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

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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:

Code:

# 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
**7.0000 504.0000 0.0684 1.0084 216.0000 0.1362 0.6462 0.9192 **
8.0000 576.0000 0.0768 *1.0168* 144.0000 0.0996 0.6096 0.9176
9.0000 648.0000 0.0849 *1.0249* 72.0000 0.0548 0.5648 0.9134
10.0000 720.0000 0.0927 *1.0327* 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:

Code:

# 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
**7.0000 504.0000 0.0684 0.9784 216.0000 0.1362 0.6462 0.8919 **
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 *1.0027* 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.

Code:

# 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
**7.0000 504.0000 0.0684 1.0084 216.0000 0.1362 0.9462 0.9949 **
8.0000 576.0000 0.0768 *1.0168* 144.0000 0.0996 0.9096 0.9939
9.0000 648.0000 0.0849 *1.0249* 72.0000 0.0548 0.8648 0.9903
10.0000 720.0000 0.0927 *1.0327* 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

Code:

# 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
**6.0000 432.0000 0.0597 0.9997 288.0000 0.1661 0.6761 0.9090 **
7.0000 504.0000 0.0684 *1.0084* 216.0000 0.1362 0.6462 0.9085
8.0000 576.0000 0.0768 *1.0168* 144.0000 0.0996 0.6096 0.9057
9.0000 648.0000 0.0849 *1.0249* 72.0000 0.0548 0.5648 0.9000
10.0000 720.0000 0.0927 *1.0327* 0.0000 0.0000 0.5100 0.8911

and 30% crit

Code:

# 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
**6.0000 432.0000 0.0597 0.9997 288.0000 0.1661 0.6761 0.9026 **
7.0000 504.0000 0.0684 *1.0084* 216.0000 0.1362 0.6462 0.9014
8.0000 576.0000 0.0768 *1.0168* 144.0000 0.0996 0.6096 0.8977
9.0000 648.0000 0.0849 *1.0249 *72.0000 0.0548 0.5648 0.8911
10.0000 720.0000 0.0927 *1.0327* 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.