The thing about Crit in D3 is that it's not just +50% damage, once Runes come into play your Crits can also proc lots of special effects.
While 1000 precision may be significantly less upfront damage than 1000 attack, it may still be worthwhile if you build a character with a ton of proc-on-crit effects.
These are the crit formulas for some levels 1-4, 9-11 and 13.
To build on what you did, in a way. I noticed that you see the amount of stats you gain per level. So, with that in mind went through all five of Force's playthroughs and here is the point increase per level (for the levels he got in the playthroughs:
I will be using these in my calculator, and update (for wizard only) right now.
Btw, has anybody been able to calculate the formula for critical hit percentage? If it's the same for all classes, the barb will have a hard time getting a high crit %
At the top of this page. The game appears to be using a precalculated table. So far nobody has figured out a formula that produces said constants, used for those few know champion levels we have from watching beta footage.
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"Traitors! Even in death, the armies of Khanduras will still obey their king!"
Thanks, but I did see your post at the top of the page. It seems unlikely that Blizz would use a formula to calculate everything else, but use a fixed table for crit %. I guess I'll have to wait until I get the full game and get some substantial data from leveling up and different gear, and hopefully I can figure this formula out.
Blizzard will be using plenty of tables in D3, trust me on this. They have in D2.
It's generally more effecient to just reference a table (costing a few hundred bytes of disk space) instead of using a 3-digit CPU cycle costing algorithm.
Concerning % to crit:
I dabbled a bit in Excel, and it seems that for a lvl 60 barb each point of precision will do almost nothing to raise your % to crit. The only info I have on a high lvl char is the one released from Blizzard with the "Stats Progression" caption, a lvl 60 female barb with 230 precision and 2.62% chance to crit. That means each point of precision adds 0.0114% to your chance to crit, which seems to be consistent with the data above for character levels 1-13.
Nice find, I forgot about that video (didn't know there was a HD version of that where you can actaully read the values). Anyway my estimate was around 0.01%. Glad to see I was close.
The almost meaningless effects of adding precision become even more ridiculous when you look at what you could be getting instead. For the almost 500 precision needed to add 5% crit chance you can instead get +500% damage (from +attack) or +500 vitality (not sure how much life this is, but I'm guessing it's either 1k or 2k life for a barb).
I have been saying this all along. Precision is very subpar at the moment, actually it's just outright bad.
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"Traitors! Even in death, the armies of Khanduras will still obey their king!"
You start with 2x7 (= one slot) initially. This is free. Each improvement (additional slot) costs gold (see above) and provides an additional 2x7 of chest inventory. These slots are account wide. There are 5 slots per tab and there are 5 tabs in total. So the maximum amount of room available is 2*7*5*5 = 14*25 = 350.
Shrines
Descrated Fortune Shrine => +25% magic and gold find (2 minute duration)
Descrated Frenzied Shrine => +25% attack speed and chance to crit (2 minute duration)
Descrated Blessed Shrine Shrine => Damage taken reduced by 25% (2 minute duration)
Descrated Enlightened Shrine => +25% experience (not working in beta)
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"Traitors! Even in death, the armies of Khanduras will still obey their king!"
Edited for clarification and corrected. Thanks.
1 Slot = 2x7 spaces. There are 5 slots per tab, and there are 5 tabs in total. 2*7*5*5 = 14 * 25 = 350.
I'm looking for "Mighty Blow" values (N monsters killed by one strike), Level 1-12 mostly to confirm my formula.
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"Traitors! Even in death, the armies of Khanduras will still obey their king!"
Nice to see you guys are doing a lot of serious work figuring out all the details. I still wonder what the "monster health multiplier is for". Also, are there other shrines in the game besides the 4 you list? Or is that it?
I'm pretty sure the monster health multiplier determines how much health enemies have vs party size.
Nice to see you guys are doing a lot of serious work figuring out all the details. I still wonder what the "monster health multiplier is for". Also, are there other shrines in the game besides the 4 you list? Or is that it?
I'm pretty sure the monster health multiplier determines how much health enemies have vs party size.
Correct.
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"Traitors! Even in death, the armies of Khanduras will still obey their king!"
The basic idea is if you plot the precision needed for max crit vs level based on current beta data, it approaches an asymptote around 1500 precision. So the gamescon level 60 stat screen showing ~9,000 precision for max crit is probably wrong.
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 = B0 + B1x1 +...
In the above, x1, x2 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.
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
While 1000 precision may be significantly less upfront damage than 1000 attack, it may still be worthwhile if you build a character with a ton of proc-on-crit effects.
To build on what you did, in a way. I noticed that you see the amount of stats you gain per level. So, with that in mind went through all five of Force's playthroughs and here is the point increase per level (for the levels he got in the playthroughs:
I will be using these in my calculator, and update (for wizard only) right now.
At the top of this page. The game appears to be using a precalculated table. So far nobody has figured out a formula that produces said constants, used for those few know champion levels we have from watching beta footage.
Blizzard will be using plenty of tables in D3, trust me on this. They have in D2.
It's generally more effecient to just reference a table (costing a few hundred bytes of disk space) instead of using a 3-digit CPU cycle costing algorithm.
Nice find, I forgot about that video (didn't know there was a HD version of that where you can actaully read the values). Anyway my estimate was around 0.01%. Glad to see I was close.
I have been saying this all along. Precision is very subpar at the moment, actually it's just outright bad.
... and some additions by myself.
Monster Health Multiplier
Kill Series, Consecutive, "Massacre"
The "level" is determind at the end of the series.
Kill Series, One-Hit, "Mighty Blow"
The formula seems to match all values I have seen so far.
Afterwards it either rounded up or down, not sure by what rules.
Most of the data is from Force Videos.
Kill Series, Dungeon, ""
*work in progress*
Chest Improvements(onehit)
You start with 2x7 (= one slot) initially. This is free. Each improvement (additional slot) costs gold (see above) and provides an additional 2x7 of chest inventory. These slots are account wide. There are 5 slots per tab and there are 5 tabs in total. So the maximum amount of room available is 2*7*5*5 = 14*25 = 350.
Shrines
1 Slot = 2x7 spaces. There are 5 slots per tab, and there are 5 tabs in total. 2*7*5*5 = 14 * 25 = 350.
I'm looking for "Mighty Blow" values (N monsters killed by one strike), Level 1-12 mostly to confirm my formula.
Correct.
http://diablo.incgamers.com/forums/showthread.php?t=813161
The basic idea is if you plot the precision needed for max crit vs level based on current beta data, it approaches an asymptote around 1500 precision. So the gamescon level 60 stat screen showing ~9,000 precision for max crit is probably wrong.
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 = B0 + B1x1 +...
In the above, x1, x2 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
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.
Monk
Witch Doctor
Wizard, Demon Hunter
Barbarian
Unfortunately, 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