I'm not sure I care enough to do this :).
Until told otherwise, for simulation and analytics purposes I assume "critical fail" means you don't get a crit and just strike normally.
Also, does anyone have a good guestimate of NPC healths in Annwyn/UW. I'm going to use a random distribution of 17,500 - 22,500 but would prefer to use real numbers.
I have never noticed a hit do no damage, and I checked because I had the same question. As far as I can tell it just removes the crit portion but you still get the normal hit.
So, simulation has some interesting results.
For context, characteristics of the sim are listed below. Any suggestions on how to improve it are welcome.
You can get a sense of how it works with this sample log with echoes enabled: https://ada-young.com/pastebin/TEhgnUhe
So, some data from the sim....
Probably some small tweaks on Crit Gambling constants would make a big difference here, because you can see at high crit chance values, Crit Gambling stops helping and eventually starts actually reducing Real DPS.
I've also noticed that while Maya overall does help, it does significantly reduce your real crit rate (as Maya procs don't crit) and quite often the overkill damage you deal is lower than your average damage per hit. In the first example on the example log above, for instance, you can see a Maya proc dealing 107 bonus damage (when average damage per hit that can crit is closer to 4,000).
Wouldn't that 33% approximation make things weird? At higher DPS/kill speeds it might not matter much but there's a big difference for lower level damage- afaik mobs use shield on a cooldown of some sort and it takes the place of their regular hit. That means you have a static window for hitting them, not an adaptive one (so a fast attacker might have 6 hits between shield to a slow attacker's 2).
Yeah, you'd tune that depending on what class you're on. I didn't bother coding in NPC balance, because I think the approximation is pretty accurate.
I wouldn't do it as NPC balance, just make a 'shield timer' and if they're below 20% hp and take a hit, de-increment it. Set it to like 10 seconds, if it hits 0 then they 'shield' and you reset it to 10 again.
Can anyone confirm that serpent lash balance is actually 1.2s? That is not my experience at 19 dex.
My lash is an auction morphing weapon and I have run into a lot of issues with it not working properly.
Vicar Cooper Ikari (male Rajamala Striker)
You are level 126 (9th Level of Penwizian Fortitude) and 83.3% of the way to the next level.
[Zhe]: You are 1241.74% of the way to dragon!
Health: 6412 / 6412 Mana: 7053 / 7053
Endurance: 29380 /29380 Willpower: 29380 /29380
Strength: 15 Dexterity: 19 Constitution: 14 Intelligence: 14
You are a full member in the Serpent class.
You are wielding:
shield12345: a Shield of Absorption in your left hand.
lash12345: Elentari's Scourge in your right hand.
You slip behind a flail-wielding knight and garrote him with your whip.
With a sad shake of his head, a flail-wielding knight warns you not to do that again.
(p) 6412h, 6872m, 24029e, 23700w guard 100%(+587m, 8.3%)
You have recovered balance on all limbs. (1.355s)
(p) 6412h, 6872m, 24089e, 23700w guard 100%
(p) 6412h, 6872m, 24076e, 23700w guard 100%
You have recovered balance on all limbs. (1.323s)
(p) 6412h, 6872m, 24076e, 23724w guard 100%
(p) 6412h, 6872m, 24063e, 23724w guard 100%
You have recovered balance on all limbs. (1.272s)
(p) 6412h, 6872m, 24123e, 23724w guard 100%
(p) 6412h, 6872m, 24110e, 23724w guard 100%
You have recovered balance on all limbs. (1.358s)
(p) 6412h, 6947m, 24110e, 23730w guard 100%(+75m, 1.1%)
(p) 6412h, 6947m, 24097e, 23730w guard 100%
You have recovered balance on all limbs. (1.256s)
(p) 6412h, 6947m, 24157e, 23754w guard 100%
(p) 6412h, 6947m, 24144e, 23754w guard 100%
You have recovered balance on all limbs. (1.432s)
(p) 6412h, 7053m, 24144e, 23754w guard 100%(+106m, 1.5%)
(p) 6412h, 7053m, 24131e, 23754w guard 100%
You have recovered balance on all limbs. (1.264s)
(p) 6412h, 7053m, 24131e, 23778w guard 100%
(p) 6412h, 7053m, 24118e, 23778w guard 100%
You have recovered balance on all limbs. (1.307s)
(p) 6412h, 7053m, 24178e, 23778w guard 100%
(p) 6412h, 7053m, 24165e, 23778w guard 100%
You have recovered balance on all limbs. (1.448s)
(p) 6412h, 7053m, 24212e, 23808w guard 100%
You have recovered balance on all limbs. (1.336s)
(p) 6412h, 7053m, 24199e, 23832w guard 100%
You have recovered balance on all limbs. (1.297s)
(p) 6412h, 7053m, 24259e, 23832w guard 100%
(p) 6412h, 7053m, 24246e, 23832w guard 100%
You have recovered balance on all limbs. (1.254s)
1.3 lines up better with what I would expect based on my own setup. Assuming the difference in dex equates to .15-.25 difference per balance with DR.
Cardinal Atalkez Al'Jafri, Hand of Dawn (male Human Rogue)
You are level 110 (2nd Stratum of Puissance) and 91.2% of the way to the next level.
