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Acc vs Surge, with mathematical proof


MGNMTTRN

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Edited May 13, 2013:

Here's a compilation of the results of my work in this thread. The thread is relatively short and all of these results are found somewhere within the first 2 pages:

  • Considering only acc vs surge: most every class wants 100% acc, dump the rest of your enh contents into surge or alac. The only exception to this is if you have an effective crit rate in excess of 30%, 181% base surge, and 91% base acc. In that case you still want 7 acc enhs, or 504 acc rating.
  • Generally, DPS are going to want between 50 and 100 points in crit
  • Generally, healers will want about 100 points in crit, since they will have higher surge ratings
  • Mainstat augments are superior to power augments for DPS and healers

 

======

 

I was inspired by the following threads

to attempt to solve the question "how much accuracy should I have?"

 

If we track what happens to each point of damage, we expect some damage to be outright lost due to misses, and we expect some damage to be boosted by our surge and crit. The mathematical expression for this expected damage is

 

E[dam] = 0*(1-acc) + 1*(acc)*(crit*surge + (1-crit)*1)

 

for 1 point of damage. And our expectation for more than 1 point of damage is E[c*dam] = c*E[dam] = c*0*(1-acc) + c*(acc)*((crit*surge) + (1-crit)*1)

 

We'll assume we can only use tier 30/level 69 Adept (+power, +72 surge), Acute (+crit, +72 acc), Initiative (+power, +72 acc), or Battle (+crit, +72 surge) enhancements. Note that characters have 10 spaces in which they can gain acc or surge (ear, 2 implants, mainhand, offhand, 5 set bonus pieces). Note also that if an enh doesn't have acc, it'll have surge. So we can have up to 720 points in surge, and we'll necessarily have this many points in acc: 720 - points in surge. Note also that I'm assuming you have a crit rate of 25%. This is not a safe assumption at all, so I promise I will address concerns about varying crit rates. I'll also assume that your toons get the +1% acc and +1% surge buffs from companions, and address bonuses to crit, surge, and acc below.

 

Anyway, so now our E[dam] function is a function of acc, crit, and surge... except acc and surge are functions of one another, and we assume for now that crit = 0.25. So our E[dam] function is really only a function of one variable, which can be the number of points that you put in surge, and which will be a multiple of 72. Since this E[dam] is a continuous function of one variable and it only has 10 values that we really care about, it's quite easy to maximize/optimize/determine how many points in surge will get you the best performance.

 

Let #acc vary from 0 to 10, and #surge = 10 - #acc.

Let acc_points = #acc* 72, surge_points = #surge * 72.

 

Let acc_rating = 0.9 + 0.01 + 30 * (1 - (1 - (0.01/0.3))^((acc_points/55)/1.2))/100

Let surge_rating = 0.5 + 0.01 + 30*(1-(1-(0.01/0.3))^((surge_points/55)/0.22))/100

E[dam] = 0*(1-acc_rating) + 1*acc_rating*(crit*surge + (1-crit)*1)

And now the results of this calculation:

# acc	accr		accb	acct	#	surge	surgeb	surget	maximizing E[dam] =0*(1-acc) + acc*(crit*surge + (1-crit)*1)				
0.0000	0.0000	0.0000	0.9400	720.0000	0.2601	0.7701	0.8860				
1.0000	72.0000	0.0109	0.9509	648.0000	0.2512	0.7612	0.8941				
2.0000	144.0000	0.0214	0.9614	576.0000	0.2403	0.7503	0.9014				
3.0000	216.0000	0.0315	0.9715	504.0000	0.2269	0.7369	0.9076				
4.0000	288.0000	0.0413	0.9813	432.0000	0.2106	0.7206	0.9127				
5.0000	360.0000	0.0506	0.9906	360.0000	0.1906	0.7006	0.9165				
6.0000	432.0000	0.0597	0.9997	288.0000	0.1661	0.6761	0.9188				
[b]7.0000	504.0000	0.0684	1.0084	216.0000	0.1362	0.6462	0.9192	[/b]			
8.0000	576.0000	0.0768	[i]1.0168[/i]	144.0000	0.0996	0.6096	0.9176				
9.0000	648.0000	0.0849	[i]1.0249[/i]	72.0000	0.0548	0.5648	0.9134				
10.0000	720.0000	0.0927	[i]1.0327[/i]	0.0000	0.0000	0.5100	0.9062				

Another way of thinking about this: if you spec for +3 acc, once you get acc to 100%, dump everything else in surge. I've italicized the lines in which you'd be boosting your accuracy past 100%, and I've bolded the line in which you maximize your damage for some allotment of surge and acc.

