I believe this statement is false. The amount of armor removed (post non-rating based debuffs) is still proportional to the amount of armor penetration rating. Therefore, nothing has changed from pre-3.0 in this regard: armor penetration rating becomes better as it is stacked.
Edit: my mistake, you are correct and the math bears that out symbolically.
Where D_0 is pre-armor DPS, q is the armor penetration % (as a decimal), w is the initial armor, and w_0 is the armor constant at whatever level.
If we imagine a small change in q (that is, delta q), then we should, after no small amount of manipulation, arrive at...
Which, as q increases, the delta D increases. So you are correct, again, my mistake.
Strange. This runs counter to previous algebra I've done on the armor formula and how a hypothetical rating might work. It could be that trying to set delta w = kw was the problem.
The effects of stacking Armor Penetration have not changed between live and beta; the mechanics by which it works, and the effects on low versus high armor bosses certainly have; but on any given boss, there's still a straight conversion of 1 point ArPen rating = -n points enemy armor. While the number is smaller than it was before, it's still a flat number and has no (known) diminishing returns that change ArPen's previous positive scaling with itself. So it's still true that the more ArPen you have, the better it gets.
Except, theres no such thing as a 6800 armor boss.
right, I knew there was something wrong there, was sure that the cap was at 1350, but couldn't see why it didn't add up, thought it might have been with improved expose armor and didn't have time to check everything up.
It almost seems that Armor Penetration might be meant to apply before other armor reduction effects instead of being applied after all other armor reduction effects.
As has been previously stated, 7 Armor Penetration currently becomes 1 Armor Penetration Rating, and at 15.39529991 rating = 1%, 1 rating is 0.064954889% reduction. Taking the 10900 boss armor value that was found for the Boss target dummies, one rating then becomes 7.080082901 armor reduction, which is almost exactly in line with current level 70 values before the rating change.
One could take this to believe that Blizzard does intend to keep Armor Penetration scaling to the same value if applied before armor reduction effects. However, that same assumption would then increase the power of the stat at level 70 since 7.40384579 rating = 1%, which would result in 8.37402628 armor reduction for a 6200 armor boss, and 10.379740639 armor reduction for 7685.
I'm rather interested to see what Blizzard has to say on the matter of armor penetration, as with the change to the mechanic, it's a rather mediocre stat to have. Also, if the same mechanic applies to the 15% armor penetration on Mace Spec. talents, it also tremendously undervalues them compared to Sword, or the various +5% crit specs.
Has the ArP Mace Spec model been tested for confirmation? Is the 15% applied before all armor debuffs, or after Sunders and what have you? Will this compete with Sword Spec with the Windfury changes causing a slight nerf?
It looks like the spirit regen formula changed. At level 80 with 687 int and 475 spi I should get 443 mp5 according to numbers in the first post. In current beta build this only gives 347 mp5. If the form is the same then coefficient changed to 0.005575.
It looks like the spirit regen formula changed. At level 80 with 687 int and 475 spi I should get 443 mp5 according to numbers in the first post. In current beta build this only gives 347 mp5. If the form is the same then coefficient changed to 0.005575.
You are right, these are the changes I found in build 8962, first post and RatingBuster also updated:
1. Mana regen from Spirit nerfed at level 71 to 80, at level 80 the amount of regen is nerfed to about 78% of the original value.
2. Players lower then level 34 will now convert resilience ratings at the same rate as level 34 players.
Level
BASE_REGEN@8962
BASE_REGEN@8926
71
0.008859
0.009079
72
0.008415
0.008838
73
0.007993
0.008603
74
0.007592
0.008375
75
0.007211
0.008152
76
0.006849
0.007936
77
0.006506
0.007725
78
0.006179
0.00752
79
0.005869
0.00732
80
0.005575
0.007125
Last edited by Whitetooth : 09/19/08 at 12:51 AM.
Hotdogee@Ner'zhul US <Bahamut>
Author of RatingBuster
We just restarted the servers to fix an issue with the diminishing returns formula we added for Dodge, Parry, and the enemy's chance to miss you. The issue fixed was that the formula now works! This will have a definite effect on all tanks ability to mitigate damage due to effectively lowered amounts of those avoidance values.
