[derangedcow]

yura fgt, fgt

[Leca]

the math here makes me sad


really the formulas is not hard at all (damie i found a few errors in your equation and i have no idea how you came up with what you did)

FULL formula is basically multiplying all the variables seperately because they are all independent.

Crit Modifier x Pet Buff Modifier % x Skill damage x Any extra modifiers (like aeh)


ok first step is the crit modifier which confuses the most people.

its pretty simple its just

1+ (your crit rate x crit damage)

but be careful!

crit rate is just your raw % so lets say 50%
but crit damage is how much your damage is increased as a result of that crit
so lets say you have 2x crits or crits that do double damage. in this case is would be increase of 1, or 100%

so using the above stats
it would be 1+ (.6 x 1)
or 1.6
this is the value that you use in multiplication to find out how average damage of your skills when taking into account crits.

yay so we got our first value

Example= 1.6



ok 2nd Slot is pet buff
ok this is so easy its just

% of time buffed x Buff %
Eir pet buffs 20 seconds every 60 seconds so 1/3 the time
1/3(.33) x .19 = .0627 or roughly 6% increase in damage on average due to pet buff

for dragon his buffs last 30 seconds every 60 and is 52% increase
For dragon it is 1/2 (.5) x .52 or .26 so 26% increase in damage on average due to pet buff

^ since above is an increase. you must add 1 the %s above if you want to use it in multiplication

1.6 x 1.0627

Ok the next step is easiest part. just read your friggen skill damage but make sure your number is correct as in if it or someone says something like +40% or +90% or anything with +. then convert it over to decimal form by adding a 1 ok

ill use typical noob using bonus 1/2 set ok (1.13)

1.6 x 1.0627 x 1.13

there!

his damage output is 1.92 compared to the damage given on a skill calculator....

so far your thinking ok big deal leca way to waste time
so i decided to make your decision process between golden dragon and Pet EIR. EASY

simply do both of theese formulas and pick the higher one. Ive simplified it for you

EIR_____________________DRAGMOM
(1+(.33 x (CBD)) x 1.0627_______(1+(CBR x .3)) x 1.26

EX my stats my dex char
(1+(.33 x .35)) x 1.06__________1+ (.5 x .3)) x 1.26
= 1.1992__________________________= 1.449
yup Gold dragon is better for a dex char who wouldve thought.

ok in Marqs case where his crits do 3x damage and he has like 40% chance base to hit them

using above formula

Eir is better than dragmom

easy?

This post has been edited by Pandora Hearts: 11 May 2010 - 11:16 PM

[Damie]

ok first of all, if you read the assumptions, i calculated an ARBITRARY EXPECTED DAMAGE OF ONE HIT. Yes, some skills do MORE DAMAGE than others, and other skills HIT MORE, but I am just calculating the EXPECTED DAMAGE of ANY ONE OF THOSE HITS. I am assuming a RANDOM PROCESS (which isn't necessarily true: people try to use skills conditional on the situation and advantage, but this complicates things way too much so we're just simplifying)

So what does expected mean probabilistically? Basically you add up all the possible values with their according probabilistic weight. Why consider expected value? Because thanks to law of large numbers, the average value of the hits converges to the expected value.

Example:

Roll a fair 6 sided die.

Possible values: 1 2 3 4 5 6
Probability of each: 1/6
Expected value: (1/6)1 + (1/6)2 + (1/6)3 + (1/6)4 + (1/6)5 + (1/6)6 = 3.5

So if I roll a die a large number of times, the average value will be close to 3.5 (this is easy to simulate).

So where does my formula come from? I am calculating the expected value of any one hit.

Possible values of that hit: Non critical damage or Critical damage
Probability of each: Depends on chance of deadly blow. Obviously, CDB tells you chance of getting a critical hit, so 1 - CDB is the chance for a non-critical hit. Note that CDB is a probability, so 1 - CDB is a probability
Expected value: ( 1 - CDB )*( Non critical damage ) + ( CDB )*( Critical damage )

The difference between noncrit and critical damage is a multiplier for crit damage, which is the Deadly Blow Rate. So both can expressed by one variable, which i call BASE

so Non critical damage = BASE, and Critical Damage = DBR * BASE, so substituting back

Expected Value: ( 1 - CDB )*( Non critical damage ) + ( CDB )*( Critical damage ) = ( 1 - CDB )*( BASE ) + ( CDB )*( DBR )*( BASE )

But of course, we can't forget the other multiplier that ALWAYS affects the skill damage, no matter if it is crit or not, and i forget the name, but it's called SKILL, so


Expected Value: ( 1 - CDB )*( BASE ) + ( CDB )*( DBR )*( BASE ) = ( 1 - CDB )*( SKILL * BASE ) + ( CDB )*( DBR )*( SKILL * BASE )

eir pet and black dragon up the CDB, lowering the chance for noncrit and upping the chance for crit, so the probabilities change weights in FAVOR for crit. it changes THE PROBABILITIES, not the DAMAGE PER SE, but since the probabilities change in favor of critical damage, the expected damage also goes up

