Guild Wars 2

nah.

you only truncate the bleeds when you want to simulate a mobs death. mob death isnt really a necessary assumption in a dps calculation, but it will make paper calculations into slight overestimations compared to empirical testing. 158.4 dps or whatever (might? no might?) is a perfectly valid theoretical calculation with sound reasoning.

no, it being random has nothing to do with anything cuz you are averaging it out and taking the randomness away. rare events work perfectly well with averaging, but they are particularly unsatisfactory from a “getting a reward” standpoint because of the nature of dry streaks in conjunction with confirmation bias. and 15% isnt that rare anyways.

I agree with insanemaniac. I can’t really add much without quoting him.

What you are doing DGraves, is assuming an encounter that lasts exactly [time] seconds, rather than averaging the damage contribution of Shrapnel. The issue you are adressing here is the same as with any other condition: Mob with conditions dies, and the remaining ones are wasted.

You won’t “majorly overreaching” anything by averaging. In fact, it gets more accurate the longer the fight goes. In 60s, (let’s assume shrapnel lasts 20s), 1/3 of the shrapnels will be cut off before running out of duration. In a 10 minute fight, only 1/30.

Damage multiplied with the chance to proc is totally legit.

DGraves.3720:

insanemaniac.2456:

no, it being random has nothing to do with anything cuz you are averaging it out and taking the randomness away. rare events work perfectly well with averaging, but they are particularly unsatisfactory from a “getting a reward” standpoint because of the nature of dry streaks in conjunction with confirmation bias. and 15% isnt that rare anyways.

The problem is that when you produce these random numbers and averages you have to truncate them because when managing events you can’t have “partial” events. For instance let’s say that a light turns green 60% of the time and red 40% but you only have two trials so how often is that light green? In those two trials it’s probably going to come out 100% of the time. You can’t have a “60% green light”. It’s either green or red.

Random events and their values change (Standard Deviation) regarding constraints. Normal averaging is without bounds so it presumes continuous eternal application which allows decimal based behavior to work; for instance:

.15(odds) x 100 (damage) x 20 (duration) = 300

This is the true averaging value of any given explosion regardless of whether it produces shrapnel or not in relation to shrapnel. This is the number that gets augmented when you add a time and divide it up.

The problem with this is that it only works in relation to an infinite set. This is any given explosion at any time over an eternal duration. If we were to set a constraint it doesn’t work out anymore. For instance let’s set the constraint of 10 explosions. Well the first thing we do is calculate the odds, which for independent events, is just adding them up or just writing it out as .15 × 10 = 150%. For averaging that would mean at least one of the ten will be guaranteed but then we have the .5 to deal with. The question becomes “Can we have half a proc?” and the answer is “No.”

So we truncate it. This means that the odds of getting one true occurrence in averaged instances must be the same between explosion sets 7 and 13. If you don’t truncate you are overstating your results. The larger the base number of sets you use (explosions, time, etc. are all working the same way here since they all produce one another) the lower that error margin.

The smaller the number of sets as seen the higher the erratic nature of the margin. So long as you average and use values that are not rounded down to real events you’re going to greatly overstate your outputs. Not that it matters to everyone. It is just a game after all.

not this again.

edit:

For instance let’s set the constraint of 10 explosions. Well the first thing we do is calculate the odds, which for independent events, is just adding them up or just writing it out as .15 × 10 = 150%. For averaging that would mean at least one of the ten will be guaranteed but then we have the .5 to deal with.

this is not how probability works. i suggest reading up on binomial, bernoulli, poisson, and other types of distributions in statistics. in particular, this experiment produces a bernoulli distribution.

I can’t tell if you’re working out bleed damage or calculating edge effects from quantum tunnelling.

15% is fine to use as an estimation; probability distributions wouldn’t be suitable for something as linear as this firing off frequently enough to ensure ~100% probability every second..

Practically, I have unrealistically had

36k dps against a Large Golem doing Explosions(1,2,2), Firearms(3,1,2), Tools(1,3,2). with Bombs, Mine field, Rifle turret. Even if I do siege rounds and mix in orbital strike, it’s a DPS loss vs just spamming bombs with shrapnel. Siege Rounds isn’t a dps trait.

