Bashing DPS Overhaul

Phaestus

I'm well aware that 1% crit chance doesn't translate to 1% increased dps, and 1% increased dps doesn't equate to 1% faster clear speed. I'm saying that human only increases dps by 1.3%, without PRC. Including PRC, the highest increase you're going to see is around 1.4% dps increase, given any crit chance between 0% and 100%. In most realistic cases, it's around a 1% dps increase.

If anything, at the high end, mayan figurine removes the discrepancies between dps and clear speed, as you're no longer wasting overkill damage and 100% of your raw dps applies to your clear speed.

Accipiter

I misunderstood, sorry.

Shecks

Er, we've had that data for many years and have made multi-thousand dollar purchase based on that data. Stay away from my crits dawg. XD

Being real though, Phaestus' numbers above are definitely wrong, there's simply no way that 1% crit translates to anywhere near 1% or 1.4% DPS increase, at least not at high level / high crit chance levels. The new bashing data tracker being shared recently could back that up with hard data pretty easily. I'm guessing that "real DPS" wasn't measured at the high end of crit rates, as Cooper suggested.

As Phaestus mention though, @Accipiter , gotta keep in mind that "2 dex" is definitely not always "2 dex". There are both hidden class-specific / ability-specific formulas involved as well as diminishing returns that are heavy factors here when comparing base stats to crit chance.

Tahquil

I thought crit rate/chance was just if you crit or not, not taking into account for what kind of crit?

Shecks

That's absolutely not the case. Crit chance determines both cance to crit as well as level. If you have 50% crit chance (including + arties) you have 50% chance to crit, then 50% chance for higher crit, then 50% for crushing crit, etc.

In other words an oblit crit is rolling 3 criticals in a row , i.e. crit chance ^ 3.

Some people have worked out the base crit chance per level from real-world data, but off the top of my head it scales like 0% to around 40% or something from level 25 to level 100 (could be a bit off on that, so don't quote me, and I've also been told that this scaling with level is not linear). Noting that crit chance doesn't increase past 100 in any way, @Accipiter .

If you have +15% crit rate (pretty extreme end and usually not possible without an event), you have approx 40% chance to NOT crit, and your chance of Crushing is higher than your chance to get a regular crit. This is before the crit gambling effect (paragon) when then also has a chance to increase crit by 1 level as well.

On the other hand if you're level 25 you might have a 1 or 2% chance to crit and only 1-2% of that 1-2% will be crushing, etc.

Is odd to me that the designers have sold so many stacking crit items and effects but at the same time PVE power creep is a thing and has definitely kept pace. Modern higher end bashing areas would be totally impossible if not grossly inefficient without high crit rates working as they do. Lately though most of the new crit items share the same buff so they tend to not stack together (loosely described by Cooper above).

Based on the above explanation, it should be easy to deduce that there is no "X % increase to DPS" for 1 point of crit chance, as crit chance DPS increase depends on how much crit chance you already have. Increasing from 1% crit chance to 2% crit chance might increase your DPS by like 1% (out of 100 hits, you will do roughly 102.2 hits worth of damage instead of 101). However going from 50% crit chance to 51% crit chance is a much bigger impact because you're getting higher crit levels more often, in addition to just getting a crit 1% more frequently.

I'm really tempted to make a graph, now. Love me some graphs.

Phaestus

Being real though, Phaestus' numbers above are definitely wrong, there's simply no way that 1% crit translates to anywhere near 1% or 1.4% DPS increase

Nowhere did I say that human bonus was 1% crit chance (it's definitely not). You're entirely welcome to continue arguing with scarecrows and holding lectures on the subject, though.

Accipiter

I didn't know crits were rolled like that. Is that admin confirmed or extrapolated from data?

Shecks

Sorry Phaestus, I definitely misunderstood what you were saying 3 posts back about the 1.4%. I was strongly disagreeing from personal experience / testing that 1% crit chance definitely was more than 1.4% increase to real DPS - which is indeed not at all what you said, you were talking about human bonus specifically and I missed that somehow.