Eir expected value: ( 1 - CDB )*( SKILL * BASE ) + ( CDB )*( DBR )*( SKILL * BASE ) --> ( 1 - CDB - Eir effect )*( SKILL * BASE ) + ( CDB + Eir effect )*( DBR )*( SKILL * BASE )
Black dragon expected value: ( 1 - CDB )*( SKILL * BASE ) + ( CDB )*( DBR )*( SKILL * BASE ) --> ( 1 - CDB - Black dragon effect )*( SKILL * BASE ) + ( CDB + Black dragon effect )*( DBR )*( SKILL * BASE )

Gold dragon just ups the deadly blow rate, meaning if you get a critical hit, the critical damage would be more than usual

Gold dragon expected value: ( 1 - CDB )*( SKILL * BASE ) + ( CDB )*( DBR )*( SKILL * BASE ) --> ( 1 - CDB )*( SKILL * BASE ) + ( CDB )*( DBR + Gold dragon effect )*( SKILL * BASE )


So those equations are done. We consider a time interval of one minute, since buffs restart every minute. For eir pet, 20 seconds of buff, 40 seconds of non buff, then start over. Black and gold dragon have 30 seconds of buff, and 30 of nonbuff. Now we consider whether our hits are done during the pet buff or not. THIS IS WHERE WE ASSUME RANDOM SKILL USE, meaning skills are used randomly independent of whether buff is on or not. Since it is purely random over time, it should statistically follow uniform distribution over this time interval.

What does this mean? For eir pet, since pet buff is 20 seconds, which is 1/3 of the time, implies that 1/3 of your hits on average should be when buff is on, and 2/3 when it isn't on. For black and gold dragon, 1/2 the time with buff, 1/2 not. SO, the expected overall damage of ONE hit, which i call TOTAL (I called it total not as in the sum of damages for a skill, but rather the total as in i considered all the parameters of the pet including the buff)

Eir pet: (1/3)( Eir buff multiplier ) * EXPECTED + 2/3 * EXPECTED
Black pet: (1/2)( Black dragon buff multiplier ) * EXPECTED + 1/2 * EXPECTED
Gold pet: (1/2)( Gold dragon buff multiplier ) * EXPECTED + 1/2 * EXPECTED

Eir has the advantage because it has a much higher cdb+ effect than the others, giving much much weight for critical hits, overshadowing it's smaller buff effect and time of buff effect. But like i said, if you focus on using hard hitting skills when buff effects are on, black dragon has a huge buff effect for that, and the chance of it being a critical hit is also high, so for those who plan and play wisely, black dragon might be your better friend. I myself usually don't notice when buff is on or not, and i prefer 2/3 of my attacks being critical, so i prefer eir, and although 30 seconds is longer than 20, 20 seconds is pretty good, especially since my skills take time to cd anyways.

Pandora Hearts, on 11 May 2010 - 11:14 PM, said:

the math here makes me sad

you're not the only one

Pandora Hearts, on 11 May 2010 - 11:14 PM, said:

really the formulas is not hard at all (damie i found a few errors in your equation and i have no idea how you came up with what you did)

please explain

Pandora Hearts, on 11 May 2010 - 11:14 PM, said:

FULL formula is basically multiplying all the variables seperately because they are all independent.

Crit Modifier x Pet Buff Modifier % x Skill damage x Any extra modifiers (like aeh)

incorrect. here you're assuming you always get critical hits, which you don't (you assume this by always multiplying the crit modifier). also, pet buff modifier is also not always on (pet effect, however, is). as for the extra modifiers, it's a nuisance variable that is uniform to all pets, so you can ignore that completely.

Pandora Hearts, on 11 May 2010 - 11:14 PM, said:

ok first step is the crit modifier which confuses the most people.

its pretty simple its just

1+ (your crit rate x crit damage)

but be careful!

crit rate is just your raw % so lets say 50%
but crit damage is how much your damage is increased as a result of that crit
so lets say you have 2x crits or crits that do double damage. in this case is would be increase of 1, or 100%

so using the above stats
it would be 1+ (.6 x 1)
or 1.6
this is the value that you use in multiplication to find out how average damage of your skills when taking into account crits.

average damage of your skills when taking into account ONLY crits. your non-crit hits have regular damage, your crit hits have the crit rate. you have to take into account both states, which is why you need to see the expected value which considers all that. what you have is the crit damage times it's probabilistic weight. no consideration for the non-crits.

as for the adding, let's say i have 50% chance deadly blow, and 200% deadly blow rate. that means i have .5 probability of getting a crit, and given that i have a critical hit, the damage would be 1 + 2.00, which is 3. The "adding the 1" rule only applies to dbr (and this makes sense, cuz if i have dbr of 40%, then i expect an increase of 40%, so my multiplier is 1.4, not 0.4, since 0.4 would mean my critical hits do less damage)

Pandora Hearts, on 11 May 2010 - 11:14 PM, said:

yay so we got our first value

Example= 1.6



ok 2nd Slot is pet buff
ok this is so easy its just

% of time buffed x Buff %
Eir pet buffs 20 seconds every 60 seconds so 1/3 the time
1/3(.33) x .19 = .0627 or roughly 6% increase in damage on average due to pet buff

for dragon his buffs last 30 seconds every 60 and is 52% increase
For dragon it is 1/2 (.5) x .52 or .26 so 26% increase in damage on average due to pet buff

once again you're not considering the times when you're not in buff

Pandora Hearts, on 11 May 2010 - 11:14 PM, said:

^ since above is an increase. you must add 1 the %s above if you want to use it in multiplication

1.6 x 1.0627

Ok the next step is easiest part. just read your friggen skill damage but make sure your number is correct as in if it or someone says something like +40% or +90% or anything with +. then convert it over to decimal form by adding a 1 ok

yeah you need to rewrite the last part: "convert it to decimal form by adding a 1"? ehh no

Pandora Hearts, on 11 May 2010 - 11:14 PM, said:

ill use typical noob using bonus 1/2 set ok (1.13)

1.6 x 1.0627 x 1.13

there!

his damage output is 1.92 compared to the damage given on a skill calculator....

so far your thinking ok big deal leca way to waste time
so i decided to make your decision process between golden dragon and Pet EIR. EASY

simply do both of theese formulas and pick the higher one. Ive simplified it for you

EIR_____________________DRAGMOM
(1+(.33 x (CBD)) x 1.0627_______(1+(CBR x .3)) x 1.26

EX my stats my dex char
(1+(.33 x .35)) x 1.06__________1+ (.5 x .3)) x 1.26
= 1.1992__________________________= 1.449
yup Gold dragon is better for a dex char who wouldve thought.

ok in Marqs case where his crits do 3x damage and he has like 40% chance base to hit them

using above formula

Eir is better than dragmom

easy?

no it's not that easy sadly. hope i cleared it up a bit.

[Marq]

awwww yea its math battle tiem. the ultimate test of who is smarter and whos pride is going to be trashed

[Leca]

Damie, on 12 May 2010 - 03:55 AM, said:

ok first of all, if you read the assumptions, i calculated an ARBITRARY EXPECTED DAMAGE OF ONE HIT. Yes, some skills do MORE DAMAGE than others, and other skills HIT MORE, but I am just calculating the EXPECTED DAMAGE of ANY ONE OF THOSE HITS. I am assuming a RANDOM PROCESS (which isn't necessarily true: people try to use skills conditional on the situation and advantage, but this complicates things way too much so we're just simplifying)

So what does expected mean probabilistically? Basically you add up all the possible values with their according probabilistic weight. Why consider expected value? Because thanks to law of large numbers, the average value of the hits converges to the expected value.

Example:

Roll a fair 6 sided die.

Possible values: 1 2 3 4 5 6
Probability of each: 1/6
Expected value: (1/6)1 + (1/6)2 + (1/6)3 + (1/6)4 + (1/6)5 + (1/6)6 = 3.5

So if I roll a die a large number of times, the average value will be close to 3.5 (this is easy to simulate).

So where does my formula come from? I am calculating the expected value of any one hit.

Possible values of that hit: Non critical damage or Critical damage
Probability of each: Depends on chance of deadly blow. Obviously, CDB tells you chance of getting a critical hit, so 1 - CDB is the chance for a non-critical hit. Note that CDB is a probability, so 1 - CDB is a probability
Expected value: ( 1 - CDB )*( Non critical damage ) + ( CDB )*( Critical damage )

^ above is pretty much my formula you know

(1 - CBD) * (non critical damage) = 0 since non critical modify damage by 0% so 1-x * 0 is always 0

its just Rate x crit damage. and plus one since its an increase

The difference between noncrit and critical damage is a multiplier for crit damage, which is the Deadly Blow Rate. So both can expressed by one variable, which i call BASE

so Non critical damage = BASE, and Critical Damage = DBR * BASE, so substituting back

Expected Value: ( 1 - CDB )*( Non critical damage ) + ( CDB )*( Critical damage ) = ( 1 - CDB )*( BASE ) + ( CDB )*( DBR )*( BASE )



But of course, we can't forget the other multiplier that ALWAYS affects the skill damage, no matter if it is crit or not, and i forget the name, but it's called SKILL, so


Expected Value: ( 1 - CDB )*( BASE ) + ( CDB )*( DBR )*( BASE ) = ( 1 - CDB )*( SKILL * BASE ) + ( CDB )*( DBR )*( SKILL * BASE )



ive finally figured out what youve done
youve taking independent variables and put them together forcing yourself to calculate the damage of a Crit + a non crit at the same time.








eir pet and black dragon up the CDB, lowering the chance for noncrit and upping the chance for crit, so the probabilities change weights in FAVOR for crit. it changes THE PROBABILITIES, not the DAMAGE PER SE, but since the probabilities change in favor of critical damage, the expected damage also goes up

Eir expected value: ( 1 - CDB )*( SKILL * BASE ) + ( CDB )*( DBR )*( SKILL * BASE ) --> ( 1 - CDB - Eir effect )*( SKILL * BASE ) + ( CDB + Eir effect )*( DBR )*( SKILL * BASE )
Black dragon expected value: ( 1 - CDB )*( SKILL * BASE ) + ( CDB )*( DBR )*( SKILL * BASE ) --> ( 1 - CDB - Black dragon effect )*( SKILL * BASE ) + ( CDB + Black dragon effect )*( DBR )*( SKILL * BASE )

