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Acc vs Surge, with mathematical proof

STAR WARS: The Old Republic > English > Classes
Acc vs Surge, with mathematical proof

MGNMTTRN's Avatar


MGNMTTRN
04.29.2013 , 12:48 AM | #11
Your Force attacks will still have 100% base accuracy, and even most tank classes only get up to 2% resistance against your attacks in standard conditions. Since there's a maximum of a 2% chance your Force attacks will be resisted in PVP, Madness PVP sorcs want surge and alacrity.

dipstik's Avatar


dipstik
04.29.2013 , 07:30 PM | #12
some tanks get 7% resist with debuffs on you

Parasi's Avatar


Parasi
05.01.2013 , 05:33 AM | #13
This is some excellent theorizing. I have often tested in game with different gear balances on my Sage and Sentinel. I have always had a tendency to favor surge over accuracy slightly, now balancing them equally with the 2.0 changes (and the +3% acc talent). However, for my Watchman Sentinel, testing is showing fully 35% critical results as an average for all abilities used (base critical being 25% from gearing). I'm not sure how other classes compare, but it is a consideration.

Furthermore, theorizing in this way doesn't take into consideration that it matters very little if certain abilities miss, while it matters very much if others do. I don't know how to model that one, however, I do know that my results are showing on average, just under 10% miss rate with 99.5% accuracy (offhand misses a lot more) while my burns are being resisted from 0-1%. My elemental burns account for about 40-45% of my overall damage and, in effect can be said to never miss (overload saber gets applied later if the first attack misses, cauterize burn effect still applies even if direct damage component misses).

I'm not sure if this is enough change the conclusion for Watchman Sentinels, but it's some other numbers to play around with.

KarethRiker's Avatar


KarethRiker
05.02.2013 , 11:24 AM | #14
Great work Meta. I'm not a very good theorycrafter, but thought I'd put a little work out there and see if others could pick up where I left off.

What might be a good way to implement this is to create a spreadsheet model which has multiple rows, one row per each ability used in a regular rotation. You would then use your parses to put in average non-crit damage, frequency of attack type use, accuracy (special vs regular) and crit percentage of that attack. You could then use a sum across all rows to determine the overall dps. This would then help optimize crit rating as well as acc/surge tradeoff. It's useful for modeling in autocrits (HIB, Force Scream, Smash) plus higher crit moves (Sentinel Burns, etc).

One thing I'm not sure how to model here is the alacrity. I guess it would show up as a proportionate increase in the frequency of use various attacks, although will be harder to model due to GCDs and attack windows (wonding shot, gore, attacks on burn, inspiration window) and the ability to improve proc relic activation on the margins.

Building something like that for acc/surge doesn't seem hard, but the alacrity piece I believe is difficult. I took a shot, by letting alacrity only affect attacks with CD = GCD. I've created a starting spreadsheet, feel free to iterate (see below for areas that I believe need to be improved on). While not perfect, I believe this is much easier to make than a simulator and is probably pretty directionally correct due to use of rotation.

After creating a template I realized that one nuance is harder to model, which is offhand damage for Sents/Marauders, Mercs and Slingers.

https://docs.google.com/spreadsheet/...vTmtxTXc#gid=0

Areas of assumption/issues with model:
1) assumption that crit per ability is a flat increase over parsed data
2) not sure I got base stat numbers right
3) easy way to add in per ability surge modifiers needed? could do it like I did with alacrity effect
4) modeling in accuracy on stat changes and offhand damage badly needed
5) could fix stat budget and use optimization model
6) In hindsight shouldn't have started with a dual wielding class, oh well
7) Could use Main stat and power bonus damage for Crit tradeoff, but not sure how much effort is involved
Kareth Kalzeth Kairieth Karzeth Karyeth
Kelschuz Staccia Karjeth Karxeth
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paowee's Avatar


paowee
05.03.2013 , 01:33 PM | #15
Question...

