about Damage per second

bennymars

i would like to ask if really the crit rate is included in the formula of damage per second in a melee class?. like seeker,blademaster and barbarian?


it so hard to believe a crit % which is based on chance can be a part of something that happens 100% of the time and not based on chance.

according to this thread: http://pwi-forum.perfectworld.com/showthread.php?t=741822

one of the guy there said that the formula of dps was:

Avg DPS = ((Max damage - Min damage)/2) x (1 + crit rate) x Attack speed


but according to this guide: (its from PW PH, wuxia means blademaster)but its still a Perfect world online game.

http://janelh.wikidot.com/pwtribune:vol12h

her formula in the DPS calculation was:

attack speed = 1/ ans
to get ans:
1(baseaspd) - (attack delay) = ans

i already look at the perfect world wiki but there is no DPS calculation but only the APS calculation.

i thank you in advance for your help and for the knowledge that you may share.

Michael_Dark - Lost City

bennymars wrote: »

Avg DPS = ((Max damage - Min damage)/2) x (1 + crit rate) x Attack speed

This makes sense. The other was confused.

A resident PWI math geek should be here shortly to help you.

Olbaze - Sanctuary

Criticals are part of your DPS calculation simply because they add an average number of hits.

This is especially true when you have a large sample, such as with high attack speed characters.

Avg DPS = ((Max damage - Min damage)/2) x (1 + crit rate) x Attack speed

That's wrong, btw. It should be Maximum + Minimum, not Maximum - Minimum.

Also, Attack Levels found factor into that as x (1 + Attack Level/100).

The DPS "formula", as it even says on the name, is average. Meaning it factors in average increment from damage and average increment from criticals. Heck, there's a ~50% chance that your actual damage will be lower than your average. But there is also a 50% chance it'll be higher.

When the number of hits increases, the actual damage you've dealt approaches your average damage.

bennymars

Olbaze - Sanctuary wrote: »

Criticals are part of your DPS calculation simply because they add an average number of hits.

can i ask how did you know about this and is there any chart online that can show that crit% is included there. I mean, crit% is a chance. it doesn't happen 100% of the time (if it's not 100% ofcourse).

for example, if the crit% is only 5, then there is a 5% chance to deal a crit. damage.

i mean to include that chance in a damage per second every time, it makes that chance percentage happens 100% of the time making that small percentage chance exact. i mean its unbelievable.

SoulRequiem - Sanctuary

Not to mention that formula doesn't consider your opponent's defence/level/def. level

bennymars

sorry for double post. but the description of crit% is the percentage chance of dealing crit damage.

the value of crit% is the value of chance of dealing crit damage. So why did they included that value and made it an exact value that happens everytime, 100% of the time. it should not be included in the damage per sec.


for example if the value of crit% is 1. the value "1" is not an exact value that happens 100% of time. that value of 1 is the value of chance..... (sorry if i can't explain it more clearly because im not that fluent in english..)


i can't believe they included the value of chance in the formula..

i hope someone enlighten me...

truekossy

bennymars wrote: »

can i ask how did you know about this and is there any chart online that can show that crit% is included there. I mean, crit% is a chance. it doesn't happen 100% of the time (if it's not 100% ofcourse).

for example, if the crit% is only 5, then there is a 5% chance to deal a crit. damage.

i mean to include that chance in a damage per second every time, it makes that chance percentage happens 100% of the time making that small percentage chance exact. i mean its unbelievable.

That's not how it works.


Say you do 10 damage per hit with 5 APS and have a 50% crit chance. That means over time you'll crit 50% of the time on average. So let's say you attacked something for 4 seconds and got the following:
10
20
10
10
10
20
20
10
20
20
10
10
10
20
20
20
10
20
20
10


Now you'll notice that while you didn't crit exactly every other hit, it did, at the end, average out to half of them being normal attacks (10s) and the other half being criticals due to the 50% crit rate. That's closer to how it works since from that, you'd see the average DPS is 75 (50 base damage per second times 1.5 due to the average chance to crit being 50%).

The DPS formula doesn't assume you'll crit every time like you seem to believe. We're simply factoring in your average chance to crit as that affects your DPS and the more time passes, the closer to that average crit rate you'll get. If we were to ignore crit, DPS calculations would become incredibly inaccurate unless the person in question had a crit rate below 10% (and even then disregarding crit would cause major inaccuracy).

