Maximizing SA/TA Damage (mathy mathy)Follow

This topic has come up on the boards in the past, about which stats to use for sa/ta. Obviously we've known the wiki basics for awhile: ie, "a single point of dex/agi increases base damage by one. the strike will be a critical which will not miss if landed correctly." Etc, etc. But being the fiends we are, many of us here would like to know "just how much better is a point of dex/agi for SA/TA than a point of attack?" or "is a point of haste ever better for SA/TA than a point of dex/agi?" and "if so, how much better is a point of haste; if not, how much worse is it?"

The veterans here, I'm sure, can easily understand that any answer to this question will not hold for all situations. The game is far too situational. Various factors such as player stats and equip, buffs, debuffs, and mob fought are all interdependent. However, it is still possible and beneficial to speak generally so long as we understand that general =/= always.

I'll post here a very abridged summary version, but for those that would like to know a lot more, the article in my blog can be found here: How to Maximize Sa/Ta Damage. So for detailed reading, I'd go there instead. Posting it all here would be 'tldr'.

I've come up with the following ratios for the relative values of various stats that can affect Sa/Ta damage (/nin).

Sneak Attack
1Dbl.Atk = 1
1TripleAtk = 2.38 (d.a.)
1Dex = 2.58 (d.a.)
1Str = 1.20 (d.a.)
1Attack = 1.19 (d.a.)
1Slow(2xMarch,Haste) = -2.64 (d.a.)
1D.Wield(2xMarch,Haste) = 2.16 (d.a.)
1Haste(2xMarch,Haste) = 2.65 (d.a.)
1Haste(1xMarch,Haste) = 2.22 (d.a.)
1Haste(NoMarch,Haste) = 1.84 (d.a.)

Trick Attack
1Dbl.Atk = 1
1TripleAtk = 2.51
1Agi = 3.35
1Dex = 0.39
1Str = 1.29
1Attack = 1.26
1Slow(2xMarch,Haste) = -3.50
1D.Wield(2xMarch,Haste) = 2.59
1Haste(2xMarch,Haste) = 3.50
1Haste(1xMarch,Haste) = 2.89
1Haste(NoMarch,Haste) = 2.43

These values are all relative to how much a single point of double attack increases damage.

I've also used this to rank SA/TA gear accordingly,

Sneak Attack
(head) Maat's Cap (26.46) > Skadi's Visor (25.41) > Gnadbhod's Helm (13.84) > AF2 (12.9) = Turban (13.25) > Emp.Pin (7.74) > Heca+1 (0.84)
(neck) Love Torque (20.04) > Kubira Bead Necklace (15.08) > Spike Necklace (11.34)
(ears) Suppanomimi (10.8) > Pixie (7.74) => Merman's (7.14) > Hollow/Adroit (5.16) = Coral (5.95) = Brutal (5.0)
(body) Dragon Harness+1 (32.34) > Skadi (26.59) = DH nq (27.38) > Anatares Harness (20.64) > BlueCote+1 (16.32) > WarAketon +1 (12.9) > Rapp (10.6)
(hand) ANNM Dragon Mitts (20.44) > Skadi Bazubands (17.9) > Dusk+1(2xMarch) (17.74)* > Enkidu's (15.12) => Tarasque Mitts +1 (14.28) => Dusk(2xMarch) (13.9)* > Merman's (8.94) > AF (7.74) > Heca +1 (4.02)
(rings) Rajas Ring (18.9) > 5Dex Ring (12.9)
(back) Charger's (23.8) => Cerberus Mantle +1 (22.65) > Forager's (21.45) > Amemet +1 (20.25) > Cuchulain's (15.12) > Commander's (11.34) > AF2 (10.32)
(waist) Cuchulain's Belt (27.38) > Ninurta's (23.04) > Warwolf (18.9) > Speed Belt (15.9) > Swordbelt +1 (14.28)
(leg)Enkidu's (18.9) > Dusk (16.66)* > Hecatomb Subligar +1 (12.44) = Heca nq (12.76) > Dragon+1 (12.9) = Barbarossa's (12.75) > Dragon nq (10.32)
(feet) Enkidu's (17.8) > Dragon +1(13.89) > Dragon (10.12) => Dusk (10.06)* > Leapers (7.74)