If i have low +crit chance talents but i have a +crit damage talent, are you able to tell from your math what my optimal stats should be? Aside from 110% tech crit chance.
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skarlson's Avatar


skarlson
05.03.2013 , 02:31 PM | #16
Good info so whats the take away. I couldn't read past the first half of line one.
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canuckly's Avatar


canuckly
05.07.2013 , 10:26 PM | #17
sitting at
sage dps telekintec
1358 bonus damage
26.8 crit chance
75.8 crit mulit
105 accuracy

i did a combat log and did 2129 so should i be dropping off crit surge or power for the 5 percent accuracy

MGNMTTRN's Avatar


MGNMTTRN
05.09.2013 , 12:44 PM | #18
So I attempted to tackle crit vs power. It turned out to be hard.

I assumed that for the ith attack in your rotation, the attack's average non-crit damage is well-modeled as bi + ci*bonus damage, where bonus damage is ranged/melee/tech/force damage depending upon what the attack type of the ith attack is. Since our original optimization equation was E(dam) = (1-acc)*dam + dam*acc*(1-crit + crit*surge) we can now replace these dam values by b+c*bonus dam. This makes E(dam) a function of both bonus damage and acc/surge. Ranged/melee Bonus damage is a composite of main stat and power, while tech/force bonus damage is a composite of mainstat, offstat (cunning for troopers, willpower for warriors, etc), tech/force power from mainhand and offhand, and power. Of these, I assumed we only really wanted to vary power.

For example, here is the data that led me to decide that incendiary round's damage is well-modeled as 662 + 2.44*tech bonus damage:
Code:
incendiary dam	tech bonus dam				
3716.50			1250.90				
3597.00			1201.70				
3471.00			1150.40				
3378.00			1112.30				
3260.00			1063.80				
					
presumed base					
662.00					
original dam	Dam  base	c	average C		
3716.50		3054.50	2.44	2.44		
3597.00		2935.00	2.44	2.44		
3471.00		2809.00	2.44	2.44		
3378.00		2716.00	2.44	2.44		
3260.00		2598.00	2.44	2.44		
					
projected base	tech bonus dam		reconstituted	actual	diff
662.00			1250.90				3716.69	3716.50		0.03
662.00			1201.70				3596.54	3597.00		0.21
662.00			1150.40				3471.27	3471.00		0.07
662.00			1112.30				3378.23	3378.00		0.05
662.00			1063.80				3259.79	3260.00		0.04
					
														total diff
														0.41
So for bonus damage values between 1250 and 1070, this was a reasonable model. The sum of squared errors (predicted - observed damage) was only 0.41, so I felt comfortable using this model in my simulations of SWTOR damage. I repeated this exercise to get b and c values for ion pulse, plasma cell, incendiary round, assault plastique's kinetic damage, assault plastique's dot damage, and high-impact bolt. The incendiary, pcell, and ion pulse sum of squared errors were really low (below 0.5), but the other values had high errors (e.g. 150 error for ap, 5500 for HIB). This b + c*bonus damage calculation is absolutely not how the game actually calculates the potential damages of your attacks, but in my opinion it is sufficient to do some estimations for values near 1250 and 1070 bonus damage.

My simulations assumed stat pools of 1239 power/crit and 720 acc/surge, and assumed that power and crit would trade off and surge and acc would trade off. We just want the highest value in a two-dimensional, 120-entry space.

In these images, the important values are to the lower right of the sheet. Crit value increases toward the right, and surge increases toward the bottom. I opened the cell of whatever value was maximized for that combination of b, c, acc, and crit.

http://i.imgur.com/w4wYnAU.png Assault plastique kinetic damage
http://i.imgur.com/nWJg2lg.png Incendiary total damage
http://i.imgur.com/5Hh6l3r.png Ion pulse total damage
http://i.imgur.com/SV5tyE6.png one tick of plasma cell

For all of these attacks except Ion Pulse, the maximum damage was gotten by getting accuracy to 100% (which we knew from the original post) and getting about 52 points in crit. Ion Pulse was the only attack which I bothered to model which needed a whole 104 points in crit to maximize its damage.

