My investigations lead me to believe that the screenshot is incorrect or simply a red herring; based on the first 13 data points, especially taking note of levels 11, 12, and 13, between which it becomes evident that the slope is decreasing, the precision formula clearly follows a logistic regression instead of an exponential regression. This immediately makes much more sense and answers many questions about precision.

1500 is the precision needed to have 100% critical chance at level 60.
1% crit chance = 15 precision
1% crit chance * 150% damage = +5% extra damage = 5 attack
15 precision = 5 attack

Now, with extra critical damage, the conversion changes.
1% crit chance * 250% damage = 15% extra damage = 15 attack
15 precision = 15 attack

So, if +critical damage % > 100, precision > attack.

My investigations lead me to believe that the screenshot is incorrect or simply a red herring; based on the first 13 data points, especially taking note of levels 11, 12, and 13, between which it becomes evident that the slope is decreasing, the precision formula clearly follows a logistic regression instead of an exponential regression. This immediately makes much more sense and answers many questions about precision.

1500 is the precision needed to have 100% critical chance at level 60.
1% crit chance = 15 precision
1% crit chance * 150% damage = +5% extra damage = 5 attack
15 precision = 5 attack

Now, with extra critical damage, the conversion changes.
1% crit chance * 250% damage = 15% extra damage = 15 attack
15 precision = 15 attack

So, if +critical damage % > 100, precision > attack.

Ok firstly i want to say that i am not a statistician (im an engineer) so i dont know a whole lot about probability distributions of which the logistic is one.

So by plotting crit chance % against precision you get:

So clearly something is up with the distribution of crit chance

So you said it followed the logistic distribution which is kind of logical but i just dont know where you got the numbers from.

Logistic distribution follows: Chance of something = 1 / (1 + e^-z) where z = B_{0} + B_{1}x_{1} +...

In the above, x_{1}, x_{2} etc are all the various criteria that could affect the chance. So in our case we would have just one, Precision (probably incorrect in reality. More likely to have many factors). And then the chance is the values shown in the graph above. I just dont see where everything else comes in. There are too many unknowns.

Ignoring all of the maths above, where did you get this asymptote of 1500 for 100% crit at lvl 60. This seems so arbitrary especially as we only have 13 levels to go by

EDIT: After some more messing around, i got the values you got for 100% crit chance and thus the required precision values per level. I then plotted these required precision values against level and i get a graph that "LOOKS" like a logistic distribution. The curve has the same shape but everything else is different. For this to truly be a logistic distribution this would have to be a plot of probability of crit on the y (between 1 for a crit and 0 for non-crit) against precision.

The newer posts in the Incgamers thread (using an emulator to datamine lv 14-60 numbers) seem to indicate that the formula for 1-30 is different from the formula for 31-60. This shows the problem with extrapolating any 1-13 numbers to the level 60 game.

To be balanced, %Crit stacking CANNOT give as much damage as +%Damage stacking. Stacking +%Damage just gives you damage, nothing else. Crits tend to generate extra Fury/Arcane Power and can sometimes proc entirely different effects (aoe explosions etc). So of course the raw damage increase from Precision will be lower than Attack.

The newer posts in the Incgamers thread (using an emulator to datamine lv 14-60 numbers) seem to indicate that the formula for 1-30 is different from the formula for 31-60. This shows the problem with extrapolating any 1-13 numbers to the level 60 game.

Care to give us the source of that.

By the way guys. I have very solid proof for the crit formula, let's say I didn't just make it up.
If I recall correctly the formula changes at level 11 or 12. And I'm careful when saying this but we don't know the actual formula. The game uses a precalculated table (many of those in D2) most likely.

The way it is right now Precision seems to be very weak at level 60, despite some abilities procing off it. However we don't know what's in store for the final.

----

Another thing. I've been thinking about is Vitatliy.
What I believe is happening is this. The early game Health values scale (depending on hero) anywhere from

Health = 6 * Vitality + C

to

Health = 8 * Vitality + C

On the way to level 60 this formula slowly goes towards...

Health = 4 * Vitality + C

We don't know how exactly, of course. This is just a theory I have.
It explains the tooltip (Vitality gives 4 Health per point spent) and the Gamescon 11 slideshow.

We desperately require some beta tester to provide us with +Vitality data to maybe figure out a formula.