 

If you're curious: the turnover point is the same when you have 91 base acc instead of 94 base acc, because acc points specced don't count toward your rating:

# acc	accr		accb	acct		#surge	surgeb	surget	maximizing E[dam] =0*(1-acc) + acc*(crit*surge + (1-crit)*1)	
0.0000	0.0000	0.0000	0.9100	720.0000	0.2601	0.7701	0.8577	
1.0000	72.0000	0.0109	0.9209	648.0000	0.2512	0.7612	0.8659	
2.0000	144.0000	0.0214	0.9314	576.0000	0.2403	0.7503	0.8732	
3.0000	216.0000	0.0315	0.9415	504.0000	0.2269	0.7369	0.8796	
4.0000	288.0000	0.0413	0.9513	432.0000	0.2106	0.7206	0.8848	
5.0000	360.0000	0.0506	0.9606	360.0000	0.1906	0.7006	0.8887	
6.0000	432.0000	0.0597	0.9697	288.0000	0.1661	0.6761	0.8912	
[b]7.0000	504.0000	0.0684	0.9784	216.0000	0.1362	0.6462	0.8919	[/b]
8.0000	576.0000	0.0768	0.9868	144.0000	0.0996	0.6096	0.8905	
9.0000	648.0000	0.0849	0.9949	72.0000	0.0548	0.5648	0.8867	
10.0000	720.0000	0.0927	[i]1.0027[/i]	0.0000	0.0000	0.5100	0.8799	

 

You might ask, as an Assault Commando I spec for +3 accuracy and +30% surge on all my attacks; does this still apply to me? It is easy to change the base surge to +0.81 and accuracy to base +0.94.

# acc	accr		accb	acct	#	surge	surgeb	surget	maximizing E[dam] =0*(1-acc) + acc*(crit*surge + (1-crit)*1)				
0.0000	0.0000	0.0000	0.9400	720.0000	0.2601	1.0701	0.9565				
1.0000	72.0000	0.0109	0.9509	648.0000	0.2512	1.0612	0.9654				
2.0000	144.0000	0.0214	0.9614	576.0000	0.2403	1.0503	0.9735				
3.0000	216.0000	0.0315	0.9715	504.0000	0.2269	1.0369	0.9805				
4.0000	288.0000	0.0413	0.9813	432.0000	0.2106	1.0206	0.9863				
5.0000	360.0000	0.0506	0.9906	360.0000	0.1906	1.0006	0.9908				
6.0000	432.0000	0.0597	0.9997	288.0000	0.1661	0.9761	0.9937				
[b]7.0000	504.0000	0.0684	1.0084	216.0000	0.1362	0.9462	0.9949	[/b]			
8.0000	576.0000	0.0768	[i]1.0168[/i]	144.0000	0.0996	0.9096	0.9939				
9.0000	648.0000	0.0849	[i]1.0249[/i]	72.0000	0.0548	0.8648	0.9903				
10.0000	720.0000	0.0927	[i]1.0327[/i]	0.0000	0.0000	0.8100	0.9837				

but the result does not change. The maximum point of damage is still 7 acc enhs, or just after you achieve 100% accuracy.

 

What DOES heavily influence the result is crit rate, which has until now been held at a constant 25%. While this is going to be approximately where your melee/force crit rate is at level 69 gear, your tech/force crit may be buffed up to 28% already and you may also benefit from autocrits (smash), crit bonuses to specific attacks (Assault Vanguard elemental attacks, Marksman Sniper), and from crit buffs (Vanguard Battle Focus, Shadow tank project) etc. So here are the results for 28% crit

# acc	accr		accb	acct	#	surge	surgeb	surget	maximizing E[dam] =0*(1-acc) + acc*(crit*surge + (1-crit)*1)			
0.0000	0.0000	0.0000	0.9400	720.0000	0.2601	0.7701	0.8795			
1.0000	72.0000	0.0109	0.9509	648.0000	0.2512	0.7612	0.8873			
2.0000	144.0000	0.0214	0.9614	576.0000	0.2403	0.7503	0.8942			
3.0000	216.0000	0.0315	0.9715	504.0000	0.2269	0.7369	0.8999			
4.0000	288.0000	0.0413	0.9813	432.0000	0.2106	0.7206	0.9045			
5.0000	360.0000	0.0506	0.9906	360.0000	0.1906	0.7006	0.9076			
[b]6.0000	432.0000	0.0597	0.9997	288.0000	0.1661	0.6761	0.9090	[/b]		
7.0000	504.0000	0.0684	[i]1.0084[/i]	216.0000	0.1362	0.6462	0.9085			
8.0000	576.0000	0.0768	[i]1.0168[/i]	144.0000	0.0996	0.6096	0.9057			
9.0000	648.0000	0.0849	[i]1.0249[/i]	72.0000	0.0548	0.5648	0.9000			
10.0000	720.0000	0.0927	[i]1.0327[/i]	0.0000	0.0000	0.5100	0.8911			