Confirmation of diminishing returns for dodge, parry, and even miss chance from defense. It sounds to me like the formula may have changed since our earlier tests. I've been trying to level to 80 before gathering more data but it's slow going.
Yeah, that was something I was going to ask about as well, the changed dodge formula.
I noted down my chance to dodge both on live, in build 8926 and now in 8970.
Live: 639 agility, 32.36% dodge (according to the character sheet)
8926: 627 agility, 31.00% dodge (missing Vitality for 2% increased agility)
8970: 627 agility, 27.78% dodge (again, missing 2% agility due to talents / talent changes)
I don't remember if the racial 1% dodge bonus was already changed into 2% miss in build 8926, but in 8970 it's in according to the spell book.
That means a decrease of about 2% dodge with 627 agility.
Everything on the server as it relates to combat ratings, critical hits, avoidance diminishing returns, etc. should now be working properly.
I'm looking forward to feedback from the community about the changes, and especially any hard data from combat logs. I'll try to help with information as possible but we're very busy right now. Compressing all the information from various code and data sources into a coherent, readable post takes time that I and others need to spend on other things right now. I also have faith in the community's ability to construct an accurate model of it from empirical data.
I did a thorough test on defense with my level 60 warrior in build 8970, the data was made possible because I my warrior happens to have over 100 level 60 epics, the data took hours to get, mix matching gear with no agi, no parry, no dodge and only defense.
From my data I was able to come up with an approximation formula.
Parry=(a*b*Def*(1+b*Def)^-1.0+c)*2^-22
a = 1.9714701932078499E+08
b = 8.9016763465833986E-04
c = 1.5681781142791745E-01
peak absolute value of absolute error: 7.12653E-07
Dodge=(a*b*Def*(1+b*Def)^-1.0+c)*2^-22
a = 3.6965103932676291E+08
b = 4.7475555142568462E-04
c = 9.7341636227010531E-02
peak absolute value of absolute error: 6.89706E-07
Def is the amount of defense you gain from items, does not include base defense.
Its not sure whether class or level has any effect on the formula.
Hopefully someone will come up with a better one.
Hotdogee@Ner'zhul US <Bahamut>
Author of RatingBuster
Whitetooth, I took your data on dodge and parry chances at different defense values and hypothesized that...
Where a is the total avoidance and x the defense (edited: not rating).
And came up with the following regression:
With an R^2 = 0.999922660243495.
I hypothesized this model based on the assumption that Blizzard had chosen to make avoidance ratings increase effective health (when such a metric includes avoidance) linearly.
Edit: I shall do an analysis of the residuals that result from this later.
Second edit: corrected to say x = total defense, not rating.
I did a really quick number crunch with spoons data, calculating your length of survival for 300, 325, 350, 375, and 400 defense.
I assumed a 10,000 hitpoint pool, and incoming damage of 100 dps. Then I calculated how long it would take for you to die. I kept parry and dodge separate, though.
Parry
300 defense = 95% taken = 105.26 seconds
325 defense = 93.9767465591431% taken = 106.41 seconds for 1.15 second increase
350 defense = 92.9970955848694% taken = 107.53 seconds for 1.12 second increase
375 defense = 92.0583190917969% taken = 108.63 seconds for 1.10 second increase
400 defense = 91.1579103469849% taken = 109.70 seconds for 1.07 second increase
Dodge
300 defense = 92.9923005104065% taken = 107.54 seconds
325 defense = 91.9585447311401% taken = 108.74 seconds for 1.20 second increase
350 defense = 90.9487600326538% taken = 109.95 seconds for 1.21 second increase
375 defense = 89.962120056152% taken = 111.16 seconds for 1.21 second increase
400 defense = 88.997838973999% taken = 112.36 seconds for 1.20 second increase
Dodge seems to follow a linear path, but parry is dropping very slowly. Perhaps it calculates the three stats as a whole, and miss chance would make up for the loss?
Dodge seems to follow a linear path, but parry is dropping very slowly. Perhaps it calculates the three stats as a whole, and miss chance would make up for the loss?