Trick Attack
(head) Maat's Cap (35.21) > Skadi's Visor (33.02) > Denali Bonnet (31.18) > Dragon+1 (16.75) > Turban (17.5) > Dragon (13.4) > Emp.Pin (11.22)
(neck) Hope Torque (16.75) > Crocodile Collar (13.4) > Love Torque (9.51) > Agile Gorget (6.7) => Justice Torque (6.45) => Tiger Stole (6.3) > Spike Necklace (5.04)
(ears) Suppanomimi (19.65) > Genin (13.4) > Drone (10.05) > Merman's (7.56) > Coral (6.3) => Brutal (5.0)
(body) Denali Jacket (44.84) > Dragon Harness +1 (41.3) > Skadi (36.22) > DH nq (35.04) > Antares Harness (26.8) > BlueCote+1(24.76) > Rapp (14.0)
(hand) AF+1 (?, ~54.77) > Skadi (35.8) > Dusk+1(2xMarch) (21.56)* = Dragon+1 (20.53) > Dusk(2xMarch) (16.8)* = Dragon (15.92) => Tarasque Mitts +1 (15.12)
(rings) 5Agi Ring (16.75) > Rajas (8.4)
(back) Charger's (25.2) => Cerberus Mantle +1 (24.06) > Forager's (22.77) > Amemet +1 (21.48) > Commander's (15.09) = AF2 (14.96)
(waist) Ninurta Sash (28.56) > Speed Belt (21.0) > Grenadier Belt (18.87) > Swordbelt +1 (15.12) => Scouter's (13.4) > Ryl. Knight's Belt (10.06) > Vanguard Belt (10.17) > Warwolf Belt (8.4) => Swift Belt (7.7)
(leg) Dusk+1 (18.9)* > Dusk (17.64)* > War Brais +1 (16.75) > Barbarossa's (15.66) > WarBrais/AF (13.4) > Heca nq (-13.68) > Hecatomb Subligar +1 (-17.77)
(feet) Enkidu's (23.26) > Dragon +1 (18.74) > Dragon (13.74) > Dusk (13.3)* > Leapers (11.22)

For the mathematically inclined, I used the following formula to measure the marginal increase of damage from an SA/TA "act":

(SA/TA round Dmg) - (TP round opportunity cost) 
= 
(Initial Critical Hit)+(Extra Swings) - (dDelay Function)*(TP round Dmg) 
 
= 
{(Main. +fStr'a +Dex/Agi)*(pDif'a+1) + [(Main. +fStr'a)*Dbl./Trip.Atks + (Off. + fStr'a)*(1 + Dbl./Trip.Atks)]*(CritRate'a*(pDif'a+1) + NonCritRate'a*pDif'a)} 
- ((delayTP - delaySA)/delayTP)*[(Main. + Off. +2fStr'b)*(CritRate'b*(pDif'b+1) + NonCritRate'b*pDif'b)*(1 + Dbl./Trip.Atks)*Accuracy

There's more detail on understanding the formula in the LJ. Also included is the method that I used to come up with the stat ratios and corresponding gear rankings, excel spreadsheets included. Short story, I used my base sa/ta gear (that I knew for sure were the best options), my tp gear, the standard lvl82 greater colibri, double-march/haste and an accuracy buff, and variable gear options to create a spreadsheet of over 950 gear combinations for SA and over 100 for TA. From there, I found the best sets for each and simply worked out how much a single point of an attribute increased total damage, and then rationalized them.

As I said earlier, these ratios/rankings won't always hold. It's more of a general guide, though I think the gear rankings should generally hold pretty well for most situations though, even if the stat ratios change.