Barbarian
Vitality = (2 x Level) + 9
HP = (6 x Vitality) + 18 so s/he gains 2 Vit per level and 6 HP per Vit
-------------------
Monk
Vitality = Level + 8
HP = (8 x Vitality) + 4 so s/he gains 1 Vit per level and 8 HP per Vit
-------------------
Witch Doctor
Vitality = Level + 9
HP = 8 x Vitality so s/he gains 1 Vit per level and 8 HP per Vit
-------------------
Wizard and Demon Hunter
Vitality = 0.25 x ((6 x Level) - ((-1)^ Level) + 29)
HP = ((20 x Vitality) / 3) + 16 for when Vitality is 9, 12, 15, 18 (i.e. multiples of 3)
HP = (8 x Vitality) + 16 for when Vitality is anything else
So this means that s/he gains an alternating amount of Vit per Level and gains 20 HP per 3 Vit

I am not sure about the progression towards a gradient of 4 but you may well be right

I'm aware of your numbers. Anyway, despite not knowing the formula (you guessed: it's a server side calculation) we can however see a trend. This is for the Wizard.

As we can see at 30 Vitality it is close to Health = 7 * Vit.

Lvl Vit Hlth Hlth / Vit
13 80 408 5.1

I also have this value, found in a youtube video. To me this appears to be based off Vitality independent of Level. As Vitality goes up (by whatever means: level, items) the benefit decreases from 8 * Vit -> 4 * Vit. This seems to be a counter messure to limit Vitality stacking. On the other hand, it's probably safe to say +health% items will still work as they used to (nvm, just got a few values. tnx mfb. they are a little bit off, but not much)

Seems the way vitality works is very complex, and not the easy linear approach it had in D2.

Concerning how precision works: I honestly don't understand how some people have arrived at the conclusion that it requires 1500 precision to get 100% crit chance at lvl 60. This value seems to merely fabricated out of thin air. None of my own work is getting values anywhere near this.

There is significant evidence that it will require considerably more precision to max out crit than those 1500. First an official screenshot from a lvl 60 character (the only one we have). Second the emulator getting results that fit both the currently known datapoints of lvl 1-13, as well as lvl 60. This is very hard evidence to me, so unless somebody comes up with some realy tangible proof at least I will continue to consider precision to be utterly worthless at endgame, with +precision on items being a wasted affix like +light radius etc.

1500 is the precision needed to have 100% critical chance at level 60.

Yeah I came to the same conclusion. So obvious.

Oh, by the way, here's more maths : wanna know the probability that a single member of the development team would suggest a 0.01% ratio ? The answer is 0.01%.
So unless somebody comes up with some realy tangible proof that the D3 team is a bunch of retarded brats, I will continue to consider precision as the work of some healthy and grown humans.

Seems the way vitality works is very complex, and not the easy linear approach it had in D2.

Concerning how precision works: I honestly don't understand how some people have arrived at the conclusion that it requires 1500 precision to get 100% crit chance at lvl 60. This value seems to merely fabricated out of thin air. None of my own work is getting values anywhere near this.

It's because if you graph precision needed for 100% crit vs level for levels 1 through 13, the graph approaches an asymptote at around 1500. The best explanation I've read is that the crit/precision vs level formula is a piecewise function.

I'm aware of your numbers. Anyway, despite not knowing the formula (you guessed: it's a server side calculation) we can however see a trend. This is for the Wizard.

I'm aware of your numbers. Anyway, despite not knowing the formula (you guessed: it's a server side calculation) we can however see a trend. This is for the Wizard.

If we assume that you get 4 HP per Vit (based on the tooltip text):
Lv 1: 76 HP = 9*4 + 40
Lv 2: 84 HP = 10*4 + 44
Lv 3: 96 HP = 12*4 + 48
Lv 4: 104 HP = 13*4 + 52
Lv 5: 116 HP = 15*4 + 56
Lv 6: 124 HP = 16*4 + 60
Lv 7: 136 HP = 18*4 + 64
etc.

Maybe you stop getting base HP from leveling after level 50?

Anyways, with this information I can calculate the proportion of Vitality and Defense which gives maximum EHP for a given attribute total. In other words, this shows you how to gem for maximum EHP.

B = Base HP with no VIT
V = Vitality
H = HP per VIT
D = Defense
T = Defense Threshold
L = Level

T=2L+6
L=60
H=4

Putting that into Wolfram Alpha comes out to:

D = B/4 + V - 54

If we substitute in Base HP:
B=4L+36

D = V+15

So in other words, you want Defense to be fifteen points higher than VIT for max EHP, OR you want to put all of your points into DEF for maximum healing effectiveness, or somewhere in-between those two. You NEVER want to put all your points into VIT as it gives less EHP than D = V + 15, and has none of the additional healing effectiveness improvements DEF has.