If the avoidance stats diminish as a whole (rather than a separate diminishing for the single stats which would put druids at a disadvantage unless the formula is different for druids), then the question is how the resulting total avoidance is split up among the single stats.
One solution would be to diminish each stat by the same percentage. The weird thing about that is that your parry would slightly decrease when you add more dodge and vice versa. Should be easy to test with an item that only adds dodge or only adds parry.
The other solution is that the entire diminishing effect is applied to one of the stats first with the result that after a certain amount of avoidance you would push dodge, parry or miss off the table (whichever of them the diminishing returns are applied to).
If the avoidance stats diminish as a whole (rather than a separate diminishing for the single stats which would put druids at a disadvantage unless the formula is different for druids), then the question is how the resulting total avoidance is split up among the single stats.
One solution would be to diminish each stat by the same percentage. The weird thing about that is that your parry would slightly decrease when you add more dodge and vice versa. Should be easy to test with an item that only adds dodge or only adds parry.
The other solution is that the entire diminishing effect is applied to one of the stats first with the result that after a certain amount of avoidance you would push dodge, parry or miss off the table (whichever of them the diminishing returns are applied to).
I did some more tests on this matter:
Build: 8970
Name: Whitetooth (60 Warrior)
Base Defense: 300
Base Agi: 83
Dodge Rating: 0
Defense
Parry Rating
Dodge%
Parry%
Increased Parry%
306
0
7.2580323219299
5.2497124671936
306
20
7.2580323219299
6.5900726318359
1.3403601646423
313
0
7.5482954978943
5.5377106666565
313
20
7.5482954978943
6.8618426322937
1.3241319656372
This proves that each stat is independent and does not affect each other, however, the amount of parry gained by parry rating diminishes with increasing defense.
Hotdogee@Ner'zhul US <Bahamut>
Author of RatingBuster
Build: 8970
Name: Whitetooth (60 Warrior)
Base Defense: 300
Base Agi: 83
Dodge Rating: 0
Defense
Parry Rating
Dodge%
Parry%
Increased Parry%
306
0
7.2580323219299
5.2497124671936
306
20
7.2580323219299
6.5900726318359
1.3403601646423
313
0
7.5482954978943
5.5377106666565
313
20
7.5482954978943
6.8618426322937
1.3241319656372
This proves that each stat is independent and does not affect each other, however, the amount of parry gained by parry rating diminishes with increasing defense.
I'd love to see how the numbers above with some fixed amount of dodge on top.
I.e. 306def/Xdodge/0parry, 306def/Xdodge/20parry, 313def/Xdodge/0parry, 313def/Xdodge/20parry.
Actually, just speccing into the +5% dodge talent and rechecking the numbers above would be interesting enough I think.
Oh, for completeness: Prepatch, +20 parry would have been 1.333333% parry and 7 defense skill would have been 0.28% parry/dodge.
So, it's a very minor gain on very low gear levels at least.
Originally Posted by Rustik
I did a really quick number crunch with spoons data, calculating your length of survival for 300, 325, 350, 375, and 400 defense.
Dodge seems to follow a linear path, but parry is dropping very slowly. Perhaps it calculates the three stats as a whole, and miss chance would make up for the loss?
It seems like your dodge is calculated first, then your parry?
If the [dodge at 300+x*25 => dodge at 300+(x+1)*25] lifetime increase is 1.21s, then maybe
[dodge at 300+(x+1)*25 + parry at 300+x*25 => dodge at 300+(x+1)*25 + parry at 300+(x+1)*25] could be a 1.21s increase as well from the (x)-to-(x+1) parry increase as well, or something similar?
Actually, just speccing into the +5% dodge talent and rechecking the numbers above would be interesting enough I think.
The dodge and parry added from talents seems to be a flat addition without diminishing returns. That means the value of those talents actually scales with gear (due to increasing returns of flat avoidance percent additions).
I've analyzed the residuals of my model; the graph showed a very obvious parabolic trend to the residuals, so I doubt it's the correct model.
Edit: after some work on the residuals, I arrived at a fourth-order model, where 1/(1-avoidance) is given by 2.0103165674588E-14 x^4 + 9.9870077774207E-11 x^3 + 1.89536760923728E-07 x^2 + 0.000937935027728877 x + 0.835164926730915, where x is defense.