Health: 7714 / 7714 Mana: 5934 / 5934
Endurance: 25700 /25700 Willpower: 24739 /25700
Strength: 15 Dexterity: 17 Constitution: 14 Intelligence: 14
You are a full member in the Serpent class.
(Also using Elentari Scourge)
He has 96% health remaining.
A hideous, writhing squid has visited the Halls of Death recently.
You have recovered balance on all limbs. 1.547s
He has 60% health remaining.
You have recovered balance on all limbs. 1.544s
[Boom! - 2X]
He has 43% health remaining.
You have recovered balance on all limbs. 1.648s
He has 34% health remaining.
You have recovered balance on all limbs. 1.54s
[Boom! - 8X]
The limp, lifeless body of a hideous squid topples end over end within the grasp of a strong ocean
[RIP RIP RIP]
You have recovered balance on all limbs. 1.562s
You have recovered balance on all limbs. 1.508s
[Boom! - 4X]
He has 62% health remaining.
You have recovered balance on all limbs. 1.457s
He has 53% health remaining.
You have recovered balance on all limbs. 1.652s
He has 17% health remaining.
You have recovered balance on all limbs. 1.465s
A small pile of sovereigns spills from the corpse, flying into your hands before they can reach the
You feel a surge of energy course through your body as a red silk cape feeds upon the lifeforce of
your fallen foe.
I got 1.27s testing 10 queued garrotes (19 dex) a second ago. (queue 10 of them, subtract the time difference, divide by 10).
For the purposes of this discussion though, the above data were really just an example of crit distribution and the relative effects of various artefacts on actual DPS. As of now, I'm not actually sure how much damage a garrote even does, or for that matter, how much HP NPCs have. I'm just going off of Phaestus' numbers and giving NPCs a bit more than one WSC garrote. These unknowns do kindof cancel out though, since my simulated NPC health is based on number of hits it takes to kill them IG - so I am not so worried about this.
If we really wanted a true measurement of theoretical real DPS for each class, I'd need to get battlerage mechanics for each of them, which is a lot harder to measure. I suppose I could try measuring it with a mount but that will be painfully slow and will have to be done separately for every BR attack (around ~100 of them to measure). It's also unclear if BR attacks scale with stats or other factors.
Entirely anecdotally, I believe all battlerage skills deal the same damage with the only exception being the configuration of how this damage is dealt. I've lost the dedicated testing I did on this for psion shenanigans but I recall my results as being somewhere along the lines of:
Damage is denoted by rage cost, with 14 doing the least, 36 doing the "standard" high damage attack and 51 being the combination of affliction + affliction consuming attack. Damage over time attacks do half of their damage up front and the other half over 6 ticks with a 0.5s~ interval.
With 14 rage attacks being the 'base' damage, 36 rage attacks appear to do roughly 2x as much damage as 14 rage attacks base. 51 rage affliction + consumer combinations do roughly 4x as much damage as the 36 rage attacks base. Consumer attacks on their own are never worth using unless an associated affliction is present - they are the least efficient conversion of rage to damage. When an affliction is present, they become the most efficient form of converting rage into damage even when adjusted for their cost and cooldowns.
DoT type battlerages have a unique interaction with critical rate since they effectively roll 7 times on the critical table to determine their total damage. This means the average on their total damage can be much higher (or also much lower) than an upfront (all at once) attack would be. This is especially notable on classes with low damage (14 rage) DoT attacks, as they can be looped whenever available to fish for high level critical hits without much risk of overkill.
Other unique interactions to explore would be attacks that consume sensitivity - do they inherit the 33% sensitivity damage bonus when consumed? If so, this would make them the single highest damage dealing skills in the game in a PvE context bar none.
I thought all BR attacks could crit (and can also proc and consume Maya effect I think). That bit about 7 rolls confused me, what do you mean? (Edit) oh I get it now. I don't think that changes much tbh and it probably is worse when using Maya. Getting low overkill Maya procs is actually really bad for your overall DPS (as the following hit can't crit), and those DoT abilities do this pretty often.
As a note, not all BR DoTs are a standard six ticks.
The one that stands out to me is Occie's, which lightly tickles the enemy for at least ten.
I think the universal standard for DoT rage attacks is that half of their damage is given immediately and the other half over the 6-10 ticks, however many there may be. It could be worth investigating whether they differ per attack? Also yes, a low overkill proc would suck with Maya given it denies you a crit on your next attack, but in practice that essentially almost never happens given how poorly damaging even a 32x crit is on such low base damage.
I'm fairly certain Apostate convulsions does not do up front damage - at least it has never once crit like the other battlerage skills.
Windlash has 3 hits outside the initial one. Haven't really paid attention to the others
It's been indicated that we will have a way to test damage directly, in game. I'm not touching BR damage estimations until though, because damage testing 100+ abilities on mounts is going to be hellaciously time consuming.
I will probably do dragon and serpent and just assume other classes do the same overall DPS until indicated otherwise.
I always saw the DoT ticks as a single slow attack, doesn't that make it worse than standard because a larger amount of overkill is wasted (even worse since you can't reclaim it with Maya)?