Anyhow please empathize a bit - it's frustrating having a lot of these things interacting together and not being able to understand how or why things work the way they do.

I think it's fair to say that nobody is here to argue - we're here to learn and share feedback.

Personally I'll still stick to human crit bonus at the expense of the main stat as I'm usually sitting at 18 to 23 main stat in human, coupled with my understanding (based purely on theory) that at super high crit chance levels, additional crit chance is exponentially more valuable than at lower crit chance levels.

I graphed out "real DPS" approximation based on 800 base damage per "hit" on a 1.8 second attack, for example - based on my THEORY of how crits work (as I described above, accounting for Maya, crit gambling, and PRC), and I see that going from 0 to 5% total crit chance takes you from around 440 real DPS to around 471 real dps (31 dps, 7% dps delta), while going from 35 to 40% total crit chance takes you from ~1230 to ~1630 real (400 dps, 32% dps delta).

So in that light if human crit bonus was even 0.25% it would be worth significantly more than a main stat increase from 23 to 24 in lesserform with diminishing returns starting at 12. I'm operating on a pretty long list of assumptions here of course, but that's all I have to go on. as mentioned above, for all we know, human bonus isn't an actual "Crit chance" modifier at all, it could just be its own thing that works in its own way - all I know is what the Help file tells me "Higher chance for critical hits".

Phaestus

So in that light if human crit bonus was even 0.25% it would be worth significantly more than a main stat increase from 23 to 24 in lesserform with diminishing returns starting at 12. I'm operating on a pretty long list of assumptions here of course, but that's all I have to go on.

This is likely the last I'll post on the crit issue, but funnily enough, you've hit the nail on the head, in a way. Going from 23 to 24 is the first stat point change where human actually shows more increase than the +1 stat point (and even then, only barely so), when in lesserform.

Gallida

Careful, you might provide data the players can use instead of failing to interpret via the limited tools available.

Shecks

There's no need to be a jerkface about it to the admin. I definitely assume that any level of secrecy is company policy and not personal decision by Phaestus himself.

We got what we wanted for limb damage. We got a fix to earrings. I'm definitely not going to be complaining for a good long time. Just asking questions and taking whatever answers are given 😃.

Cooper

Shecks this is going to sound insane, but bear with me. Together we have the ability to calculate crit chance effect on DPS if we work with each other.

I need to find a very old email from Clementius that I'm not sure I have access to in order to confirm your critical hit rolling is accurate - it feels like the right direction but I have solid info from him somewhere.

I can help provide crit chances for various abilities, the crit formula (assuming I can find that email), and testing to verify data. You can do the data molding and actual calculating.

You up for it?

Shecks

@Cooper I already have 8000 dummy test data points (taken today) from Veldrin at +2% and +8% crit and with and without paragons to feed my data addiction. So far every result has fit my prediction of how things work, adjusted for the observed baseline for dragon (100+) base crit rate of approx. 42% to 42.25% or so. Bit iffy on that though, still working on really nailing down the baseline for dragons.

Side objective is to extra the constants / mechanics involved with crit gambling which as far as I know are still a total mystery.

Once I have enough confirmed theory combined with real data, I'll toss it all into a sim and run it 50,000 times to chug out some "real" DPS across a few scenarios, which will also account for overkill and such.

Through this process I've also encountered an interesting factor that I bet nobody has considered in all of these DPS balancing acts, which is that some classes simply miss a lot of attacks either naturally or due to clumsiness, which other classes don't have to deal with. When you average killing things in 4 hits, as a random example, missing one hit out of four from clumsiness is an absolutely massive factor vs things that give clumsiness. Same logic for lethargy vs physical balance classes. I'm not going to simulate this but it's good food for thought.

To answer your question, yes I'm quite happy to work on this with you. Will definitely incorporate mechanics, insights, or data you have that could be useful, and of course intend on sharing any findings I arrive at publicly.

I would be cautious with anything coming from Clem though. While it may offer great insight into design thought process, it's unlikely things that old are still in place, without any modification. Base code probably yes, but constants and interactions with artefacts/abilities probably have changed in some cases.