 

and 30% crit

# acc	accr		accb	acct	#	surge	surgeb	surget	maximizing E[dam] =0*(1-acc) + acc*(crit*surge + (1-crit)*1)	
0.0000	0.0000	0.0000	0.9400	720.0000	0.2601	0.7701	0.8752	
1.0000	72.0000	0.0109	0.9509	648.0000	0.2512	0.7612	0.8828	
2.0000	144.0000	0.0214	0.9614	576.0000	0.2403	0.7503	0.8894	
3.0000	216.0000	0.0315	0.9715	504.0000	0.2269	0.7369	0.8948	
4.0000	288.0000	0.0413	0.9813	432.0000	0.2106	0.7206	0.8990	
5.0000	360.0000	0.0506	0.9906	360.0000	0.1906	0.7006	0.9017	
[b]6.0000	432.0000	0.0597	0.9997	288.0000	0.1661	0.6761	0.9026	[/b]
7.0000	504.0000	0.0684	[i]1.0084[/i]	216.0000	0.1362	0.6462	0.9014	
8.0000	576.0000	0.0768	[i]1.0168[/i]	144.0000	0.0996	0.6096	0.8977	
9.0000	648.0000	0.0849	[i]1.0249	[/i]72.0000	0.0548	0.5648	0.8911	
10.0000	720.0000	0.0927	[i]1.0327[/i]	0.0000	0.0000	0.5100	0.8809	

 

Which crit% should you use? I recommend you upload logs to torparse.com and see what your effective crit rate is. On sustained fights on my Vanguard DPS I'm getting a solid 30.5% crit rate, while on moving fights it's closer to 26%. And Vanguards are well-known for their high crit rates. Also note that the deciding factor here is really your crit%; with a low crit no matter how much acc you spec for you'll want to get 7 acc enhs, while with higher crit your surge becomes so valuable that your recommended acc enh count drops all the way to 6.

 

This is using the formulae for surge and acc from Keyboard Ninja's thread, linked above. I did indeed check to ensure that my surge and acc functions were predicting the correct values on my Vanguard DPS. This accuracy-heavy result corroborates KeyBoardNinja's discovery that surge has even harsher DRs in 2.0 and should also be intuitive (crit dropped, surge dropped -> acc is comparatively better). Please let me know if you spot any errors, as I did post an enormous volume and I'm sure I did something wrong.

 

Don't link to this thread or consult this thread and then go babbling about soft caps. There is no soft cap at which we stop putting points in surge. There is a point at which surge becomes less useful than accuracy, and it's at about 216 points in surge.

 

Assumptions and ackknowledgements:

  • ranged and tech attacks now have the same miss% on bosses
  • almost all classes have a free attack that they use when they run out of other options; this free attack has a -10% accuracy debuff (base 80% accuracy) which would positively weight accuracy even more. However, this autoattack is hardly something we should optimize our damage for, because it does so little damage compared to our non-free filler (Ion Pulse, Double Strike/Clairvoyant, Charged Bolts/Grav Round, Snipe, and such) and maybe 25% of the damage that a class's hard-hitting attacks do. Furthermore, to counterbalance this accuracy loss that we're not optimizing for, most classes spec for autocrits which increase the value of surge
  • I wasn't able to level my toons until maybe two weeks ago, so it may turn out that 25% crit rate is not a good base assumption. If you post in this thread with details about what you'd like me to account for (autocrits, specced surge, higher mainstat/crit contributions than around 28%) I'd be happy to account for them. Please post your class, spec, your melee/ranged crit%, your tech/force crit%, your crit rating, your surge%, your surge rating, your acc%, accuracy rating, and give me some way of estimating your effective crit rate. For example if you were a smash warrior I'd need a torparse link to estimate your total crit%.
  • In practice your damage output is just going to be sort of a gaussian about a center. If you put in 5 surge enhs and then get 2500 DPS on a dummy and then switch to 3 surge enhs and get 2450 DPS on a dummy, it's not my fault. The variability in DPS parses that you'll see is enormous even when you play in exactly the same conditions for 20 minutes, and I should also point out that nobody is going to play with the same style for 40 minutes. What this will do is set you up to perform well; whether the dice fall in your favor has surprisingly little to do with your gear.
  • I need more data, and I need people to seriously review this work, and I need people to ask questions. If you have a different model, please post it. If you want me to reevaluate something, just let me know what it is.
  • Once people (ie this poster) start hitting full 69 I'll start worrying about the allocations for full level 72 gear. The gist of it is going to be that surge will be better, since you'll have slightly more mainstat and crit.