I really hope this can be of decently useful reference to some of the devoted thieves we have on the forums here. This project took far longer to finish than originally anticipated, and I was really glad when it was over. Also, double-checking of the math here is welcome and definitely encouraged, though I feel pretty comfortable with it. The biggest errors would probably be some truncation shortcomings, but I'm pretty confident this hasn't affected the end results in any major ways.

Edited, Jul 30th 2009 12:33pm by Shamaya
Edited, Sep 24th 2009 5:12am by Shamaya
Edited, Sep 25th 2009 12:51pm by Shamaya

Edited, Sep 25th 2009 3:16pm by Shamaya

Interesting stuff Shamaya.

Especially the TA list:
(leg) Dusk+1 > Dusk > War Brais +1 > Barbarossa's = WarBrais/AF > Heca nq > Hecatomb Subligar +1 >

I thought I was doing okay with macroing NQ heca for TA. It has 20 attack and all. But it is nearly at the bottom of the list because of the 12% slow.

I am going to make a few changes to my TA setup now.

I think im reading it wrong, but how does haste affect damage? SA and TA are a one-off attack and while Haste will let you land it quicker, I don't see how it will actually make it land harder. Don't misunderstand, I realise that Haste is great for the DoT and raising TP and everything, but for the actual SA/TA, I fail to see where it's benefitting you.

Here I was thinking that my lack of a decent SA/TA macro set was ruining my THF, but according to this I've been doinitrite :D

its not for the actual SA/TA round, its for the melee round after it.

All the movement + / - options are italicized, which I'm guessing means it's hard to quantify them. If you don't have to run anywhere for your SA/TA, you can effectively take trotters/striders off the list. If you do, though, they could be better then anything else (and by default, dusk would then be worse then everything else)

Thanks for the list Shamaya. For now I'll just edit my suppa in place of the brutal and call it a day. Also might have to work on a chargers.

I think attack is a bit over rated in this system. 2.2 attack is not 1 dex in SA.

These are all for SA/TA with out weapon skill. How would they compare with weapon skills?

He has the spreadsheets up for download on his LJ, the link is in the OP.
I was gonna tweak them with Dolch/Siro myself, but I'll jus let ya do it. ;p

well, first of all, the equivalencies plainly don't generalize. compare X ATT vs gcolibri against X ATT vs debuffed kirin against X ATT vs non-debuffed kirin. also compare the value of 1 DEX in a heavy DEX setup vs in a not very heavy DEX setup. also note that 1% DA on top of 0% is a different DoT increase than on top of 5%.

however, to the people saying that ATT is being overvalued here, don't be so sure. notice:

a) DEX is 1 base damage. "hoho, must be a big increase!" well, if you have a lot of DEX, 1 DEX will be well below 1% damage increase.

b) "hey, i've been at this for a long time. 1STR generally = 2ATT for 1handers with a decent amount of ATT." this is true, but see (a). base damage gets bumped the fuck up by all the DEX (or AGI). this lowers the value of STR. ("but what about the ATT that STR adds?" not sure if OP factored that in; no offense, i can't really be bothered to read the whole thing;;;).

c) "yeah but surely DA doesn't care about all the DEX..." but yes it does. your first hit is gonna crit and have a high base damage (the DA isn't a guaranteed crit nor does it have the DEX enhanced BD does it?). therefore, as on hagun WSs (for example), the DA's value takes a big hit.

(a)-(c) is what's inflating the goodness of ATT. it's hard to swallow still; we're talking about a guaranteed crit, so you wouldn't expect ATT to do much (as crits simply add 1 to pDIF). nonetheless, the biggest source of damage in a THF's SA/TA is the base damage increase. therefore, once your base damage reaches a certain level (relatively ill defined and situational what that level will be), it makes sense that you'd want to raise the pDIF side of the equation.

edit: note,

Greater Colibri  Level:81-82 Def:322-327 VIT:67     
Kirin            Level:92    Def:413     VIT:120

Edited, Jul 31st 2009 4:07am by milich

no, run the numbers. i thought the value of ATT was high, but when i thought about it and postulated some base damages, i saw that 1 DEX was only giving like .6% DoT.