Olbaze - Sanctuary

bennymars wrote: »

sorry for double post. but the description of crit% is the percentage chance of dealing crit damage.

the value of crit% is the value of chance of dealing crit damage. So why did they included that value and made it an exact value that happens everytime, 100% of the time. it should not be included in the damage per sec.


for example if the value of crit% is 1. the value "1" is not an exact value that happens 100% of time. that value of 1 is the value of chance..... (sorry if i can't explain it more clearly because im not that fluent in english..)


i can't believe they included the value of chance in the formula..

i hope someone enlighten me...

The reason they turned it into a multiplier is because we're talking averages. The 1 + crit% multiplier is the average increase in damage that you will gain from all of your crits.

The reason that it's considered rather accurate is because with more hits, your damage gets closer and closer to the average.

Here is a damage log I took just now. The stats that you can count from there are:
Number of hits: 21
Number of crits: 6
Minimum Damage: 120
Maximum Damage: 239
Average damage of all hits: 154

In this sample, my average crit % is 28.5%. In my stats, it's 33%.

bennymars

SoulRequiem - Sanctuary wrote: »

Not to mention that formula doesn't consider your opponent's defence/level/def. level

truekossy wrote: »

That's not how it works.


Say you do 10 damage per hit with 5 APS and have a 50% crit chance. That means over time you'll crit 50% of the time on average. So let's say you attacked something for 4 seconds and got the following:
10
20
10
10
10
20
20
10
20
20
10
10
10
20
20
20
10
20
20
10


Now you'll notice that while you didn't crit exactly every other hit, it did, at the end, average out to half of them being normal attacks (10s) and the other half being criticals due to the 50% crit rate. That's closer to how it works since from that, you'd see the average DPS is 75 (50 base damage per second times 1.5 due to the average chance to crit being 50%).

The DPS formula doesn't assume you'll crit every time like you seem to believe. We're simply factoring in your average chance to crit as that affects your DPS and the more time passes, the closer to that average crit rate you'll get. If we were to ignore crit, DPS calculations would become incredibly inaccurate unless the person in question had a crit rate below 10% (and even then disregarding crit would cause major inaccuracy).

wow i really really thank you for that information. it really helps a lot.

but the word "inaccurate" caught my attention. the fact that you included that crit% chance. that makes the value of dps inaccurate too.

i mean if your going to compute your damage per second. then you will not get the same amount or figure. because the value of crit% was not exact. i mean its so inaccurate too.

so the amount of DPS is indefinite.. because of that crit% chance..

i think there is something wrong with that formula...

Olbaze - Sanctuary

bennymars wrote: »

wow i really really thank you for that information. it really helps a lot.

but the word "inaccurate" caught my attention. the fact that you included that crit% chance. that makes the value of dps inaccurate too.

i mean if your going to compute your damage per second. then you will not get the same amount or figure. because the value of crit% was not exact. i mean its so inaccurate too.

so the amount of DPS is indefinite.. because of that crit% chance..

i think there is something wrong with that formula...

No there isn't. It's called a limit.

Averages are only inaccurate when you have a small sample size.

You do realize that you could make the exact same argument about average damage? After all, there's a 50% chance you'll score higher damage than your average and a 50% chance you'll score lower than that.

The point with average DPS calculation isn't accuracy. They're simply used as a comparative tool. Since it's all just theory, you can ignore the "chance" factor.

DemansPsy - Lost City

bennymars wrote: »

wow i really really thank you for that information. it really helps a lot.

but the word "inaccurate" caught my attention. the fact that you included that crit% chance. that makes the value of dps inaccurate too.

i mean if your going to compute your damage per second. then you will not get the same amount or figure. because the value of crit% was not exact. i mean its so inaccurate too.

so the amount of DPS is indefinite.. because of that crit% chance..

i think there is something wrong with that formula...

But the crit % IS exact, if you have 10% crit then you have 10% crit, you'll do double damge every time you crit which is 10% over a long period of time which is EXACTLY what dps is, damage you deal on average over a very long (as the limit of T(time) approches infinity) the forumula above thoguh is incompltle, it doesn't take into account your chacne to miss an attack and also assumes rage damage is 200% which isn't the case for sage sins at least since they can be perma 220%, and like someone mentioned ealier, it doesnt take into account att level, def level, and enemy's resist.

