Bashing DPS Overhaul

Kshavatra · August 2021

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.

https://forums.achaea.com/discussion/comment/305752/#Comment_305752

Archaeon · August 2021

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.

Accipiter · August 2021

@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.

Kshavatra · August 2021

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

Phaestus · August 2021

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.

Cooper · August 2021

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.

Cooper · August 2021

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.

Accipiter · August 2021

@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.

Shecks · August 2021

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:

Shecks · August 2021

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.

Adrik · August 2021

What a bunch of nerds.

Realistically though, mathing this stuff out is amazing.

Shecks · August 2021

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.

Accipiter · August 2021

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.

Shecks · August 2021

So, simulation has some interesting results.

For context, characteristics of the sim are listed below. Any suggestions on how to improve it are welcome.

input primary attack damage and balance used (I used garrote at 563 damage every 1.2s based on 469 damage figure from Phaestus for L3 lash 19 dex serpent garrote)
input shield attack damage (I used camus with silver fangs using same logic as above)
I used (configurable) 20,000 +/- 2,500 HP NPCs for this data, which seems like a pretty good approximation of UW NPCs.
respects shield by assuming NPC shields at 20% health and that 33% of all hits below 20% are vs shielded NPCs (seems like a good approximation)
respects Maya (when enabled) and tracks overkill
can enable either crit paragon or both
assumes a 0.25s average delay between NPCs (most powerbashers will have zero time between kills usually but will occasionally have to walk a few rooms without doing anything)
didn't include BattleRage because it's witchcraft (if someone gives me the numbers/mechanics on it I'll include it) This may have a pretty big impact on interaction with NPC Shielding since you would usually use BR to strip it.
didn't include any damage resistances on NPCs in the following data
Doesn't account for being hindered or missing attacks. (this can be enabled though if anyone wants that)
obviously, ignores incoming damage and assumes you bash continuously (accommodating for walking) without having to shield or heal up

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).

Kog · August 2021

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).

Shecks · August 2021

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.

Kog · August 2021

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.

Cooper · August 2021

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.