Gold dragon just ups the deadly blow rate, meaning if you get a critical hit, the critical damage would be more than usual

Gold dragon expected value: ( 1 - CDB )*( SKILL * BASE ) + ( CDB )*( DBR )*( SKILL * BASE ) --> ( 1 - CDB )*( SKILL * BASE ) + ( CDB )*( DBR + Gold dragon effect )*( SKILL * BASE )


So those equations are done. We consider a time interval of one minute, since buffs restart every minute. For eir pet, 20 seconds of buff, 40 seconds of non buff, then start over. Black and gold dragon have 30 seconds of buff, and 30 of nonbuff. Now we consider whether our hits are done during the pet buff or not. THIS IS WHERE WE ASSUME RANDOM SKILL USE, meaning skills are used randomly independent of whether buff is on or not. Since it is purely random over time, it should statistically follow uniform distribution over this time interval.

What does this mean? For eir pet, since pet buff is 20 seconds, which is 1/3 of the time, implies that 1/3 of your hits on average should be when buff is on, and 2/3 when it isn't on. For black and gold dragon, 1/2 the time with buff, 1/2 not. SO, the expected overall damage of ONE hit, which i call TOTAL (I called it total not as in the sum of damages for a skill, but rather the total as in i considered all the parameters of the pet including the buff)

Eir pet: (1/3)( Eir buff multiplier ) * EXPECTED + 2/3 * EXPECTED
Black pet: (1/2)( Black dragon buff multiplier ) * EXPECTED + 1/2 * EXPECTED
Gold pet: (1/2)( Gold dragon buff multiplier ) * EXPECTED + 1/2 * EXPECTED

Eir has the advantage because it has a much higher cdb+ effect than the others, giving much much weight for critical hits, overshadowing it's smaller buff effect and time of buff effect. But like i said, if you focus on using hard hitting skills when buff effects are on, black dragon has a huge buff effect for that, and the chance of it being a critical hit is also high, so for those who plan and play wisely, black dragon might be your better friend. I myself usually don't notice when buff is on or not, and i prefer 2/3 of my attacks being critical, so i prefer eir, and although 30 seconds is longer than 20, 20 seconds is pretty good, especially since my skills take time to cd anyways.

Pandora Hearts, on 11 May 2010 - 11:14 PM, said:

the math here makes me sad

you're not the only one

Pandora Hearts, on 11 May 2010 - 11:14 PM, said:

really the formulas is not hard at all (damie i found a few errors in your equation and i have no idea how you came up with what you did)

please explain

Pandora Hearts, on 11 May 2010 - 11:14 PM, said:

FULL formula is basically multiplying all the variables seperately because they are all independent.

Crit Modifier x Pet Buff Modifier % x Skill damage x Any extra modifiers (like aeh)

incorrect. here you're assuming you always get critical hits, which you don't (you assume this by always multiplying the crit modifier). also, pet buff modifier is also not always on (pet effect, however, is). as for the extra modifiers, it's a nuisance variable that is uniform to all pets, so you can ignore that completely.

Pandora Hearts, on 11 May 2010 - 11:14 PM, said:

ok first step is the crit modifier which confuses the most people.

its pretty simple its just

1+ (your crit rate x crit damage)

but be careful!

crit rate is just your raw % so lets say 50%
but crit damage is how much your damage is increased as a result of that crit
so lets say you have 2x crits or crits that do double damage. in this case is would be increase of 1, or 100%

so using the above stats
it would be 1+ (.6 x 1)
or 1.6
this is the value that you use in multiplication to find out how average damage of your skills when taking into account crits.

average damage of your skills when taking into account ONLY crits. your non-crit hits have regular damage, your crit hits have the crit rate. you have to take into account both states, which is why you need to see the expected value which considers all that. what you have is the crit damage times it's probabilistic weight. no consideration for the non-crits.

as for the adding, let's say i have 50% chance deadly blow, and 200% deadly blow rate. that means i have .5 probability of getting a crit, and given that i have a critical hit, the damage would be 1 + 2.00, which is 3. The "adding the 1" rule only applies to dbr (and this makes sense, cuz if i have dbr of 40%, then i expect an increase of 40%, so my multiplier is 1.4, not 0.4, since 0.4 would mean my critical hits do less damage)

Pandora Hearts, on 11 May 2010 - 11:14 PM, said:

yay so we got our first value

Example= 1.6



ok 2nd Slot is pet buff
ok this is so easy its just

% of time buffed x Buff %
Eir pet buffs 20 seconds every 60 seconds so 1/3 the time
1/3(.33) x .19 = .0627 or roughly 6% increase in damage on average due to pet buff

for dragon his buffs last 30 seconds every 60 and is 52% increase
For dragon it is 1/2 (.5) x .52 or .26 so 26% increase in damage on average due to pet buff

once again you're not considering the times when you're not in buff

Pandora Hearts, on 11 May 2010 - 11:14 PM, said:

^ since above is an increase. you must add 1 the %s above if you want to use it in multiplication