Edited by MGNMTTRN
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edit 5/12/2013: I address acc vs surge and crit vs power together here, on the second page of this thread.

 

I address mainstat vs power augments and healer itemization here, also on the second page of this thread.

Edited by MGNMTTRN
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interesting analysis. i have been using the following toy model of dps:

 

(1-miss_chance)*(average_hit+main+power+force_power)*(1+crit*surge)/(1-alacrity)

 

miss_chance=fraction_melee*(1.1-melee_accuracy)+fraction_force*(1.1-force_accuracy)

melee_accuracy=accuracy boost+0.9+0.3*(1-(1-0.01/(0.3))^((1/55)*accuracy_rating/(1.2)))

force_accuracy=accuracy boost+1+0.3*(1-(1-0.01/(0.3))^((1/55)*accuracy_rating/(1.2)))

average hit is determined by taking a parse with known values for everything else and solving for average hit

main=0.2*(1+main_boost)*main_rating

power=0.23*(1+power_boost)*power_rating

force_power=0.23*(1+power_boost)*force_power_rating

crit=crit_boost+0.05+0.3 * ( 1 - ( 1 - ( 0.01 / 0.3 ) )^( ( crit_rating / 55 ) / 0.9 ) )+0.2 * ( 1 - ( 1 - ( 0.01 / 0.2 ) )^( ( main_rating*(1+main_boost) /55 ) / 5.5 ) )

surge=surge_boost+0.5+0.3*(1-(1-0.01/(0.3))^((1/55)*surge_rating/(0.22)))

alacrity=alacrity_boost+0.3*(1-(1-0.01/(0.3))^((1/55)*alacrity_rating/(1.25)))

 

so i get effective crit_boost from parses and using SUM_i(crit_chance_i*fraction_dps_i). where i is for each ability

effecttive surge boost is really hard to get out of the parses, but if you have abilities that have surge_boost_i with fraction_dps_i, effective surge_boost=SUM(surge_boost_i*fraction_dps_i), where surge_boost_i will just be your surge from surge rating unless you get something from a tree/proc.

 

i have tried using an alacrity matters term as a coefficent for alacrity before(so if 30% of your dps comes from abilities affected by alacrity, then you use 0.3), but have removed it now that it alacrity reduces the gcd, but it may need to be added back in.

 

what i have found is that stat weights for maxing dps heavily depend on the average hit value (i used to use a 1 there when i first started this type of analysis for healing). this has mainly to do with the average hit value affecting the power/ critbalance and that affecting the surge balance. there is also no bonus damage coefficent here, which is really bad since it can both diminish and exagerate the benifits of power. if we had what some people call coefficents per second (cps) for each build, then that could be appended to the (main+force_power+power term), to give (main+force_power+power term)*cps... i think. pretty short sighted, but without simulators, this is as far as a rough model can get without simulating a rotation full force.

 

typically i will get rid of the main, power and force power boosts since people give me the final value, so i can just plug those in and get rid of the boosts so i can find balance between surge/accuracy and alacrity. i can also just solve for power_rating by diving their power by 1.05 for a crit/power analysis. i have my spreadsheet set up to give me optimal power, crit, accuracy, surge and alacrity, based on gear assumptions about sum of power+crit and sum of alacrity+accuracy+surge possible.

 

i have found that alacrity is better (use more rating) than surge for quite a few builds.

Edited by dipstik
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you are forgetting the fact that alacrity doesn't reduce cooldowns; so for most classes, alacrity is not a straight percentage increase, since it allows you to finish a rotation faster, but does not allow you to start a new one any faster. As a consequence, it just allows to do another autoattack or filler(snipe, vicious slash, etc). which have rather low dmg/gcd.

It would be better to just parse the average damage of an energy neutral rotation, add enough alacrity to allow for 1 additional gcd before the new rotation and add in the damage from an additional basic or filler depending on energy and compare that to the damage from the lost surge.

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i have seen others use that methodology before, but i dont really agree with it. maybe some classes have no choice but to auto attack, but most can do a tracer missile, snipe etc.

 

alacrity reduces the gcd for instants, and anything that is cast will be able to beat the gcd for the next ability. so your next ability will ALWAYS come faster... more actions per minute.

 

like i said, i could add an alacrity matters term where i take % of dps from casts that would have activation time under 1.5 seconds, and channeled abilities (here alacrity directly increases dps) and use that.