Two major unknowns I'm working on right now:

1) Does Auspicious paragon (20% chance to increase critical hit level, not counting WSCs) increase chance for non-crits to become crits, or does it work literally as it says, and also, I want to confirm that it does indeed not increase WSCs to PRCs as the text implies.

2) What is crit gambling proc rate, and what is critical failure rate.

We are already testing these (separately).

As for human bonus and DW bonus, these are very easy to test. Will run these at a later time. I'm currently working on the operating assumption that human crit bonus is either a 0.2% crit bonus that doesn't show on Def because it's rounded down, OR it's just a completely separate mechanic. Will suss it out from the data. From a design perspective, it would follow that crit pendants (old school arties) were aimed at 5, 10, and 15% increase in overall PVE bashing speed (as those ratios were ubiquitous back then). It also follows that human bonus would be targeted at 1%, one 5th of an artefact level. This matches test data so far as well as Phaestus' comments.

One interesting observation that I've made (months ago) along with probably dozens of powerbashers, is that very quickly it because completely impractical (both for exp and for gold) to bash things that you can't crit, which is a bit of a design paradox considering that most of them are high-end NPCs aimed at stronger artied players. No complaint I guess, just don't bash them - just seems weird.

Veldrin

That is to say 2000 hits at 2% (sceptre + trait) and then 2000 at 8% (sceptre + trait + stygian) and then 2000 of each crit paragon at 8% (maya messed a tiny bit with the two firsts since, getting a WSC on a dummy with 2% health triggered it. So that's 29 hits on the first one that had a guaranteed non-crit followed up by 54 in the second bit). I'll redo them without the figurine in my inventory later.

Also fun fact, the pendant keeps providing your DEF with an increase crit score as long as it's in your inventory, worn or not.

Shecks

Another fun fact, you can force DROP LILY to ruin people's day.

Shecks

Just as a quick update, looking at +2% and +8% crit data (4k data points) without any paragons or Maya, you can see how well these 4k data points are fitting the very simple model explained previously. Graph basically shows how many crits are expected (X) vs what's observed (•). A good data-minded person would note that the values on the left are far more relevant as there's far more data points compared to PRCs where a handful of lucky / unlucky rolls can massively sway things.

Purple is +2% data, Red is +8% data. Strangely linear regression is showing that an overall crit rate of 41% or maybe even lower fits better, but right now we're assuming that those 2% and 8% are actually accurate which is not a safe assumption because we're assuming lucky trait and environmental sceptre are both an even 1% when they very well could be higher and rounded down to display 2%.

Will suss that out later at true 0% bonus with like 5k raw data points to really nail down base crit rate, which will help.

There is a very slight indication here that crit level might have a slight bonus to it (as in 45% chance to get a crit, but 46% used for escalation), but will circle back on that possibility later when I have more data. Could just be random, 2k data runs really are not that rich in this test.

Cooper

I can clear up some of that.

Crit chance stops increasing at level 99 - no crit change for level 100.

Crit chance is 40% at level 99.

Auspicious paragon works exactly how it is described and does not have a chance to increase a not-critical to a critical hit.

Critical hit gambling and failure should be a flat 20% chance but this needs to be confirmed. It's rolled after the critical hit roll so it isn't like adding 20% crit chance, it's a 20% chance after the crit is rolled.

Human bonus is less than 1% and is dropped on DEF due to Achaea's rounding.

Clementius (not the shortened version of his name, cause the only thing he ever asked of players was to not shorten his name) gave accurate into that aligns with your testing, I just need to dig through emails and find it. I think it's in an old email I haven't accessed in at least 10 years so it will take some time to get access to the account.

When critical hit pendants were introduced it is very unlikely that they crunched numbers on how effective of a boost they are so I would hesitate to assume they were going after a 5%/10%/15% increase with that.

The rest of this post is tangential rambling about bashing faster and not related to critical hits.

Something most people don't consider:

Each time you kill something the time between the kill and you recovering balance and moving rooms is wasted time.