34k dps againt normal golem using the same setup. 33k with battering ram instead of minefield.

32k if I do grenades instead of bombs, battering ram, and rifle turret, and stay at range.

Simply speaking, if you can keep up a lot of conditions on a boss, DPS engi is on par with Daredevil and Tempest. The problem is that with every condition not on the boss you lost 2% damage.

i can tell you, rather than explain in the most boring fashion, that it quite simply is the answer to this problem, and since you dont know that i can only assume you have no background in statistics (as youve claimed you have before).

I just did the deviation for you. All you derive is the original rate of success, the failure rate, any given sample success rate, and the variance expected.

But those won’t help you in a finite series resolve partials of non-events in averaging. But as always you really can’t explain yourself.

DGraves.3720:

I just did the deviation for you. All you derive is the original rate of success, the failure rate, any given sample success rate, and the variance expected.

But those won’t help you in a finite series resolve partials of non-events in averaging. But as always you really can’t explain yourself.

my bad. i always end up confusing bernoulli and binomial distributions. bernoulli is a single trial, while binomial is an aggregate distribution of bernoulli trials. the thing wrong with your previous statement,

For instance let’s set the constraint of 10 explosions. Well the first thing we do is calculate the odds, which for independent events, is just adding them up or just writing it out as .15 × 10 = 150%. For averaging that would mean at least one of the ten will be guaranteed but then we have the .5 to deal with.

is that such a setup will produce a distribution from which you randomly select an outcome. have a look at this for a concise example. youll probably need to click the “use as a Probability Distribution instead” link, because wolframalpha doesnt really play nice with URLs. as you can see, 10 trials, 15% success rate. our random variable X lives in the discrete set {0,1,2,3,4,5,6,7,8,9,10}, and the PDF, or Probability Density Function, tells you the probability that you will get a certain outcome for X each time you “roll the dice” (so to speak). when you integrate the pdf (or in this case, sum, since its a discrete distribution), the probability of getting any outcome from the set of {0,1,2,3,4,5,6,7,8,9,10} is 100%.

there is no such thing as 150% in these numbers.

you are literally not guaranteed to get any bleeds, and in fact, you have a 19.69% chance of getting 0 bleeds. this is how i know that you do not know what you are talking about. plus, standard deviation is entirely irrelevant to this conversation.

have i explained myself well enough yet?

DGraves.3720:

Math is a tool, not magic, so if you don’t know what to do with the numbers it won’t help you to get the answer.

clearly you dont know how to use the tool.

DGraves.3720:

.39 isn’t a mean, it’s a deviation, 1-.85^3 = .385875. That’s the deviation for shrapnel in a set of three grenades (one salvo).

that’s the chance of at least one success, not the standard deviation of the distribution

So, to bring all this stats back into the real world, let’s realize what’s happening for the Engi player in both Method A and Method B.

In Method A, the Engi doing a DPS test spams bomb autos for 60 seconds, using some method to clock his shrapnel DPS over those 60 seconds, and stops at 60 seconds. All good.

In Method B, however, the Engi does his DPS test, but after 60 seconds… he just lets the timer run for an additional 12 seconds. Doing nothing. Applying no extra Shrapnel uses. This is not a reasonable scenario for any sort of test.

Xyonon.3987:

You won’t “majorly overreaching” anything by averaging. In fact, it gets more accurate the longer the fight goes. In 60s, (let’s assume shrapnel lasts 20s), 1/3 of the shrapnels will be cut off before running out of duration. In a 10 minute fight, only 1/30.

Damage multiplied with the chance to proc is totally legit.

I think this was the best answer so far, the accuracy of the calculations depends on the length of the fight compared to the ramp up time of said trait/skill. This is true for many condition trait for which the condi duration is smaller than the internal CD (or availability of application). If one is puzzled by shrapnel, then sharpshooter should also be considered, especially since depending on the rotation, the frequency of crits will be affected.