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Ok, I haven't had time to go through everything yet, but I've got a question about your first equation, specifically:

 

E[dam] = 0*(1-acc) + 1*(acc)*(crit*surge + (1-crit)*1)[/Quote]

 

In this equation, what are you using for Surge? If you have a surge of 50%, are you using 0.5, or 1.5? Because it looks like you're using the former (unless I'm reading your data wrong), but I'm pretty sure you should be using the latter.

 

Let me just break the equation down to make sure I understand everything:

 

0*(1-acc) = the proportion of attacks that miss, and thus do zero damage

 

1*(acc) = the proportion of attacks that hit

 

(1-crit)*1 = the proportion of attacks that do not critically hit, and thus do normal damage

 

crit*surge = the proportion of attacks that do critically hit, and thus have the surge multiplier applied. But if you have a surge of 50%, in this equation, you would have (crit*0.5), which would mean you're critical hits are only doing 50% normal damage, when in reality it should be (crit*1.5). This would be expressed by (crit*(1+surge)).

 

Now, if your equation already handles surge as (1+ surge_bonus), and thus always has surge > 1, everything makes sense. The way I was interpreting the equation, though, it looks like you are multiplying the critical hits by just the surge bonus, which would be effectively reducing their damage.

 

However, the way I wrote it also has the benefit of letting you simplify the equation. If it's written as 1*(acc)*((1-crit)*1 + crit*(1+surge)), you can expand (1-crit)*1 to (1 - crit) and crit*(1+surge) to (crit + crit*surge). Since these get added together, the crit terms cancel, and you are left with (1+ crit*surge). The final equation would then be:

 

E[dam] = 0*(1-acc) + (acc)*(1+ crit*surge)

 

Where acc, crit, and surge are just the values you see in your character window in game (but in decimals, rather than percentages).

 

 

EDIT:

 

Ok, it definitely looks like something is not quite right in your equation. In your data, E[dam] never goes above 1.00, which doesn't make sense. Let's stop thinking about numbers for a second, and just use logic: if you have 100% accuracy, you won't lose any damage to misses, so you should be doing your nominal damage, without accounting for crit/surge. Since crit and surge are strictly beneficial, your actual damage should be higher than the nominal damage, meaning E[dam] should be greater than 1.

 

Since this is not the case in your data, the only explanation I can come up with is that you are multiplying your critical hits by just the surge bonus. Since your critical hits actually do more damage than normal attacks, you need to multiply them by surge bonus + 1.

Edited by Delta_V
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crit*surge = the proportion of attacks that do critically hit, and thus have the surge multiplier applied. But if you have a surge of 50%, in this equation, you would have (crit*0.5), which would mean you're critical hits are only doing 50% normal damage, when in reality it should be (crit*1.5). This would be expressed by (crit*(1+surge)).

 

...

 

E[dam] = 0*(1-acc) + (acc)*(1+ crit*surge)

 

Where acc, crit, and surge are just the values you see in your character window in game (but in decimals, rather than percentages).

 

You are right, I have added 1 to my base surge to correct this. As you said, previously crit damage was being miscalculated as doing less damage than a non-crit attack, so the best way to maximize damage would have been to drop crit to 0%. I was wondering why my expectation for 1 point of damage was less than 1 point of damage outright, but I was hoping I was missing a lot of attacks.

 

I also added a min(acct, 1) check to make sure we're not rewarded for going past 100% accuracy.

 

The simplified equation might be less clear to some readers.

 

If you manage to drop crit down to 20%, have 151% surge base, and 91% base acc, things change a bit. At those amounts, since you have so little acc and you're not critting much, you still need to bring acc to 100%.

# acc	accr		accb	acct		surger	surgeb	surget	maximizing E[dam] =0*(1-acc) + acc*(crit*surge + (1-crit)*1)
0.0000	0.0000	0.0000	0.9100	720.0000	0.2601	1.7701	1.0502
1.0000	72.0000	0.0109	0.9209	648.0000	0.2512	1.7612	1.0611
2.0000	144.0000	0.0214	0.9314	576.0000	0.2403	1.7503	1.0711
3.0000	216.0000	0.0315	0.9415	504.0000	0.2269	1.7369	1.0803
4.0000	288.0000	0.0413	0.9513	432.0000	0.2106	1.7206	1.0883
5.0000	360.0000	0.0506	0.9606	360.0000	0.1906	1.7006	1.0953
6.0000	432.0000	0.0597	0.9697	288.0000	0.1661	1.6761	1.1008
7.0000	504.0000	0.0684	0.9784	216.0000	0.1362	1.6462	1.1049
8.0000	576.0000	0.0768	0.9868	144.0000	0.0996	1.6096	1.1071
[b]9.0000	648.0000	0.0849	0.9949	72.0000	0.0548	1.5648	1.1073[/b]
10.0000	720.0000	0.0927	1.0000	0.0000	0.0000	1.5100	1.1020

 

Here is the updated table for 25% crit, base 151% surge, and 91% acc. Since you don't spec for +3 acc, you want to max out your acc at 100%/576 rating, and just get 2 surge enhs.