1.6 x 1.0627

Ok the next step is easiest part. just read your friggen skill damage but make sure your number is correct as in if it or someone says something like +40% or +90% or anything with +. then convert it over to decimal form by adding a 1 ok

yeah you need to rewrite the last part: "convert it to decimal form by adding a 1"? ehh no

Pandora Hearts, on 11 May 2010 - 11:14 PM, said:

ill use typical noob using bonus 1/2 set ok (1.13)

1.6 x 1.0627 x 1.13

there!

his damage output is 1.92 compared to the damage given on a skill calculator....

so far your thinking ok big deal leca way to waste time
so i decided to make your decision process between golden dragon and Pet EIR. EASY

simply do both of theese formulas and pick the higher one. Ive simplified it for you

EIR_____________________DRAGMOM
(1+(.33 x (CBD)) x 1.0627_______(1+(CBR x .3)) x 1.26

EX my stats my dex char
(1+(.33 x .35)) x 1.06__________1+ (.5 x .3)) x 1.26
= 1.1992__________________________= 1.449
yup Gold dragon is better for a dex char who wouldve thought.

ok in Marqs case where his crits do 3x damage and he has like 40% chance base to hit them

using above formula

Eir is better than dragmom

easy?

no it's not that easy sadly. hope i cleared it up a bit.

sorry sophie i have class so i will update this later

[iLunian]

derangedcow, on 11 May 2010 - 09:23 PM, said:

yura fgt, fgt

who ya calling fgt, fgt

[derangedcow]

gj fgt

[iLunian]

fgt!

[derangedcow]

have u read it yet fgt

[Marq]

can u 2 fgts take ur bickering to pms and stop ruining my thread?

[derangedcow]

i wasnt the one being the fgt

[Damie]

Meant for leca. Don't need to read it all. You can jump to the end if you're bored.

try not to respond in my quotes, i barely saw your comments, especially since in my posts i use bold

Pandora Hearts, on 12 May 2010 - 12:28 PM, said:

^ above is pretty much my formula you know

Yours: Crit Modifier x Pet Buff Modifier % x Skill damage x Any extra modifiers (like aeh)
Mine: ( 1 - CDB )*( SKILL * BASE ) + ( CDB )*( DBR )*( SKILL * BASE )

They are not the same at all. Like I said, you are only considering crits, so your formula is the SECOND half of mine (excluding the extra modifiers, since this applies INDEPENDENTLY of having a pet or not, so it can be considered a NUISANCE variable and IGNORED or considered as part of BASE)

Don't believe me? Crit modifier is basically a consideration of crit rate and crit damage multiplier, aka CDB * DBR. Pet buff modifier applies to CDB or DBR depending on the pet; this is very loose, so your formula isn't really clear. Both have skill mentioned.

Pandora Hearts, on 12 May 2010 - 12:28 PM, said:

(1 - CBD) * (non critical damage) = 0 since non critical modify damage by 0% so 1-x * 0 is always 0

its just Rate x crit damage. and plus one since its an increase

(1 - CBD) * (non critical damage) = 0??? Are you saying you don't have noncritical hits?

Let's say I have base damage of 100. Let's also say i have a skill rate of 50% increase, so my base damage now should be close to 150.

Now, let's say i have a 30% chance of deadly blow (so out of 100 hits, 30 are critical), and if critical, my deadly blow rate is 200% increase, meaning my damage is multiplied by 3. So a crit hit damage would be 450.

According to my formula: ( 1 - CDB )*( SKILL * BASE ) + ( CDB )*( DBR )*( SKILL * BASE ) = ( 1 - .3 )*( 1.5 * 100 ) + ( .3 )*( 3 )*( 1.5 * 100 ) = 240

So my average damage should be 240 (including CRITICAL HITS AND NON CRITICAL HITS)

Here's a little simulation of using ONLY ONE SKILL SO I HAVE A FIXED BASE DAMAGE (I even allowed a 5% deviation for base damage). 100 hits:

156 152 154 154 154 153 152 154 146 149 149 149 154 148 148 147 152 155 143 148 151 148 142 156 154 156 145 153 146 146 153 143 150 143 151 148 150 146 147 151 152 149 144 149 154 143 150 153 156 147 150 145 153 151 149 153 149 156 150 145 155 145 151 144 145 154 144 156 151 144 146 150 155 154 155 154 147 153 150 143 146 145 145 149 153 144 146 153 143 156 155 156 156 152 154 150 142 152 152 152

(the mean is 149.91, close to 150)

Next i sampled a list of crit hits (expected is 30%, and 1 represents normal hit, 3 represents critical hit):

1 3 1 1 1 1 1 1 1 3 1 1 1 1 3 1 3 1 1 3 3 3 1 1 1 1 1 1 3 1 1 1 1 1 1 3 1 1 3 1 3 1 3 1 3 1 3 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1 3 1 1 3 1 1 3 1 3 1 1 3 1 1 1 1 3 1 1 1 1 3 1 3 1 3 1 3 3 3 1 1 1 1 3 1

(there are 29 critical hits, expected was 30)

SO OUR NEW VALUES:

156 456 154 154 154 153 152 154 146 447 149 149 154 148 444 147 456 155 143 444 453 444 142 156 154 156 145 153 438 146 153 143 150 143 151 444 150 146 441 151 456 149 432 149 462 143 450 153 156 147 150 145 153 151 149 153 149 468 450 145 155 145 151 144 435 154 144 468 151 144 438 150 465 154 155 462 147 153 150 143 438 145 145 149 153 432 146 459 143 468 155 468 468 456 154 150 142 152 456 152

When we take the mean: 237.23, really close to 240.