Example: two people are bashing and kill 100 denizens. The first person is a serpent with a 1.4s balance and the second is a dragon with a 3.0s balance. The serpent waits for a total of 140 seconds while recovering balance after kills, the dragon waits 300 seconds for a difference of 160 seconds/2 minutes and 40 seconds of time that you can't do anything about.

The other portion of that is attack/battlerage attack versus battlerage attack/attack. When you do battlerage first you have the chance of killing something using no balance and can move immediately.

One more thing is utilizing searing glyph talisman on SoA. In big groups (like the 9 zombies, 9 vampires, graveyard in Azdun) this does enough damage to make a noticeable difference when combined with high crit chance.

Shecks

@Cooper

Very valuable info to have. I do think you are mixing up crit gambling though (or i'm misreading it, more likely).

Critical hit gambling and failure should be a flat 20% chance but this needs to be confirmed. It's rolled after the critical hit roll so it isn't like adding 20% crit chance, it's a 20% chance after the crit is rolled.

What we're actually seeing is roughly 8% critical failure (notably, at 8% crit chance stat). We're running another test at 2% to see if it sticks to that 8% or if it scales somehow with crit chance. Notably, 8% crit failure means that 8% of critical hits get canceled. Another way to view the exact same data is that you just have a flat 10% lower chance of getting a critical hit, but once you do, you get a bonus to crit chance for the purposes of escalation. Still sussing out that math, but it's not too hard. Once we do a separate run at 2% or 0% we will nail that down easily.

Data referenced here (for crit gambling at 8% crit chance, no Maya):

Note on this, we do know that crit gambling does not always proc. There's a chance to proc the effect, then you roll again apparently to determine if it critical fails or gets boosted. Two different constants / formulas that need to be pulled out. Are you saying it's a 20% chance to proc the effect?

I am still remaining very cautious about trusting any crit chance DEF line other than pendant which we can safely assume is flat 2, 4, 6%. Veldrin's 2% could easily be 2.5% or 2.9% for all we know (from lucky and sceptre). This actually seems even more likely to be the case if indeed base is 40%, because we're seeing closer to 42.5%, which would imply that one of those two bonuses is actually 1.5% crit chance.

Cooper

The 20% is the proc chance, yeah. And 20% would correlate to your 8% - 40% crit with 20% proc chance. The 20% value is the one I'm least confident on but it might be in the original announce post.

Agreed on not trusting DEF.

Shecks

Feeling pretty good about my algorithm for crit gambling. Will publish after I confirm with another data set at other crit bonus values.

X = algorithm, • = test data (2k data points at 8 to 8.5% bonus crit chance).

Updated:

Yeah it seems pretty safe to say there's a 20% chance for crit gambling to proc, notably taking effect when you DON'T get a natural crit at all, resulting in the only way to actually score a Critical Hit while using the paragon. Once the proc occurs, it appears to just be 50/50 on either no crit at all or a free escalation of one critical level.

Alternate theory is that crit gambling has an 80% chance to proc but doesn't proc on natural non-crits, which would also result in 20% chance for natural crits to slip through at your normal crit chance rate. I don't know order of operations in the code, but it works out being exactly the same thing anyways. Shrug.

Kshavatra

@Cooper said:

Example: two people are bashing and kill 100 denizens. The first person is a serpent with a 1.4s balance and the second is a dragon with a 3.0s balance. The serpent waits for a total of 140 seconds while recovering balance after kills, the dragon waits 300 seconds for a difference of 160 seconds/2 minutes and 40 seconds of time that you can't do anything about.

Assuming equivalent DPS, the actual 'wasted time' is significantly lower, but still offensively in favour of faster attacks (to a small degree).

Take a mob with 301 health and 3 different attacks: 1 damage @ 0.01 second balance, 100 damage @ 1 second balance, and 300 damage @ 3 second balance.

Takes 301 attacks (3.01s) for the fastest to kill, 4 attacks (4s) for the middle, and 2 attacks (6s) for the slowest. This is the time from start of fight to being able to move after it's dead. This is absolute worst case scenario for the 3s attack, and it's actually 2.99 seconds wasted rather than the 3 that you suggest.