500/322-.3 = 1.252
502/322-.3 = 1.259
-> 5%~ increase.

it was definitely more (a)-(c) than any underestimation of how much ATT you have.

edit: p.s. by the way, i find relativizing everything to DA to be pretty bizarre. and by bizarre i mean... a bad enough idea to justify redoing the whole thing. the value of DA on SA/TA is based on

a) how much DA you start with,
b) how much DEX/AGI you stack,
c) how much ACC you have,
d) how much ATT you have,
e) your crit rate on the additional hit

shamaya, if you read this, i urge you to redo the whole thing, b/c making it all relative to DA is a bad choice. pick some amount of ATT and a target mob and relativize to that, or something else more stable than DA or base damage.

Edited, Jul 31st 2009 5:15am by milich

0.55% actually.

GRAAAAAAAAAAAAAAAAAGH RAGE MODE

Decimal points are going in the wrong places in milich's posts due to beer (either a shortage or a surplus, I'm not sure which yet).

0.32% increase, not 3.2%.

To co-opt a meme:

milich does not sleep.

He waits.

Sleep has never been my forte as well. I forced myself into a *wake up at 8-10ish* "schedule" a week or two ago. And I just slowly drifted back into my nocturnal nature. I love being a night person.. but due to the fact that this conflicts with all my societies except my rave society I sometimes end up skipping a day of sleep.

Sleep fails. Why can't everything be open 24/7 so that it can agree with me.

edit: oo oo, if I add in sirocco's DMG plus the fstr to it, does that mean I can just use that number and the percent will still be correct?

Like, 33 + 8 + 133 + 26 + 8 = 208, 1/208 = ~0.48?

Edited, Jul 31st 2009 6:35am by Deadgye

I'm not surprised that attack would be worth more than we originally give it credit for, and I agree with the conclusion given. In addition I agree with the haste versus stats on everything Shamaya said. In the recent month I've been playing around with not only X's knife and crit setups, but also my tp burn setup and evisceration versus dancing edge (and more). I was going to post a summary of my data in a new topic, but since Shamaya went and posted this here I'll just summarize it in this post instead.

-----
1:) Slow versus Haste

I used to try and maximise every critical hit I did by swappping into the strongest damage options avaiilable to me for the critical no matter what. In the case of sneak attack that involved the hecatomb cap +1, gloves +1, and leggings +1.... and in the case of trick attack it simply meant losing all haste. I DID NOT enjoy swapping into my solo sneak attack set, especially when using my x's knife. As much as it sounds weird, I found my performance lessened drastically every time I solod a sneak attack with x's. The reason is that with x's delay of 201 being high to begin with, losing 17% melee haste and swapping in 27% slow (does slow cap at 25% like haste?) was NASTY!! It was ACTUALLY PAINFUL to see. I would go from swinging rounds every few seconds to a HUGE delay of 5++ seconds to get another in. I would just stop and stand there frozen in time, and that sucked!!! I've since modified my sneak attack set to remove the heca cap hands and feet, and replace em with dragon feet +1, artifact hands +1 (no annm hands yet) and my assassin's bonnet.

Yes, I actually dusted off my assassin's bonnet in place of heca cap +1 for solo sneak attack. The reason is that this IS part of our DoT, so swinging again soon matters. I refer to solo criticals as "Spike DoT" but they are still melee DoT nonetheless, and part of our tp building routine.


----
2:) Attack versus stats

I have always valued attack, and I've been preaching the merits of the charger mantle for the past two years. When I got sea access I bought in order, the brutal followed by the charger followed by the boxer's mantle. The charger is a NICE item for solo crits and I've been using it for years.