I hope the simulation explained it better, I don't really want to get into the math of it. Basically the last list of numbers i gave is the simulation of skill hits (while using one skill ;

*******************

ALL I AM SAYING IS:

• Your formula does not consider whether an attack is critical or not
• my formula and yours are not the same
• if you DO noncrit damage, there's no way it can be 0
• No, this simulation is NOT the best simulation of a stage run or myth run, but the effect is the same (all that changes is the base damage depending on the skill, and the amount of hits per time interval, either way, under a random process hypothesis which in this case is NOT NECESSARILY TRUE but isn't so bad, they are uniform, so under lots and lots of runs convergence is still satisfied
• These variables are NOT independent. First: You either DO a CRITICAL HIT, or DO NOT, AKA mutually exclusive. They do NOT multiply because they are independent, they multiply out of how the game is set. You do a base damage, where you raise it up due to a skill multiplier. If it's not a critical hit, check for any other multipliers and if it's a critical hit, raise up damage to include critical hit multiplier, and then check for other multipliers. That's it, no more.
• The expected value is basically the long-run average, and when you have two distinct events, aka mutually exclusive, such as damage depending on noncrit and crit, both which are mutually exclusive, then the expected value of damage is the SUM of the probability weighted value of the events.

This post has been edited by Damie: 24 May 2010 - 12:22 AM

[Leca]

Damie, on 24 May 2010 - 12:18 AM, said:

Meant for leca. Don't need to read it all. You can jump to the end if you're bored.

try not to respond in my quotes, i barely saw your comments, especially since in my posts i use bold




Yours: Crit Modifier x Pet Buff Modifier % x Skill damage x Any extra modifiers (like aeh)
Mine: ( 1 - CDB )*( SKILL * BASE ) + ( CDB )*( DBR )*( SKILL * BASE )

They are not the same at all. Like I said, you are only considering crits, so your formula is the SECOND half of mine (excluding the extra modifiers, since this applies INDEPENDENTLY of having a pet or not, so it can be considered a NUISANCE variable and IGNORED or considered as part of BASE)

Don't believe me? Crit modifier is basically a consideration of crit rate and crit damage multiplier, aka CDB * DBR. Pet buff modifier applies to CDB or DBR depending on the pet; this is very loose, so your formula isn't really clear. Both have skill mentioned.




(1 - CBD) * (non critical damage) = 0??? Are you saying you don't have noncritical hits?

Im saying that Non crits modify your damage by 0
im solving this equations for a modifer % here.
it doesnt matter if u have 70% chance for a noncrit since non crits dont modify damage
1+ .7(0) = 1
anything multiplied by 1 is itself so the 1 is useless

Damie, on 24 May 2010 - 12:18 AM, said:

Let's say I have base damage of 100. Let's also say i have a skill rate of 50% increase, so my base damage now should be close to 150.

Now, let's say i have a 30% chance of deadly blow (so out of 100 hits, 30 are critical), and if critical, my deadly blow rate is 200% increase, meaning my damage is multiplied by 3. So a crit hit damage would be 450.

According to my formula: ( 1 - CDB )*( SKILL * BASE ) + ( CDB )*( DBR )*( SKILL * BASE ) = ( 1 - .3 )*( 1.5 * 100 ) + ( .3 )*( 3 )*( 1.5 * 100 ) = 240

according my forumula it should be
1 + (.3) x (3) x 1.5 = 235

Damie, on 24 May 2010 - 12:18 AM, said:

So my average damage should be 240 (including CRITICAL HITS AND NON CRITICAL HITS)

Here's a little simulation of using ONLY ONE SKILL SO I HAVE A FIXED BASE DAMAGE (I even allowed a 5% deviation for base damage). 100 hits:

156 152 154 154 154 153 152 154 146 149 149 149 154 148 148 147 152 155 143 148 151 148 142 156 154 156 145 153 146 146 153 143 150 143 151 148 150 146 147 151 152 149 144 149 154 143 150 153 156 147 150 145 153 151 149 153 149 156 150 145 155 145 151 144 145 154 144 156 151 144 146 150 155 154 155 154 147 153 150 143 146 145 145 149 153 144 146 153 143 156 155 156 156 152 154 150 142 152 152 152

(the mean is 149.91, close to 150)

Next i sampled a list of crit hits (expected is 30%, and 1 represents normal hit, 3 represents critical hit):

1 3 1 1 1 1 1 1 1 3 1 1 1 1 3 1 3 1 1 3 3 3 1 1 1 1 1 1 3 1 1 1 1 1 1 3 1 1 3 1 3 1 3 1 3 1 3 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1 3 1 1 3 1 1 3 1 3 1 1 3 1 1 1 1 3 1 1 1 1 3 1 3 1 3 1 3 3 3 1 1 1 1 3 1

(there are 29 critical hits, expected was 30)

SO OUR NEW VALUES:

156 456 154 154 154 153 152 154 146 447 149 149 154 148 444 147 456 155 143 444 453 444 142 156 154 156 145 153 438 146 153 143 150 143 151 444 150 146 441 151 456 149 432 149 462 143 450 153 156 147 150 145 153 151 149 153 149 468 450 145 155 145 151 144 435 154 144 468 151 144 438 150 465 154 155 462 147 153 150 143 438 145 145 149 153 432 146 459 143 468 155 468 468 456 154 150 142 152 456 152

When we take the mean: 237.23, really close to 240.