However the amount of DPS IS definite as long as you take time to approach infinitly (and yes you can do that easliy and it will make mathmatical sense.)

bennymars

Olbaze - Sanctuary wrote: »

No there isn't. It's called a limit.

Averages are only inaccurate when you have a small sample size.

You do realize that you could make the exact same argument about average damage? After all, there's a 50% chance you'll score higher damage than your average and a 50% chance you'll score lower than that.

The point with average DPS calculation isn't accuracy. They're simply used as a comparative tool. Since it's all just theory, you can ignore the "chance" factor.

i beg to disagree but in a computation like this accuracy matters.. i think with a correct formula we can get an accurate results.

in your said formula (like you said i change the - to +)
Avg DPS = ((Max damage + minimum damage)/2) x (1 + crit rate) x Attack speed

Every variable there are exact. The max damage,the minimum damage, the attack speed they are all exact figures. The variable crit rate which is the amount of chance, an indefinite figure became an exact figure by including it in the above formula. just looking at the formula. im sure there is something wrong there....

i think the chance crit% should be computed separately together with the defense of the enemy (like what SoulRequiem said) .

upsides

Imagine 2 people with equal base attack and attack and defense levels. One with 33% crit and the other with 10% crit. Ignoring crit in the formula would mean that both of those character's DPS is the same. That is not the case.

The crit I think is something we want to be exact in order to approximate the average fluctuation in damage due to crit.

bennymars

DemansPsy - Lost City wrote: »

But the crit % IS exact, if you have 10% crit then you have 10% crit, you'll do double damge every time you crit which is 10% over a long period of time which is EXACTLY what dps is, damage you deal on average over a very long (as the limit of T(time) approches infinity) the forumula above thoguh is incompltle, it doesn't take into account your chacne to miss an attack and also assumes rage damage is 200% which isn't the case for sage sins at least since they can be perma 220%, and like someone mentioned ealier, it doesnt take into account att level, def level, and enemy's resist.

However the amount of DPS IS definite as long as you take time to approach infinitly (and yes you can do that easliy and it will make mathmatical sense.)

crit% is a chance. like you said. if you have 10% crit, you have 10% chance to deal a crit damage. its not an exact figure.

bennymars

upsides wrote: »

Imagine 2 people with equal base attack and attack and defense levels. One with 33% crit and the other with 10% crit. Ignoring crit in the formula would mean that both of those character's DPS is the same. That is not the case.

The crit I think is something we want to be exact in order to approximate the average fluctuation in damage due to crit.

like you, i also like to know the exact dps. but i think the formula is wrong. every variable in the formula are exact other than the chance value of the crit%. i think probability computation should also be included that way we can have an acceptable result.


Anyway i think i stop here.. i really really thank all of you for the information that you share. its really a big help. thank you

upsides

bennymars wrote: »

like you, i also like to know the exact dps. but i think the formula is wrong. every variable in the formula are exact other than the chance value of the crit%. i think probability computation should also be included that way we can have an acceptable result.


Anyway i think i stop here.. i really really thank all of you for the information that you share. its really a big help. thank you

But from what I know, whether you include in in the formula or later you'd still get the exact same results. It's a case where it doesn't matter whether it's exact or not because you're approaching a limit. I'm not a math geek though so I don't have much credibility.
You're welcome.

bennymars

HOLY MOTHER OF GOD NOW I GET IT.!!!!

crit% should not be included in the dps because crit% is what affects the whole dps.

crit% is the same as the defense of the enemy in a sense that it affects the value of dps.

what makes our dps result indefinite?. the defense of the enemy and of course the probability of our crit%, the level of the enemy, the enemies' resistance, the buff etc.

Olbaze - Sanctuary

bennymars wrote: »

HOLY MOTHER OF GOD NOW I GET IT.!!!!

crit% should not be included in the dps because crit% is what affects the whole dps.

crit% is the same as the defense of the enemy in a sense that it affects the value of dps.

what makes our dps result indefinite?. the defense of the enemy and of course the probability of our crit%, the level of the enemy, the enemies' resistance, the buff etc.