# acc	accr		accb	acct		surger	surgeb	surget	maximizing E[dam] =0*(1-acc) + acc*(crit*surge + (1-crit)*1)
0.0000	0.0000	0.0000	0.9100	720.0000	0.2601	1.7701	1.0852
1.0000	72.0000	0.0109	0.9209	648.0000	0.2512	1.7612	1.0961
2.0000	144.0000	0.0214	0.9314	576.0000	0.2403	1.7503	1.1061
3.0000	216.0000	0.0315	0.9415	504.0000	0.2269	1.7369	1.1150
4.0000	288.0000	0.0413	0.9513	432.0000	0.2106	1.7206	1.1226
5.0000	360.0000	0.0506	0.9606	360.0000	0.1906	1.7006	1.1289
6.0000	432.0000	0.0597	0.9697	288.0000	0.1661	1.6761	1.1336
7.0000	504.0000	0.0684	0.9784	216.0000	0.1362	1.6462	1.1365
[b]8.0000	576.0000	0.0768	0.9868	144.0000	0.0996	1.6096	1.1372[/b]
9.0000	648.0000	0.0849	0.9949	72.0000	0.0548	1.5648	1.1354
10.0000	720.0000	0.0927	1.0000	0.0000	0.0000	1.5100	1.1275

 

Here is the result for 30% crit, 181% surge base before rating, and 94% acc base before rating. This will be more similar to what an Assault Vanguard or Commando would gear for, or a Marksman sniper, and some knight specs as well. This higher crit rate and +3 acc pushes your maximizing point down to 6 accuracy enhs, but still 100%.

# acc	accr		accb	acct		surger	surgeb	surget	maximizing E[dam] =0*(1-acc) + acc*(crit*surge + (1-crit)*1)
0.0000	0.0000	0.0000	0.9400	720.0000	0.2601	2.0701	1.2418
1.0000	72.0000	0.0109	0.9509	648.0000	0.2512	2.0612	1.2536
2.0000	144.0000	0.0214	0.9614	576.0000	0.2403	2.0503	1.2643
3.0000	216.0000	0.0315	0.9715	504.0000	0.2269	2.0369	1.2737
4.0000	288.0000	0.0413	0.9813	432.0000	0.2106	2.0206	1.2817
5.0000	360.0000	0.0506	0.9906	360.0000	0.1906	2.0006	1.2880
[b]6.0000	432.0000	0.0597	0.9997	288.0000	0.1661	1.9761	1.2925[/b]
7.0000	504.0000	0.0684	1.0000	216.0000	0.1362	1.9462	1.2839
8.0000	576.0000	0.0768	1.0000	144.0000	0.0996	1.9096	1.2729
9.0000	648.0000	0.0849	1.0000	72.0000	0.0548	1.8648	1.2594
10.0000	720.0000	0.0927	1.0000	0.0000	0.0000	1.8100	1.2430

 

This is for 30% crit, 181% surge, and 91% acc. Finally you don't need to max acc out at 100% for this spec.

# acc	accr		accb	acct		surger	surgeb	surget	maximizing E[dam] =0*(1-acc) + acc*(crit*surge + (1-crit)*1)
0.0000	0.0000	0.0000	0.9100	720.0000	0.2601	2.0701	1.2508
1.0000	72.0000	0.0109	0.9209	648.0000	0.2512	2.0612	1.2629
2.0000	144.0000	0.0214	0.9314	576.0000	0.2403	2.0503	1.2738
3.0000	216.0000	0.0315	0.9415	504.0000	0.2269	2.0369	1.2832
4.0000	288.0000	0.0413	0.9513	432.0000	0.2106	2.0206	1.2910
5.0000	360.0000	0.0506	0.9606	360.0000	0.1906	2.0006	1.2971
6.0000	432.0000	0.0597	0.9697	288.0000	0.1661	1.9761	1.3010
[b]7.0000	504.0000	0.0684	0.9784	216.0000	0.1362	1.9462	1.3025[/b]
8.0000	576.0000	0.0768	0.9868	144.0000	0.0996	1.9096	1.3010
9.0000	648.0000	0.0849	0.9949	72.0000	0.0548	1.8648	1.2961
10.0000	720.0000	0.0927	1.0000	0.0000	0.0000	1.8100	1.2835

 

I'd love to move toward a model which takes the following vectors: proportions/frequencies of attacks, base crit rates, surge from spec, and maximizes that weighted average of damage, instead of just 1 dummy damage with fixed crit, surge, and acc. Then I could give results better tailored to each spec.