My eye sight may not be as good as it used to be but I am pretty sure that the HP is actually 8072! At the top, the dmg increase is 533 and these threes dont look like the HP. Me thinks gear and passives

The screen isn't full front and the image is kinda blurry, could be a 3 or an 8. You are right. Still the best one of those I have seen so far. Most of them videos (even at 1080p) are impossible to read, as they were screencaptured.

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"Traitors! Even in death, the armies of Khanduras will still obey their king!"

Crit specific gear will need serious bonuses from talents and other sources to match pure damage bonuses.

It's really confusing if you ask me. High end items gives only +90 Precision (usually) wich is only +5% critical rate, fairly weak compered to +90% damage from +90 Attack or +90% Class Damage. The whole point of stats (Attack, Precision, Vitality, Defence) is that one point in any of those should have the same "power level". So, if you find a +20 attack ring it should give the same damage bonus as a +20 precision ring (and both items would have the same level requeriment).

Crit specific gear will need serious bonuses from talents and other sources to match pure damage bonuses.

It's really confusing if you ask me. High end items gives only +90 Precision (usually) wich is only +5% critical rate, fairly weak compered to +90% damage from +90 Attack or +90% Class Damage. The whole point of stats (Attack, Precision, Vitality, Defence) is that one point in any of those should have the same "power level". So, if you find a +20 attack ring it should give the same damage bonus as a +20 precision ring (and both items would have the same level requeriment).

I wish people would stop equating 1 Attack to +1% total damage output.

Let's say you start with 600 Attack. Your 100 base damage spell will deal 700 damage. Now you gain 1 Attack. Your spell deals 701 damage. 1/700 = +0.14% damage increase, not 1%.

Precision still increases total damage less than Attack does, but it is not by a ridiculously large ("15:1") margin.

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1500 is the precision needed to have 100% critical chance at level 60.

1% crit chance = 15 precision

1% crit chance * 150% damage = +5% extra damage = 5 attack

15 precision = 5 attack

Now, with extra critical damage, the conversion changes.

1% crit chance * 250% damage = 15% extra damage = 15 attack

15 precision = 15 attack

So, if +critical damage % > 100, precision > attack.

It's better than nothing, but it still seems attack will be better unless you have exorbitant +crit damage. Gah.

Ok firstly i want to say that i am not a statistician (im an engineer) so i dont know a whole lot about probability distributions of which the logistic is one.

So by plotting crit chance % against precision you get:

So clearly something is up with the distribution of crit chance

So you said it followed the logistic distribution which is kind of logical but i just dont know where you got the numbers from.

Logistic distribution follows: Chance of something = 1 / (1 + e^-z) where z = B

_{0}+ B_{1}x_{1}+...In the above, x

_{1}, x_{2}etc are all the various criteria that could affect the chance. So in our case we would have just one, Precision (probably incorrect in reality. More likely to have many factors). And then the chance is the values shown in the graph above. I just dont see where everything else comes in. There are too many unknowns.Ignoring all of the maths above, where did you get this asymptote of 1500 for 100% crit at lvl 60. This seems so arbitrary especially as we only have 13 levels to go by

EDIT: After some more messing around, i got the values you got for 100% crit chance and thus the required precision values per level. I then plotted these required precision values against level and i get a graph that "LOOKS" like a logistic distribution. The curve has the same shape but everything else is different. For this to truly be a logistic distribution this would have to be a plot of probability of crit on the y (between 1 for a crit and 0 for non-crit) against precision.

To be balanced, %Crit stacking CANNOT give as much damage as +%Damage stacking. Stacking +%Damage just gives you damage, nothing else. Crits tend to generate extra Fury/Arcane Power and can sometimes proc entirely different effects (aoe explosions etc). So of course the raw damage increase from Precision will be lower than Attack.

I direct you to my equations:

http://www.diablofans.com/topic/29779-beginning-a-full-calculator/

I am not sure about the progression towards a gradient of 4 but you may well be right

As we can see at 30 Vitality it is close to Health = 7 * Vit.

I also have this value, found in a youtube video. To me this appears to be based off Vitality independent of Level. As Vitality goes up (by whatever means: level, items) the benefit decreases from 8 * Vit -> 4 * Vit. This seems to be a counter messure to limit Vitality stacking. On the other hand, it's probably safe to say +health% items will still work as they used to (nvm, just got a few values. tnx mfb. they are a little bit off, but not much)

Source: base values

Concerning how precision works: I honestly don't understand how some people have arrived at the conclusion that it requires 1500 precision to get 100% crit chance at lvl 60. This value seems to merely fabricated out of thin air. None of my own work is getting values anywhere near this.