The defenses of the enemy make results "indefinite" just because they are a variable instead of a constant.

Crit% is a constant.

Also, I think you should educate yourself on the law of large numbers.

As for your point about affecting the whole spectrum of DPS: DPS is multiplicative, so the same is true of your APS and your Attack Levels. If you ignore those, then you're claiming that Average DPS = Average DPS, which is obviously false.

The point is the following:
As your sample size increases, the amount of critical hits you get per your sample approaches the percentage stated in your Character Info Window.

bennymars

Olbaze - Sanctuary wrote: »

As your sample size increases, the amount of critical hits you get per your sample approaches the percentage stated in your Character Info Window.

This. and thanks for the link of law of large numbers.

SO even if the results are indefinite, the amount of every result are very close with it each other.

by the way thanks for all of you guys who answered me. i appreciate it.

--
i really really love this forum. so much reliable info to get. ^_^

truekossy

bennymars wrote: »

--
i really really love this forum. so much reliable info to get. ^_^

Yeah. While we do love some of our trolls and the like, when a person genuinely asks for information in a decent manner and isn't an obnoxious *** about the responses they get we tend to treat them fairly well... most of the time. b:chuckle

_Skai_ - Raging Tide

The crit % rate averages out over time. It gets more accurate the larger your sample. If you get a sample file of damages you log for 10,000,000 hits, then the average DPS will be exactly the formula you stated.

I'm glad for someone like Olbaze. He's one of the only sins I can count on for any PWI math related subject that I'm not sure about.

bennymars wrote: »

i beg to disagree but in a computation like this accuracy matters.. i think with a correct formula we can get an accurate results.

in your said formula (like you said i change the - to +)
Avg DPS = ((Max damage + minimum damage)/2) x (1 + crit rate) x Attack speed

Every variable there are exact. The max damage,the minimum damage, the attack speed they are all exact figures. The variable crit rate which is the amount of chance, an indefinite figure became an exact figure by including it in the above formula. just looking at the formula. im sure there is something wrong there....

i think the chance crit% should be computed separately together with the defense of the enemy (like what SoulRequiem said) .

This is where you're a lil wrong. You said every variable is exact. That also includes the crit rate. The crit rate is a solid x%, as is your min damage, max damage, and attack speed.

20% crit is a solid 20% crit. 38% crit is a solid 38% crit. That formula is doing exactly what it's supposed to, which is to calculate the average DPS.


By average it has to include the crit rate, because let's say your crit rate is 20%. That means on average (statistically), 1 in 5 of your hits will be a critical. Let's say your max damage is 10000 and your min damage is 7500, and you're attacking with 5 attacks per second. In this example I will be excluding attack and defense levels, to make it easier to understand.

Let's say you hit these numbers:
8435
9622
7712
8172
16700 (crit)

The average of those numbers (by simple add everything and divide by the number of hits) is 10128.2, and over the course of a second, which was 5 attacks per second, averages your DPS to 50641 damage.

If we take the formula above, and plug in the appropriate numbers:

Avg DPS = ((Max damage + minimum damage)/2) x (1 + crit rate) x Attack speed
Avg DPS = ((10000 + 7500)/2) * (1 + .20) * 5
Avg DPS = 52500

So as you can see, the formula works out around the same average as the small sample of 5 hits that I decided to randomly generate. Do this on a large scale, such as 10,000 hits, and the numbers would end up closer to the average given by the formula.

DemansPsy - Lost City

bennymars wrote: »

crit% is a chance. like you said. if you have 10% crit, you have 10% chance to deal a crit damage. its not an exact figure.

But like i mentioned in the post, as you let time past or as you attack a target more and more over an extremly long time, it becomes an exact figure, example, lets say you hit a target a million times, you crit % was 10%, and you ended up criting 100100 times. Thats over 10% but equal to 10.01%. lets say 10 million attacks, and you crited 999750 times, thats equivalent to 9.9975%, you critied 250 less times than the average yet this number is less than 1/100th of a percent off of 10% and if you plug it into a dps formula, the difference between using 9.9975% or using 10% is completely negligible. For all realistic purposes you crited 10% of the time for 2x damage, increasing your overall dps by 10%.