I have the impression that the debate is more about theory versus simulation here…. and personally I am an experimentalist

DGraves.3720:

insanemaniac.2456:

DGraves.3720:

.39 isn’t a mean, it’s a deviation, 1-.85^3 = .385875. That’s the deviation for shrapnel in a set of three grenades (one salvo).

that’s the chance of at least one success, not the standard deviation of the distribution

Well let’s test it instead.

https://www.wolframalpha.com/input/?amp;rawformassumption=%7B“C”,“Binomial”%7D->%7B"ProbabilityDistribution"%7D&i=Binomial(3,.15)&rawformassumption=%7B"C",“Binomial”%7D+->+%7B"ProbabilityDistribution"%7D

So the standard deviation is .61…

If that’s the case 1 – .61 = .39.

So that’s where the number comes from. I “skipped” a step in the sequence since I figured you already knew how to work it.

It’s binomial distribution method since it best fits imo.

the standard deviation for a binomial distribution is sqrt(np(1-p)), not (1-p)^n.

they are similar to 2 significant figures in this case. the step you skipped is an important concept.

I solved it!

So that’s that. Sorry for offending anyone along the way.

Also, you’re absolutely right. Have a good one.

Better hold on to that IP

Man what a pun. Doesn’t that make this all seem worth it.

OK, it’s been a long time since I did statistics so be kind if I’ve not followed this completely. I get what both rikkity and dgraves are saying, kinda. Rikkity is correct in that there is a chance of never proccing the bleed in a trial with a small time limit, the 15% only becomes the true solution when you integrate the function over time to Infinity. Makes sense, people should agree on that. What we are looking for is the maximum DPS, and it’s here that the methodology differs. I’m going to use an analogy to explain my thinking, so people can give me a real world example if I fluff my logic.

Statistically speaking, the DPS from a trait like this has a build up time and a maximum DPS value, the current DPS value depending on how long the player has kept up the damage rotation and if they have done it for longer than the base duration of the bleeds procced, after which point current DPS will have reached its maximal value.

This means that the damage inflicted can be roughly modeled with the same equation as charging a capacitor: DPS[t]=DPS[max]e^(¥/t), where ¥ is an arbitrary time constant in this case determined by the rate of attack, the duration of the bleeds and the chance to proc, and the integral of this function with regards to time (the area under the curve, put simply) giving the total damage inflicted since you started the trial. This models an exponential curve that begins at zero and asymptotes at a set maximum y value for DPS when (¥/t)=0 at t=Infinity, and it’s this value that we’re all interested in.

What dgraves is saying is that when you stop the damage, so you remove the voltage source that is charging the capacitor in my example, DPS would decay exponentially until it returns to zero, much like the voltage across the capacitor would, and that we should include this discharge time in our calculations because there is still damage being done. Correct so far?

The problem is that this assumes that there is a body for the damage to flow through. In the capacitor example, if there is no resistor in the circuit then the capacitor would discharge almost instantly after the current was removed, as there is noting to stop the flow of charge back to its original state. In our case, the boss is dead. Were not going to stop the DPS before the boss is dead, so any discussion on the decay of the bleed damage after the boss dies is meaningless, and shouldn’t contribute to the DPS calculations. In this case, t would be the time from engaging the mob until the integral of the function equals the health of the mob: the line drops straight to zero after that point, as there is no longer a mob to damage. So as long as the time period of your DPS test is greater than the time needed to kill the mob, your calculated DPS needs no further adjustments beyond accounting for the wind up time.

This is why statistics requires a sufficient size pool of data to work, and does not work for small groups or values of time!

Tldr: the time period of your DPS test should only be equal or greater than the time taken to kill a given boss, assuming that time is greater than the time needed to reach the maximum possible stacks from the trait. You’re not going to stop the DPS til the boss is dead, and after the boss is dead the DPS is nil, and so is not relevant to the discussion.

Forgive the messy formatting, I typed this on my phone

Phaeton.9582:

Better hold on to that IP

Man what a pun. Doesn’t that make this all seem worth it.

sometimes i dont feel like its worth it to engage him, but then again i fear people might believe in Math™ by DGraves.