Admittedly, I'm not entirely happy with this fourth-order model. While the residuals show no specific trend (to indicate a higher order model is needed), they do increase in spread as a function of defense, which doesn't make sense to me...but I suppose it could be a result of Blizzard's internal rounding.
It seems like your dodge is calculated first, then your parry?
If the [dodge at 300+x*25 => dodge at 300+(x+1)*25] lifetime increase is 1.21s, then maybe
[dodge at 300+(x+1)*25 + parry at 300+x*25 => dodge at 300+(x+1)*25 + parry at 300+(x+1)*25] could be a 1.21s increase as well from the (x)-to-(x+1) parry increase as well, or something similar?
If this is true, wouldn't we still have to figure out where miss falls in this calculation? If it calculates it in a specific order, then miss would be first/second/third also.
Whitetooth pointed out that RATING does not effect another stat, but is it possible defense follows it's own formula, combining dodge/parry/miss as a whole, then parry/dodge rating affect their respective rating, by themselves?
Is there any way to determine actual miss chance except to go get swung at 5000 times? The character sheet only displays it before diminishing returns.
It's entirely possible I'm making this more complicated than it is...
EDIT FOR MATH: I decided to follow Roywyn's thought process:
If I've understood you correctly, you're saying that if I gain 25 defense, then it calculates in dodge first, netting a x second increase in lifespan, then it adds in parry, increasing lifespan -in relation to how long I live with the new dodge number-.
So I find the lifespan for 325 worth of dodge, plus 300 worth of parry, then compare it to the 325 defense for both. 300 defense combined included just to be thorough.
300 defense = 87.9923005104065% taken = 113.65 seconds
I'd love to see how the numbers above with some fixed amount of dodge on top.
I.e. 306def/Xdodge/0parry, 306def/Xdodge/20parry, 313def/Xdodge/0parry, 313def/Xdodge/20parry.
Build: 8970
Name: Whitetooth (60 Warrior)
Base Defense: 300
Defense
Dodge Rating
Parry Rating
Dodge%
Parry%
Increased Dodge%
Increased Parry%
Agility
321
0
0
7.8776865005493
5.8625373840332
0.0000000000000
0.0000000000000
83
321
0
60
8.5295963287354
9.5704746246338
0.6519098281861
3.7079372406006
98
421
0
0
11.795427322388
9.5704746246338
3.9177408218387
3.7079372406006
83
We know currently in TBC at level 60: 60 Parry Rating gives 4% Parry, and 100 Defense also gives 4% Parry.
This test shows that regardless of the source, whether its from Parry Rating or Defense, the diminishing returns effects are calculated using the same formula.
So if we have the formula for dodge from defense, the same formula will work for dodge from agi, dodge rating, defense combined. The same goes for parry rating.
Last edited by Whitetooth : 09/22/08 at 5:01 PM.
Hotdogee@Ner'zhul US <Bahamut>
Author of RatingBuster
So we know now that dodge, parry and probably also miss diminish separately from each other and the diminishing is done on that level and not on defense level.
We also know that flat additions from talents do not diminish. Base dodge and parry does not seem like it is diminished either.
So my guess is:
Defense and Agi is calculated into dodge, parry and miss rating and the dodge and parry rating from gear added. So you get 3 ratings before diminishing.
For each of the avoidance percentages there is a cap value: pcap, dcap and mcap.
Then a function that gets closer and closer to the separate caps with increasing ratings is used to compute the avoidance percentage from gear. And last the flat additions from talents and the base value is added.
The function could look similar to:
1/(pcap - p) = f(prating)
with f as a low order function, probably linear.
If that is the case, then the question is if the caps are different for different classes e.g. druids having a higher dodge cap to account for not having parry.
I'm not so sure, Selmarix. I basically performed a regression for 1/(1-avoidance) as a function of defense according to the long table of data earlier, and it came out to a fourth-order polynomial before I could eliminate trends in the residuals. Granted, as to why four and not five, I don't understand, but something's off about it, I think.
09/15/08, 3:56 PM
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