Summary, in a small sample size, your right, its not an exact figure, however, practically, when your hiting a mob several times a second and killing mob after mob, your sample size becomes so large that it acts exactly like an exact figure.

BTW, you know the (max att + min att)/2 part of the forumla? Thats exactly the same as assuming the crit is an exact number, in reality you'll hit ANYWHERE between your max and min and taking the average of those two ONLY works if your assuming that you are attacking many many times, otherwize it makes as much sense as assuming crit is an exact number.

JPsi - Raging Tide

What Skai/Olblaze have said prior is correct, but have also missed one thing.
These DPS calculations do not take into account Sacrificial Strike weapons or Crit Damage buffs.
For Sage Wolf emblem its easy enough (perma buff), simply multiply crit rate by 1.2 when calculating.
Demon Wolf emblem 1.2 will approximate this also assuming a long enough timeframe/it being cast the instant its gone off CD, but is highly inaccurate for any short durations or if people cant keep up with casting. Holds while its a 1.4 dmg multiplier while wolf emblem is on, but back to 1.0 while its off at 30 second intervals between.

Sac Strike and other proc buffs can be added in also to the dps calculations but it gets a little more in depth trying to calculate that.

At the time of writing this its a little late for me and I cant remember the strength of the crit dmg buff from guild base so cant account for that atm. may do so later

Olbaze - Sanctuary

JPsi - Raging Tide wrote: »

What Skai/Olblaze have said prior is correct, but have also missed one thing.
These DPS calculations do not take into account Sacrificial Strike weapons or Crit Damage buffs.
For Sage Wolf emblem its easy enough (perma buff), simply multiply crit rate by 1.1 when calculating.
Demon Wolf emblem 1.1 will approximate this also assuming a long enough timeframe/it being cast the instant its gone off CD, but is highly inaccurate for any short durations or if people cant keep up with casting. Holds while its a 1.2 dmg multiplier while wolf emblem is on, but back to 1.0 while its off at 30 second intervals between.

Wrong. For Wolf Emblem, you get the following with, say, 30% crit:

70 hits at 100% damage
30 hits at 200% + Rage Damage%
You get: 70 * 1 + 30 * (2 + R%) = 70 + 60 + 30*R% = 100 + 30 + 30*R% = 100 + 30*(1+R%)
Averages to: 1 + Crit%*(1+Rage Damage%)

As for SS and GoF, those have a proc rate of 15% and 20% respectively, so they get a 1.15 or 1.2 multiplier after all others.

JPsi - Raging Tide

Edit : Ah yes, a little tired and didn't quite see it, while yes a wolf emblemed sage crit is only a 1.1 multiplier on total dmg from a crit, it would go in there as a 1.2 due to the way crits are treated as an additive not multiplicative in the formula. correcting original post now

Quilue - Sanctuary

OK if you want to talk about chance, then what's the chance of not scoring a crit over time?

Suppose my crit rate is 50%, what's the probability of not scoring a crit after 5 hits?

That would be 0.5^5 = 0.03125 = ~3%.

There is about 3% chance that I won't crit in 5 hits, how can you disregard crit rate and claim to be accurate? There would have been 3% chance that you were right.

Think about what else you were averaging - you were averaging base damage right? How can you be comfortable with that but not be comfortable with factoring in crit rate?

bennymars

guys i have a new question about the crit% in the DPS formula again. In the DPS formula:

Avg DPS = ((Max damage + minimum damage)/2) x (1 + crit rate) x Attack speed

Every variable in the formula increases the average DPS right?. the a.)max damage, b.) minimum damage c.) crit rate, and d.) attack speed.

Now about the crit rate, why is that the value of the crit rate as it is, is the one that increases the damage?. for example if the value of the crit rate is 20%. then if we will read the crit% in the formula above, the dps was increased by the crit rate of .2.

but the value 20% is not an amount that increases damage, but a percentage of chance to deal crit damage.

and if we choose to follow that formula, then there is just a small difference between 20% and 50%. because if we use the value of 20% and 50% as it is. the difference in damage will be just .3 only.

but you need to understand that the crit% is a value of chance. with 50% crit rate, that will obviously will deal way and more damage than with 20% crit rate.with a 50% crit rate the activation of crit is so much higher.

i hope you understand me here... thanks in advance for your help.