DGraves.3720:

insanemaniac.2456:

Phaeton.9582:

Better hold on to that IP

Man what a pun. Doesn’t that make this all seem worth it.

sometimes i dont feel like its worth it to engage him, but then again i fear people might believe in Math™ by DGraves.

Yet you yourself make terrible math errors. Very, very often. You know, like suggesting Poisson distribution as an option? Which of course doesn’t even make sense and would never work because of the requirements not being met.

its not an error to suggest to you a broad swath of material so you can better understand the things you are messing around with. i couldve also said gaussian and chi^2 distributions, and theyre no more relevant to this specific problem, yet are core to statistics as a whole.

insanemaniac.2456:

DGraves.3720:

insanemaniac.2456:

Phaeton.9582:

Better hold on to that IP

Man what a pun. Doesn’t that make this all seem worth it.

sometimes i dont feel like its worth it to engage him, but then again i fear people might believe in Math™ by DGraves.

Yet you yourself make terrible math errors. Very, very often. You know, like suggesting Poisson distribution as an option? Which of course doesn’t even make sense and would never work because of the requirements not being met.

its not an error to suggest to you a broad swath of material so you can better understand the things you are messing around with. i couldve also said gaussian and chi^2 distributions, and theyre no more relevant to this specific problem, yet are core to statistics as a whole.

Part of me wonders what your background with statistics is. You seem to have a lot of theoretical knowledge but also seem young in it (hence mixing up methods like Bernoulli and Binomial Distribution, suggesting something that doesn’t apply like Poisson, suggesting something that was already being done in the case of Bernoulli and being unable to explain your suggestion, excusing yourself for getting your terms backwards and throwing around new terms, etc.) as if you yourself are just learning it.

Even with that said it’s nice that you are tutoring. I myself do this though for a group slightly higher than high school. It’s a good way to keep your brain fresh and ensure mastery over both theory and application.

Just be careful about claiming you understand things. While I may not necessarily be confused a lot of people are afraid of math and analysis so they’ll buy into anything even if it’s completely wrong. I’m not popular (we’re both thankful for that actually) so the burden isn’t mine to bear.

DGraves.3720:

Part of me wonders what your background with statistics is. You seem to have a lot of theoretical knowledge but also seem young in it (hence mixing up methods like Bernoulli and Binomial Distribution, suggesting something that doesn’t apply like Poisson, suggesting something that was already being done in the case of Bernoulli and being unable to explain your suggestion, excusing yourself for getting your terms backwards and throwing around new terms, etc.) as if you yourself are just learning it.

ive taken a couple of the general requirement grad level stats courses, where there is a bunch of analysis and very exact language, and passed them with A’s, but its been a couple years, and several years before that. im not learning it, im remembering it, and not perfectly, which is why i corrected myself. and my main focus was applied math, especially acoustics, which does not require the really heavy statistics that could potentially be applied to it for things like error correction or something.

you see, this a game, not a job. if someone finds it fun to go through these calculations in their spare time, power to them. i can take a look at it if they post it publicly and check if its believable at the fairly rigorous level of a grad student who passed his classes, but i am not going to do more than take a look and i am not a teacher of this kind of material. because doing the calculations is a job to me, it isnt something im particularly keen to do in my spare time. but i like math, so i do enjoy having a look at the work others do about a game i enjoy.

insanemaniac.2456:

DGraves.3720:

Part of me wonders what your background with statistics is. You seem to have a lot of theoretical knowledge but also seem young in it (hence mixing up methods like Bernoulli and Binomial Distribution, suggesting something that doesn’t apply like Poisson, suggesting something that was already being done in the case of Bernoulli and being unable to explain your suggestion, excusing yourself for getting your terms backwards and throwing around new terms, etc.) as if you yourself are just learning it.

ive taken a couple of the general requirement grad level stats courses, where there is a bunch of analysis and very exact language, and passed them with A’s, but its been a couple years, and several years before that. im not learning it, im remembering it, and not perfectly, which is why i corrected myself. and my main focus was applied math, especially acoustics, which does not require the really heavy statistics that could potentially be applied to it for things like error correction or something.

you see, this a game, not a job. if someone finds it fun to go through these calculations in their spare time, power to them. i can take a look at it if they post it publicly and check if its believable at the fairly rigorous level of a grad student who passed his classes, but i am not going to do more than take a look and i am not a teacher of this kind of material. because doing the calculations is a job to me, it isnt something im particularly keen to do in my spare time. but i like math, so i do enjoy having a look at the work others do about a game i enjoy.