There is significant evidence that it will require considerably more precision to max out crit than those 1500. First an official screenshot from a lvl 60 character (the only one we have). Second the emulator getting results that fit both the currently known datapoints of lvl 1-13, as well as lvl 60. This is very hard evidence to me, so unless somebody comes up with some realy tangible proof at least I will continue to consider precision to be utterly worthless at endgame, with +precision on items being a wasted affix like +light radius etc.

Yeah I came to the same conclusion. So obvious.

Oh, by the way, here's more maths : wanna know the probability that a single member of the development team would suggest a 0.01% ratio ? The answer is 0.01%.

So unless somebody comes up with some realy tangible proof that the D3 team is a bunch of retarded brats, I will continue to consider precision as the work of some healthy and grown humans.

It's because if you graph precision needed for 100% crit vs level for levels 1 through 13, the graph approaches an asymptote at around 1500. The best explanation I've read is that the crit/precision vs level formula is a piecewise function.

Actually it's 6.667. If you ignore level, then 1 Vit adds +8, +6, +6, +8 ,+6, +6...

( 8+6+6 )/ 3 = 6.667

If we assume that you get 4 HP per Vit (based on the tooltip text):

Lv 1: 76 HP = 9*4 + 40

Lv 2: 84 HP = 10*4 + 44

Lv 3: 96 HP = 12*4 + 48

Lv 4: 104 HP = 13*4 + 52

Lv 5: 116 HP = 15*4 + 56

Lv 6: 124 HP = 16*4 + 60

Lv 7: 136 HP = 18*4 + 64

etc.

By the way I have to say this, you guys are doing an amazing job here, keep up the good work.

Summary of Health and VitalityMonkWitch DoctorWizard, Demon HunterBarbarianUnfortunately, the formula is off by +40 compared to this image, which is strange. (shown: 3072, expected: 3112)Sources: mfb, Nicro

Anyways, with this information I can calculate the proportion of Vitality and Defense which gives maximum EHP for a given attribute total. In other words, this shows you how to gem for maximum EHP.

http://diablo.incgamers.com/forums/showpost.php?p=8063180&postcount=18

In order to maximize gains, set marginal cost = marginal benefit. In this case, that comes out to:

EHP formula with +1 DEF = EHP formula with +1 VIT

((B + V * H) * (1+((D+1) - T)/(3*L))) / ((B + (V+1)*(H) )*(1+(D - T)/(3*L))) = 1

B = Base HP with no VIT

V = Vitality

H = HP per VIT

D = Defense

T = Defense Threshold

L = Level

T=2L+6

L=60

H=4

Putting that into Wolfram Alpha comes out to:

D = B/4 + V - 54

If we substitute in Base HP:

B=4L+36

D = V+15

So in other words, you want Defense to be fifteen points higher than VIT for max EHP, OR you want to put all of your points into DEF for maximum healing effectiveness, or somewhere in-between those two. You NEVER want to put all your points into VIT as it gives less EHP than D = V + 15, and has none of the additional healing effectiveness improvements DEF has.

My eye sight may not be as good as it used to be but I am pretty sure that the HP is actually 8072! At the top, the dmg increase is 533 and these threes dont look like the HP. Me thinks gear and passives

Yeah exactly. By having any amount of % gain to health at level 60 it would have a large impact

I wanted to check with the thread, do we have the equations for the basic attack per second value. If not I want to look at that and the crits also

Still, Precison seens completly UP. The amount of critical damage you need in order for 1 Precision match 1 Attack is 1500! Prove:

1 Attack = +1 %Damage

1 Precision = +0.0666...% critical rate at lvl 60

1 Precision = (+0.0666...*CritDmg) %Damage at lvl 60

For 1 Precision = 1 Attack

0.0666...*CritDmg = 1

CritDmg = 1/0.0666...

CritDmg = 15

Crit specific gear will need serious bonuses from talents and other sources to match pure damage bonuses.

It's really confusing if you ask me. High end items gives only +90 Precision (usually) wich is only +5% critical rate, fairly weak compered to +90% damage from +90 Attack or +90% Class Damage. The whole point of stats (Attack, Precision, Vitality, Defence) is that one point in any of those should have the same "power level". So, if you find a +20 attack ring it should give the same damage bonus as a +20 precision ring (and both items would have the same level requeriment).

I wish people would stop equating 1 Attack to +1% total damage output.

Let's say you start with 600 Attack. Your 100 base damage spell will deal 700 damage. Now you gain 1 Attack. Your spell deals 701 damage. 1/700 = +0.14% damage increase, not 1%.

Precision still increases total damage less than Attack does, but it is not by a ridiculously large ("15:1") margin.