 

The results seem to favor acc pretty strongly, which I find suspicious.

Edited by MGNMTTRN
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Glad to see that it got sorted out. I wasn't really expecting that to change the relative value of surge vs. accuracy, and it looks like it didn't, but just wanted to make sure everything was set up right.

 

As for accuracy vs. surge, I'm pretty sure that's the way it's been for as long as I remember. Stack accuracy to 100%, then surge until you hit diminishing returns, then if you've got any slots left, stack power.

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On my madness sorc should I need any accuracy? I'm at 101% now and could go to 103% but I would have to lose sap strength and either 1 percent crit or alacrity from healing tree. I only pvp and I read in another thread that it doesn't make as big a difference in pvp
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On my madness sorc should I need any accuracy? I'm at 101% now and could go to 103% but I would have to lose sap strength and either 1 percent crit or alacrity from healing tree. I only pvp and I read in another thread that it doesn't make as big a difference in pvp

 

Well, I'm not an expert on PVP, but I know that accuracy was supposed to become important for all dps classes in 2.0. Of course, alacrity was supposed to be useful for all classes now, too, and look how that turned out. I'm pretty sure Madness Sorcs want accuracy in PVE, but I don't know if that applies to PVP as well. That said, even if you do need accuracy you should never push your basic accuracy past 100% (and your special accuracy past 110%), since those points would be better spent in surge.

 

This might be a question better suited for the Sorc forums, since they'll know more about the class specifics.

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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.
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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.

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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/ccc?key=0AjXwzPy-0UfAdHEzQ2FTT3FwVm9vU3BuRmRvTmtxTXc#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

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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. :)

Edited by paowee
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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

Edited by canuckly
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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:

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.

Edited by MGNMTTRN
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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.

Edited by MGNMTTRN
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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.

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  • 2 weeks later...

I noted a bit of a gaffe in my 5/10/2013 post. Not a typo or formula error, I just didn't analyze the correct values. I showed the difference between 1.09 and 1.14 mainstat modifiers, but I should have shown the difference between 1.05 and 1.14 mainstat. I'll report them here.

 

I simulated an attack with the form 662 + 2.44199*tech bonus damage, with +6 crit and +0 surge from spec. Here are the results for a 5% increase in tech bonus damage and 5% increase in mainstat. This is meant to demonstrate that even when a character does not spec for +mainstat or +surge on its attacks, it is still more rewarding to use mainstat augs (+bonus damage, +crit) instead of pure power augs (+bonus damage). An unchanging 2330 base mainstat from ear, implants, armorings, mods, and stim was assumed. 14 augments were varied from mainstat (+32) to power (+32):

  • with mainstat augs, damage was maximized at 0.9997 acc/432 rating, 1.676 effective surge/288 rating, 0.2079 tech crit/0 rating, 1286 tech bonus damage, at 4492.16 expected damage
  • with power augs, damage was maximized at 0.9997 acc/432 rating, 1.676 effective surge/288 rating, 0.1969 tech crit/0 rating, 1296 tech bonus damage, and 4462.83 expected damage

 

Despite receiving 0.2 bonus damage per point of mainstat vs 0.23 bonus damage per point of power, mainstat augments were still superior (4492 > 4462) due to their contributions to increases in crit rate. I'll repeat my conclusions from this simulation:

 

  1. even when a character does not spec for +% increases in mainstat, mainstat is superior to power. When a character does spec for +% increases in mainstat, mainstat must maintain its superiority over power
     
  2. even when a character does not spec for +% increases in surge on an attack, mainstat is superior to power. When a character does spec for +% increases in surge on an attack, mainstat must maintain its superiority over power, since this specced +% surge would reward increased crit rates which only mainstat can provide, not power
     
  3. for an attack of the type b+c*bonus damage, the value simulated (c = 2.44)is a relatively high c value, which rewards tech bonus damage relatively more than other attacks. Despite mainstat contributing less to an increase in tech bonus damage, mainstat was superior to power for attacks with a high c due to increases in crit rate. If I simulated a lower c that might be more representative of other attacks, the contribution to tech bonus damage would decrease while the contribution to crit rate would remain the same. If mainstat is superior to power in a situation that favors tech bonus damage/favors power then situations less favorable to increased tech bonus damage (low c) must be even better for mainstat. I.e., for most attack coefficients mainstat will be superior to power

Edited by MGNMTTRN
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I noted a bit of a gaffe in my 5/10/2013 post. Not a typo or formula error, I just didn't analyze the correct values. I showed the difference between 1.09 and 1.14 mainstat modifiers, but I should have shown the difference between 1.05 and 1.14 mainstat. I'll report them here.