That explains it perfectly. Now that I know this I know exactly how to interact.

Thank you.

Jugglemonkey.8741:

OK, it’s been a long time since I did statistics so be kind if I’ve not followed this completely. I get what both rikkity and dgraves are saying, kinda. Rikkity is correct in that there is a chance of never proccing the bleed in a trial with a small time limit, the 15% only becomes the true solution when you integrate the function over time to Infinity. Makes sense, people should agree on that. What we are looking for is the maximum DPS, and it’s here that the methodology differs. I’m going to use an analogy to explain my thinking, so people can give me a real world example if I fluff my logic.

Statistically speaking, the DPS from a trait like this has a build up time and a maximum DPS value, the current DPS value depending on how long the player has kept up the damage rotation and if they have done it for longer than the base duration of the bleeds procced, after which point current DPS will have reached its maximal value.

This means that the damage inflicted can be roughly modeled with the same equation as charging a capacitor: DPS[t]=DPS[max]e^(¥/t), where ¥ is an arbitrary time constant in this case determined by the rate of attack, the duration of the bleeds and the chance to proc, and the integral of this function with regards to time (the area under the curve, put simply) giving the total damage inflicted since you started the trial. This models an exponential curve that begins at zero and asymptotes at a set maximum y value for DPS when (¥/t)=0 at t=Infinity, and it’s this value that we’re all interested in.

What dgraves is saying is that when you stop the damage, so you remove the voltage source that is charging the capacitor in my example, DPS would decay exponentially until it returns to zero, much like the voltage across the capacitor would, and that we should include this discharge time in our calculations because there is still damage being done. Correct so far?

The problem is that this assumes that there is a body for the damage to flow through. In the capacitor example, if there is no resistor in the circuit then the capacitor would discharge almost instantly after the current was removed, as there is noting to stop the flow of charge back to its original state. In our case, the boss is dead. Were not going to stop the DPS before the boss is dead, so any discussion on the decay of the bleed damage after the boss dies is meaningless, and shouldn’t contribute to the DPS calculations. In this case, t would be the time from engaging the mob until the integral of the function equals the health of the mob: the line drops straight to zero after that point, as there is no longer a mob to damage. So as long as the time period of your DPS test is greater than the time needed to kill the mob, your calculated DPS needs no further adjustments beyond accounting for the wind up time.

This is why statistics requires a sufficient size pool of data to work, and does not work for small groups or values of time!

Tldr: the time period of your DPS test should only be equal or greater than the time taken to kill a given boss, assuming that time is greater than the time needed to reach the maximum possible stacks from the trait. You’re not going to stop the DPS til the boss is dead, and after the boss is dead the DPS is nil, and so is not relevant to the discussion.

Forgive the messy formatting, I typed this on my phone

Tbh this is all I thought, bit of calculus

Model max dps (X) when t = infinity

Model time (-Tm) to get to x = X (max dps) (to within a practical probability that’s when you want to use a distribution?)

You’ve then got a model to find dps (x) at time (t) within a sensible probability when T > Tm

If the above isn’t feasible and t<<Tm, then to me damage per second seems a bit unhelpful to calculate anyway and you’d be looking at the rate of damage increase (which is also calculus?) to find x for an encounter.

Also yes the mob dies so there would be no decay a la capacitor

I think this is the definition of boredom.

10g to anyone who can explain how RNG would impact outlier probabilities, and 20g to anyone that can relate the implications of this to quantum theory when modelling in the real world.

And a popgun to runners up – aren’t giveaways fun!