I hope the simulation explained it better, I don't really want to get into the math of it. Basically the last list of numbers i gave is the simulation of skill hits (while using one skill ;

*******************

ALL I AM SAYING IS:

• Your formula does not consider whether an attack is critical or not
• my formula and yours are not the same
• if you DO noncrit damage, there's no way it can be 0
• No, this simulation is NOT the best simulation of a stage run or myth run, but the effect is the same (all that changes is the base damage depending on the skill, and the amount of hits per time interval, either way, under a random process hypothesis which in this case is NOT NECESSARILY TRUE but isn't so bad, they are uniform, so under lots and lots of runs convergence is still satisfied
• These variables are NOT independent. First: You either DO a CRITICAL HIT, or DO NOT, AKA mutually exclusive. They do NOT multiply because they are independent, they multiply out of how the game is set. You do a base damage, where you raise it up due to a skill multiplier. If it's not a critical hit, check for any other multipliers and if it's a critical hit, raise up damage to include critical hit multiplier, and then check for other multipliers. That's it, no more.
• The expected value is basically the long-run average, and when you have two distinct events, aka mutually exclusive, such as damage depending on noncrit and crit, both which are mutually exclusive, then the expected value of damage is the SUM of the probability weighted value of the events.

yes criticals are mutually exclusive. but crits to pet to aeh to skilldamage. they are all independent therefore you can multiply each of them


i think we both had a similiar idea but for me i rather take the average crit dmg then calculate the total damage of both variables

having 30% to do 300% is the same as having x1.90% dmg on average so i rather put that into my calculations
or same with pet dragon
+50% dmg 50% of the time is just x 1.25



i think if we want to settle this i will run my own experiment

i will hit the scarecrow 20 times with my blow of wind spell because it is 1 hit and fairly easy to see


ill run the experiment with you

[iLunian]

im just saying fgt cause im bored


or am i?

[Damie]

^ nah, you're still a fgt

[Damie]

Pandora Hearts, on 24 May 2010 - 11:24 AM, said:

Damie, on 24 May 2010 - 12:18 AM, said:

Meant for leca. Don't need to read it all. You can jump to the end if you're bored.

try not to respond in my quotes, i barely saw your comments, especially since in my posts i use bold




Yours: Crit Modifier x Pet Buff Modifier % x Skill damage x Any extra modifiers (like aeh)
Mine: ( 1 - CDB )*( SKILL * BASE ) + ( CDB )*( DBR )*( SKILL * BASE )

They are not the same at all. Like I said, you are only considering crits, so your formula is the SECOND half of mine (excluding the extra modifiers, since this applies INDEPENDENTLY of having a pet or not, so it can be considered a NUISANCE variable and IGNORED or considered as part of BASE)

Don't believe me? Crit modifier is basically a consideration of crit rate and crit damage multiplier, aka CDB * DBR. Pet buff modifier applies to CDB or DBR depending on the pet; this is very loose, so your formula isn't really clear. Both have skill mentioned.




(1 - CBD) * (non critical damage) = 0??? Are you saying you don't have noncritical hits?

Im saying that Non crits modify your damage by 0
im solving this equations for a modifer % here.
it doesnt matter if u have 70% chance for a noncrit since non crits dont modify damage
1+ .7(0) = 1
anything multiplied by 1 is itself so the 1 is useless

• what you said is wrong: "im saying that non crits modify your damage by 0", since damage isn't something that is modified by crits, rather it is a function dependent on a base damage with multipliers, where there is an additional multiplier if there is a crit hit. so, damage is affected positively when there's a crit
• there are no equations to solve.
• noncrits ARE damage without the crit multiplier (dbr)

Pandora Hearts, on 24 May 2010 - 11:24 AM, said:

Damie, on 24 May 2010 - 12:18 AM, said:

Let's say I have base damage of 100. Let's also say i have a skill rate of 50% increase, so my base damage now should be close to 150.

Now, let's say i have a 30% chance of deadly blow (so out of 100 hits, 30 are critical), and if critical, my deadly blow rate is 200% increase, meaning my damage is multiplied by 3. So a crit hit damage would be 450.