 

I simulated an attack with the form 662 + 2.44199*tech bonus damage, with +6 crit and +0 surge from spec. Here are the results for a 5% increase in tech bonus damage and 5% increase in mainstat. This is meant to demonstrate that even when a character does not spec for +mainstat or +surge on its attacks, it is still more rewarding to use mainstat augs (+bonus damage, +crit) instead of pure power augs (+bonus damage). An unchanging 2330 base mainstat from ear, implants, armorings, mods, and stim was assumed. 14 augments were varied from mainstat (+32) to power (+32):

  • with mainstat augs, damage was maximized at 0.9997 acc/432 rating, 1.676 effective surge/288 rating, 0.2079 tech crit/0 rating, 1286 tech bonus damage, at 4492.16 expected damage
  • with power augs, damage was maximized at 0.9997 acc/432 rating, 1.676 effective surge/288 rating, 0.1969 tech crit/0 rating, 1296 tech bonus damage, and 4462.83 expected damage

 

Despite receiving 0.2 bonus damage per point of mainstat vs 0.23 bonus damage per point of power, mainstat augments were still superior (4492 > 4462) due to their contributions to increases in crit rate. I'll repeat my conclusions from this simulation:

 

  1. even when a character does not spec for +% increases in mainstat, mainstat is superior to power. When a character does spec for +% increases in mainstat, mainstat must maintain its superiority over power
     
  2. even when a character does not spec for +% increases in surge on an attack, mainstat is superior to power. When a character does spec for +% increases in surge on an attack, mainstat must maintain its superiority over power, since this specced +% surge would reward increased crit rates which only mainstat can provide, not power
     
  3. for an attack of the type b+c*bonus damage, the value simulated (c = 2.44)is a relatively high c value, which rewards tech bonus damage relatively more than other attacks. Despite mainstat contributing less to an increase in tech bonus damage, mainstat was superior to power for attacks with a high c due to increases in crit rate. If I simulated a lower c that might be more representative of other attacks, the contribution to tech bonus damage would decrease while the contribution to crit rate would remain the same. If mainstat is superior to power in a situation that favors tech bonus damage/favors power then situations less favorable to increased tech bonus damage (low c) must be even better for mainstat. I.e., for most attack coefficients mainstat will be superior to power

 

I guess it all comes down to 1 simple fact: The contribution from Crit percent is multiplicative while the contribution from power is additive. Once the base value is sufficiently high, the multiplicative contribution wins out.

 

I am interested however whether this is skewed when factoring in auto crit abilities that contribute a high percentage of DPS such as Smash in Rage spec. I suspect that even if Power wins out for these at the current tier that, given a few more tiers, main stat will win out in the end.

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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. :)

Your optimal stats are probably 100% melee/ranged acc, and assuming your +surge% from spec is less than 30% you probably want between 0 and 52 points in crit.

 

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

You could decrease your crit multiplier and increase your acc by moving points from surge into acc. The spreadsheets show that this would maximize your damage in PVE.

 

2.0+ has me so confused on what I should be using to optimize my dps output. I hope you can help.

 

AMR Profile Link

Ops Dummy Parse

 

No adrenals, no Inspiration, all class buffs, Reusable Nano-Infused Might Stim. 5m 19.949s.

 

Do you need more than that?

It looks like you have 400+ points in surge and crit. I'd decrease my points in surge and move those points into accuracy until you reach 100% melee/ranged accuracy, and I'd move all my crit points in mods and enhancements into power where possible.

 

For the attack I'm simulating in the spreadsheet at the moment, the maximum expected damage and the minimum expected damage from the worst gear differ by about 5%. Things like spec, playstyle, rotation, and strategy are going to affect damage output significantly, and even a player in full crit/surge gear can still do competitive DPS. I've seen this firsthand in raids.

Edited by MGNMTTRN
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It looks like you have 400+ points in surge and crit. I'd decrease my points in surge and move those points into accuracy until you reach 100% melee/ranged accuracy, and I'd move all my crit points in mods and enhancements into power where possible.

Thanks for the tips. Now, I have another question. Could you possibly edit the AMR Profile I posted and change it to what you believe (based your epic mathing skills) would be optimal stats? If you could that would be awesome, very helpful, and very appreciated.

Edited by Bugattiboy
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