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Acc vs Surge, with mathematical proof

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

MGNMTTRN's Avatar


MGNMTTRN
05.21.2013 , 08:07 PM | #21
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

grallmate's Avatar


grallmate
05.21.2013 , 08:33 PM | #22
Quote: Originally Posted by MGNMTTRN View Post
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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Bugattiboy's Avatar


Bugattiboy
05.22.2013 , 12:05 AM | #23
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?

MGNMTTRN's Avatar


MGNMTTRN
05.22.2013 , 03:24 AM | #24
Quote: Originally Posted by paowee View Post
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.

Quote: Originally Posted by canuckly View Post
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.

Quote: Originally Posted by Bugattiboy View Post
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.

Bugattiboy's Avatar


Bugattiboy
05.22.2013 , 09:11 AM | #25
Quote: Originally Posted by MGNMTTRN View Post
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.

Degalian's Avatar


Degalian
06.05.2013 , 08:35 AM | #26
Is it just me or does your formula look weird (ly partially useless)?

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

I mean "0*(1-acc_rating)" is always 0 and has no influence whatsoever, so why even mention it?

Basically: Damage = AvgPotentialDmg * Acc% * (1+crit%*Surge%)

with AvgPotentialDmg being whatever Damage you would do if you hit and didn't crit.

I just find your formula very confusing, I didn't read everything you wrote, but hey ... 0 is 0 and will always be 0, no matter what you multiply it with

MGNMTTRN's Avatar


MGNMTTRN
06.05.2013 , 11:03 AM | #27
Quote: Originally Posted by Degalian View Post
Is it just me or does your formula look weird (ly partially useless)?

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

I mean "0*(1-acc_rating)" is always 0 and has no influence whatsoever, so why even mention it?

Basically: Damage = AvgPotentialDmg * Acc% * (1+crit%*Surge%)

with AvgPotentialDmg being whatever Damage you would do if you hit and didn't crit.

I just find your formula very confusing, I didn't read everything you wrote, but hey ... 0 is 0 and will always be 0, no matter what you multiply it with
That's true, you can simplify
E[dam] = (1-acc)*0*dam + dam*1*acc*(1-crit + crit*surge)
E[dam] = dam*1*acc*(1-crit + crit*surge)
E[dam] = dam*acc*(1-crit + crit*surge)

but I don't see how you can simplify this to E[dam] = dam*acc*(1+crit*surge)

In my original equation I wanted to be clear about where each term came from.

Degalian's Avatar


Degalian
06.06.2013 , 04:31 AM | #28
Quote: Originally Posted by MGNMTTRN View Post
That's true, you can simplify
E[dam] = (1-acc)*0*dam + dam*1*acc*(1-crit + crit*surge)
E[dam] = dam*1*acc*(1-crit + crit*surge)
E[dam] = dam*acc*(1-crit + crit*surge)

but I don't see how you can simplify this to E[dam] = dam*acc*(1+crit*surge)

In my original equation I wanted to be clear about where each term came from.
Thanks for your reply. I still don't understand what (1-crit+crit*surge) is supposed to represent (esp. the 1-crit part).
I think my equation is totally correct because: dam*acc (is clear) and the added dmg for crits is crit*surge, which as a factor is 1+crit*surge. I.e. if you have 50% crit and 70% surge, you do 35% more dmg on average when you hit. That would be dam*acc * (1+50%*70%) so dam * acc * 1.35.

Update:
I now understand the difference. In your formula when someone has 80% surge, for some reason you represent that with 1.8, where I do it with 0.8. So both formulas are correct, you just have to have some term to make the 1.8 into 0.8......

Altheran's Avatar


Altheran
06.06.2013 , 04:42 AM | #29
Quote: Originally Posted by MGNMTTRN View Post
E[dam] = dam*acc*(1-crit + crit*surge)

but I don't see how you can simplify this to E[dam] = dam*acc*(1+crit*surge)
In fact, it should be ( (1-crit) *1 + crit * (1+surge) )
That's it, if you consider surge as the crit bonus, not the crit itself. ( the "*1" is just for show)

And so if written like this, you can transform like this :
( 1*1 - crit*1 + crit*1 + crit*surge)
(1 + crit*surge)

Degalian's Avatar


Degalian
06.06.2013 , 04:43 AM | #30
Quote: Originally Posted by Altheran View Post
In fact, it should be ( (1-crit) *1 + crit * (1+surge) )
That's it, if you consider surge as the crit bonus, not the crit itself.

And so if written like this, you can transform like this :
( 1*1 - crit*1 + crit*1 + crit*surge)
(1 + crit*surge)

Seems we read forums at the same time, I just updated my post while you answered :-)