For a mob with 600 health, all 3 cases take 6 seconds, resulting in no 'wasted time'. For this mob, the slowest attack leaves the mob alive for 3 seconds, compared to 5 seconds for the middle, and 5.99 seconds for the quickest, so you're essentially trading defensive 'wasted time' for offensive 'wasted time'. This is the best case scenario for slow attacks. If you're in no or minimal danger of dying/having to run then obviously the mob being alive longer doesn't matter.

So if Serp and Dragon have equivalent DPS, the maximum 'wasted time' per kill is actually going to be 1.6s with your numbers, but will fall in the range of 0-1.6s depending on the specific breakpoints of the things you bash. Real world scenario is unlikely to be the full 160 wasted seconds and if you have Maya then I think most cases are going to be much lower, since the largest sources of overdamage/wasted time are the big crits.

Shecks

I mean group bashing is a whole other thing though. BR works differently, and a whole lot of class synergies start to come into play. Generally speaking though, I can't see how group bashing could be efficient compared to just bashing separately. I only do that for fun or if I REALLY want to zone out and watch netflix.

Cooper

Maya makes the discrepancy larger, not smaller. A PRC with Maya means the 1.4s balance gets to kill two denizens in 2.8s while the dragon takes 6s.

Have you bashed at the extreme level of crits and arties? The higher your crit and damage are, the more effective a fast balance attack is. The more attacks you do the more times you one shot kill something.

Eurice

There is also the giant elephant in the room of normalizing marathon DPS based on a class' given willpower/endurance consumption. Some consume a lot of either stat, some consume only a little. Others still consume none, which seems like an oversight of some kind. Weaving in particular is notable in that none of its abilities consume any endurance or willpower ever when used on denizens, so a Psion is limited only by their curing pool before needing to resupply.

Group bashing is only really viable if Nicator is involved in smaller numbers since the +30% bonus appears to cover most of the discernible deficit for sharing experience on kills, though I have nothing but anecdotes and feelings to back that up.

Shecks

@Eurice endurance/WP not really an elephant in the room. These things were definitely considered during DPS normalization, with classes that use a lot having higher DPS. Tankiness was also considered.

Kshavatra

Maya makes the discrepancy larger, not smaller. A PRC with Maya means the 1.4s balance gets to kill two denizens in 2.8s while the dragon takes 6s.

Have you bashed at the extreme level of crits and arties? The higher your crit and damage are, the more effective a fast balance attack is. The more attacks you do the more times you one shot kill something.

I know faster attacks are better, I even mentioned that in my post. One 3 second, 300 damage attack on a 300 health denizen has no 'wasted time' though, whereas by your initial logic you'd count it as 3 seconds of wasted time. I'm just pointing out that in real world cases it's not as you described (160 seconds of wasted time). In every case of equivalent DPS attacks, faster attacks have less wasted time, but it's not as simple as gut balance - garrote balance = additional wasted time.

edit: Regarding Maya, cases where it allows one crit to kill 2 enemies with both (fast and slow) attacks certainly skew it further in favour of faster attacks, but if there are cases where garrote won't get 2 kills off 1 crit and gut would, then it's again not so cut-and-dry. I don't have Maya or crit paragons and the last time I cared about bashing other than to get to dragon, neither of these existed, so I'm making the assumption that there are some cases where crit carryover damage won't kill the second mob. If that's never the case then I agree with you that Maya always comes out in favour of faster attacks.

Cooper

I think you have a misunderstanding of how bashing works at the top end. Your example makes sense for lower tier bashing but we are talking about the extreme top end of bashing.

Kshavatra

Certainly possible. Which misunderstanding would that be? Which part of my post/logic do you take issue with?

Cooper

Not to be overly arrogant but I have been the fastest basher in the game for about 10-15 real life years.

Your misunderstanding comes from not knowing how effective critical hits, arties, and talismans are at the top end - I have everything in the game that effects bashing speed except for Culling Blade and very few other people are in that position. 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.

I don't have time to teach you why, you can find the basics in my original lengthy post. 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.

Vinzent

I'm only missing a culling blade too, but never really bashed in Human. Maybe I should play with that for awhile instead.