According to my formula: ( 1 - CDB )*( SKILL * BASE ) + ( CDB )*( DBR )*( SKILL * BASE ) = ( 1 - .3 )*( 1.5 * 100 ) + ( .3 )*( 3 )*( 1.5 * 100 ) = 240

according my forumula it should be
1 + (.3) x (3) x 1.5 = 235

• if i change it so that base is 100, skill is 400%, crit is 20%, and dbr is 600%, then my formula gives around 1100, yours 800. Run another simulation, mean is 1108.
• Note that in your equation the lower the crit probability, the damage is brought a lot lower, LOWER than the damage you actually do, because it does not consider the damage that normal attacks do.
• what mine does: damage is composed of normal damage times the expected frequency of normal damage adding on critical damage times the expected frequency of critical damage, aka overall long-run average
• what yours does: Crit Modifier x Pet Buff Modifier % x Skill damage x Any extra modifiers problems: if i have 0% crit rate, does that mean i do only normal damage even though i have pet buff? you have it multiplied here, so basically pets do nothing for my crits if i have 0% crit rate. these pets are ADDITIVES, they add to crit rate, or add to crit damage, so it makes no sense to have it here multiplied

Pandora Hearts, on 24 May 2010 - 11:24 AM, said:

Damie, on 24 May 2010 - 12:18 AM, said:

So my average damage should be 240 (including CRITICAL HITS AND NON CRITICAL HITS)

Here's a little simulation of using ONLY ONE SKILL SO I HAVE A FIXED BASE DAMAGE (I even allowed a 5% deviation for base damage). 100 hits:

156 152 154 154 154 153 152 154 146 149 149 149 154 148 148 147 152 155 143 148 151 148 142 156 154 156 145 153 146 146 153 143 150 143 151 148 150 146 147 151 152 149 144 149 154 143 150 153 156 147 150 145 153 151 149 153 149 156 150 145 155 145 151 144 145 154 144 156 151 144 146 150 155 154 155 154 147 153 150 143 146 145 145 149 153 144 146 153 143 156 155 156 156 152 154 150 142 152 152 152

(the mean is 149.91, close to 150)

Next i sampled a list of crit hits (expected is 30%, and 1 represents normal hit, 3 represents critical hit):

1 3 1 1 1 1 1 1 1 3 1 1 1 1 3 1 3 1 1 3 3 3 1 1 1 1 1 1 3 1 1 1 1 1 1 3 1 1 3 1 3 1 3 1 3 1 3 1 1 1 1 1 1 1 1 1 1 3 3 1 1 1 1 1 3 1 1 3 1 1 3 1 3 1 1 3 1 1 1 1 3 1 1 1 1 3 1 3 1 3 1 3 3 3 1 1 1 1 3 1

(there are 29 critical hits, expected was 30)

SO OUR NEW VALUES:

156 456 154 154 154 153 152 154 146 447 149 149 154 148 444 147 456 155 143 444 453 444 142 156 154 156 145 153 438 146 153 143 150 143 151 444 150 146 441 151 456 149 432 149 462 143 450 153 156 147 150 145 153 151 149 153 149 468 450 145 155 145 151 144 435 154 144 468 151 144 438 150 465 154 155 462 147 153 150 143 438 145 145 149 153 432 146 459 143 468 155 468 468 456 154 150 142 152 456 152

When we take the mean: 237.23, really close to 240.

I hope the simulation explained it better, I don't really want to get into the math of it. Basically the last list of numbers i gave is the simulation of skill hits (while using one skill ;

*******************

ALL I AM SAYING IS:

• Your formula does not consider whether an attack is critical or not
• my formula and yours are not the same
• if you DO noncrit damage, there's no way it can be 0
• No, this simulation is NOT the best simulation of a stage run or myth run, but the effect is the same (all that changes is the base damage depending on the skill, and the amount of hits per time interval, either way, under a random process hypothesis which in this case is NOT NECESSARILY TRUE but isn't so bad, they are uniform, so under lots and lots of runs convergence is still satisfied
• These variables are NOT independent. First: You either DO a CRITICAL HIT, or DO NOT, AKA mutually exclusive. They do NOT multiply because they are independent, they multiply out of how the game is set. You do a base damage, where you raise it up due to a skill multiplier. If it's not a critical hit, check for any other multipliers and if it's a critical hit, raise up damage to include critical hit multiplier, and then check for other multipliers. That's it, no more.
• The expected value is basically the long-run average, and when you have two distinct events, aka mutually exclusive, such as damage depending on noncrit and crit, both which are mutually exclusive, then the expected value of damage is the SUM of the probability weighted value of the events.

yes criticals are mutually exclusive. but crits to pet to aeh to skilldamage. they are all independent therefore you can multiply each of them

no, they were multiplied out of construction of the game. they are multipliers. they aren't random events. skill% isn't random, pet effect isn't random, and eq effects aren't random (in fact, these aren't even probabilities, so you can't declare them to be independent).

Pandora Hearts, on 24 May 2010 - 11:24 AM, said:

i think we both had a similiar idea but for me i rather take the average crit dmg then calculate the total damage of both variables

two variables? average of averages does not mean its an average of total damage.

Pandora Hearts, on 24 May 2010 - 11:24 AM, said:

having 30% to do 300% is the same as having x1.90% dmg on average so i rather put that into my calculations
or same with pet dragon
+50% dmg 50% of the time is just x 1.25



i think if we want to settle this i will run my own experiment

i will hit the scarecrow 20 times with my blow of wind spell because it is 1 hit and fairly easy to see


ill run the experiment with you

[iLunian]

mean damie is mean