Olbaze - Sanctuary

bennymars wrote: »

guys i have a new question about the crit% in the DPS formula again. In the DPS formula:

Avg DPS = ((Max damage + minimum damage)/2) x (1 + crit rate) x Attack speed

Every variable in the formula increases the average DPS right?. the a.)max damage, b.) minimum damage c.) crit rate, and d.) attack speed.

Now about the crit rate, why is that the value of the crit rate as it is, is the one that increases the damage?. for example if the value of the crit rate is 20%. then if we will read the crit% in the formula above, the dps was increased by the crit rate of .2.

but the value 20% is not an amount that increases damage, but a percentage of chance to deal crit damage.

and if we choose to follow that formula, then there is just a small difference between 20% and 50%. because if we use the value of 20% and 50% as it is. the difference in damage will be just .3 only.

but you need to understand that the crit% is a value of chance. with 50% crit rate, that will obviously will deal way and more damage than with 20% crit rate.with a 50% crit rate the activation of crit is so much higher.

i hope you understand me here... thanks in advance for your help.

The formula for the increment is derived from the way crits function, which is something I explained earlier.

As for the increments being small, they aren't, they just look that way. When you go from 20% crit to 50%, your multiplier goes from 1.2 to 1.5, meaning you get 1.5/1.2 = 1.25 = 25% more average DPS, which is massive.

truekossy

What the above said... but you may want to edit that to say it's from 1.2 multiplier to 1.5 to avoid confusing someone, Olba.

Olbaze - Sanctuary

truekossy wrote: »

What the above said... but you may want to edit that to say it's from 1.2 multiplier to 1.5 to avoid confusing someone, Olba.

Do as I do, not as I say.

_Skai_ - Raging Tide

bennymars wrote: »

guys i have a new question about the crit% in the DPS formula again. In the DPS formula:

Avg DPS = ((Max damage + minimum damage)/2) x (1 + crit rate) x Attack speed

Every variable in the formula increases the average DPS right?. the a.)max damage, b.) minimum damage c.) crit rate, and d.) attack speed.

Now about the crit rate, why is that the value of the crit rate as it is, is the one that increases the damage?. for example if the value of the crit rate is 20%. then if we will read the crit% in the formula above, the dps was increased by the crit rate of .2.

but the value 20% is not an amount that increases damage, but a percentage of chance to deal crit damage.

and if we choose to follow that formula, then there is just a small difference between 20% and 50%. because if we use the value of 20% and 50% as it is. the difference in damage will be just .3 only.

but you need to understand that the crit% is a value of chance. with 50% crit rate, that will obviously will deal way and more damage than with 20% crit rate.with a 50% crit rate the activation of crit is so much higher.

i hope you understand me here... thanks in advance for your help.

Because as the crit rate increases, the crit numbers in a large sample increase, thus making the overall DPS higher.

For example, let's use small static numbers and solid crit numbers, with a solid APS of 5 attacks per second.

For this example, (remember I'm leaving a lot of variables out, just to make my point here clear), the min and max damage will be 200.

The crit rate in the first sample will be 20%, so 1 in 5 hits (again, statistically) will be a crit. This sample will have 20 hits.

01. 200
02. 200
03. 200
04. 200
05. 400 (crit)
06. 200
07. 200
08. 200
09. 200
10. 400 (crit)
11. 200
12. 200
13. 200
14. 200
15. 400 (crit)
16. 200
17. 200
18. 200
19. 200
20. 400 (crit)

The average DPS of these 20 hits, with 5 attacks per second, averages out to 240 damage. And that's with a 20% crit rate.

The next sample will have the same damages, but with a 25% crit rate. This means that 1 in 4 hits will be a crit.

01. 200
02. 200
03. 200
04. 400 (crit)
05. 200
06. 200
07. 200
08. 400 (crit)
09. 200
10. 200
11. 200
12. 400 (crit)
13. 200
14. 200
15. 200
16. 400 (crit)
17. 200
18. 200
19. 200
20. 400 (crit)

The average DPS of these 20 hits, with 5 attacks per second, averages out to 250 damage. And this is with a 25% crit rate.

So as you can see, as the crit rate increases, the average DPS increases as well. I hope this small example can clear things up for you.