Notes:
  • I hoped to take a weighted sum of all my attacks, to simulate a rotation. If I migrated this modelling to MATLAB, it would become extremely easy to optimize the rotation instead of maximizing for a single attack at a time. But I'm not sure doing additional work on it is necessary, since the results all corroborate with each other and with "tests" conducted on the PTS; keep your crit low. Also, do note that the results indicate that a small amount of crit is better than 0 crit.
  • Some general advice: I've seen people passing on gear with 173 mainstat, 84 crit, and 73 acc because they have a gear piece with 123 mainstat and 83 power. They said they were doing a "zero crit" build. But here's the problem: power is just slightly better than crit. At 52 crit and 100% acc our maximum incendiary round damage was 4952, and with 416 points in crit it dropped to 4906 damage. This is a change of less than 1%. It's probably in your interest to wear gear with crit in it if it provides large upgrades to your other stats.
  • 52 crit points is not the magical number at which everyone wants to start dumping power. It may be that it's actually 60 or 70 or maybe even 100 points that optimizes the distribution for your class and spec. However, my Vanguard does get +30% surge on most everything, which would have encouraged a higher crit value.

MGNMTTRN's Avatar


MGNMTTRN
05.10.2013 , 11:58 AM | #19
Also, this information is somewhat relevant to healers. You can round your surge rating to the nearest surge value in the table (0...720) and look up what the maximum crit rating is for any attack. Each attack may have a different maximizing crit, but the general idea is that since you will have significantly more surge as a healer, you will want slightly more crit than a DPS would. At 720 surge and +30% surge from spec, somewhere around 104 crit tended to be better.

Oh, and one more thing. Using incendiary round's 622 + 2.44*Tech bonus damage, I simulated the results of changing all augments from mainstat (+32 mainstat, +20 end) to power (+32 power, +20 end). This dropped my mainstat from 2656.2 to 2145.48, and increased my power from 1239 to 1687. I was specced for +9% aim. As a result, moving from mainstat augs to power augs
  • with mainstat augs, crit bonus was 0.0725 and maximized expected damage was 4952.01
  • with power augs, crit bonus was 0.06099 and maximized expected damage was 4911.24

Note that incendiary round has a high c value (2.44) and +30% surge, which means that it benefits relatively more than other attacks from both increases in crit (mainstat augs) and power (power augs).

Then I simulated the results of this work without the +30% surge and without +9% mainstat from spec.
  • with mainstat augs, mainstat crit bonus was 0.06998. Maximized expected damage was 4553.99; notably it now was maximized by having 100% acc and 0 crit/full power
  • after migrating to power augs, mainstat crit bonus was 0.0587. Maximized expected damage was 4540.96, again maximized at 100% acc and 0 crit/full power
So even with a 1.05 modifier on mainstat instead of 1.14 and 0% surge, and on an attack with a high c which rewards bonus damage increases heavily, mainstat augs got better damage returns.

Based on these results, I'd make the generalizations that
  • I can't think of a reason to use power augs. Mainstat looks slightly better due to its increase in crit rate, even if you don't have +6%/+9% mainstat or +30% surge.
  • If you are one of the rare classes that gets +0% surge on all its basic attacks (I can't think of any), you might be better off with 0 crit. If you spec for +surge on any of your attacks, you probably want closer to 52 points in crit. not 0 crit.

dipstik's Avatar


dipstik
05.13.2013 , 02:43 PM | #20
not sure about maras, but after playing around with sin spreadsheet for infiltration i got better dps (by around 8 dps) for full power augments (the author assumed mainstat was better but i actually checked and had to use some crit mods to balance it out). they, however, do require some crit (almost 250 points). the maker of the spreadhseet also found alacrity (2 enhancements) was BiS, which seems to be the case based on my experience with the spreadsheet.

even in my toy model i found that around 9% (after 5% willpower buff) was the cutoff (for wanting main stat augs), but it depends on base crit chance and surge and bonus damage coefficients (obviously).

fyi, there is a sorc simulation craft for 2.0 in beta right now.