The concept is simple, and I've touched upon it before. If you have a huge base damage but low attack, raising attack will do a lot more than raisng base damage by a little more. My base damage in my max stats set is around 185, so raising base damage by 1 is worth about half a % of the crit, whereas raising the pDIF by 1 is worth almost twice as much, or two stat points. pDIF goes up by 1% around every 3-5 attack (usually 3-4) so attack DOES matter, and even though it will be a critical hit it's still going to play an important role in the outcome. I gave the ratio around 1 base stat to 4-5 attack but in actual practice that still underestimates its strength. Whenever I use berserk or cap my attack the damage shoots through the ROOF on solo criticals, and as /nin in a burn scenario THAT kind of attack is rarely seen (barring bard/cor of course).

-----------------
3:) Summary:

I agree with Shamaya on his analysis. However I think he should edit his OP. In his OP he accounts a hierarchy for each solo piece and gives heca a higher rank than I think it should get. Slow is exponentially cumulative. While ONE piece of heca will possibly fit into the grid, donning them ALL will have catastrophic results on your soloed sneak attacks. As I said, I even removed my heca cap +1 and replaced it with relic.

Thief Damage can be divided into two parts. Weaponskills and Melee DoT. As I said I like to call our solo criticals "Spike DoT", but they are melee DoT nevertheless. They are in the ritual of building tp to get to the point of weaponskill, so adding unnecessary slow when the difference is going to be minimal is generally a bad idea. The heca set will give monstrous slow for a very SMALL bonus to the overall damage of that crit when you consider the relativity of the siituation. In comparison to the wait time to attack again (it really is THAT painful) it's not worth it. Heca is weaponskill only --- The only possible exception may be the hecatomb subligar. THAT piece I would probably ok for a solo sneak attack if used alone. Just don't combine it with any of the other 4 and you should be fine.

Edited, Aug 3rd 2009 2:24pm by Melphina

I went to bed at about 4 AM last night and work up at about 7:40 AM. Wasn't a great day, but if I had to do it over I'd still stay up. :D

It also saves you 150 ABCs, or about 1.35 mil. If you have the gil to throw around, no big deal. I don't. _(._.)_




Edited, Aug 1st 2009 12:29am by bsphil

Unfortunately, no, gear slow does not cap. For that matter, total slow does not cap either, meaning that it's possible to be at ~200% slow (full HQ Heca + weakness + Slow II + Elegy).

The only reason I can see to use Heca for SA is if there's some obscure call for you to go THF/DRG and do SA+Jump (assuming that even works).

Some crappy estimation maths tell me that changing Heca Cap+1 to Ass head +1, Heca Mittens+1 to Enkidu Mittens, Heca Subligar to Dragon Subligar+1, and Heca Leggings+1 to Dragon Leggings+1 will lower your SA round damage by about 70(before piercing) and increase your damage from normal attack rounds because there's no slow by 30(before piercing). Therefore better to keep on the slow. Of course, this doesn't account for missing sneak attack, but meh.

Unless I did something wrong, here's the crappy lolnapkinmath that I spent maybe 15 minutes on. The gear choices may be.. a little out of wack. I didn't feel like using Mirke because I don't plan on ever getting it.

Main: X's Knife
Sub: Blau Dolch
Range: -
Ammo: Fire Bomblet
Head: Anwig Salade
Neck: Love Torque
Ear1: Brutal Earring
Ear2: Suppanomim
Body: Homam Corazza
Hands: Homam Manopolas
Ring1: Rajas Ring
Ring2: Toredor's Ring
Back: Cuchulain's Mantle
Waist: Swift Belt
Legs: Skadi's Chausses
Feet: Homam Gambieras

Level 82: Defense 327, Evasion 339, VIT 67, AGI 67
Coeurl Sub: Str+5 Agi+1 Attack+20(75)
1BRD: Attack+66 Haste+11%
haste: Haste + 15%

Str: 62 + 9 + 5 [76]
Dex: 80 + 14 [94]
Attack: 8 + 38 + 269 + 16 + 7 + 16 + 6 + 5 - 5 + 5 + 66 + 75 [506]
Acc: 200 + 82 + 47 + 5 + 6 + 10 + 15 + 4 + 7 + 5 + 3 + 4 + 6 [394]
Haste: 3 + 3 + 4 + 2 + 3 + 11 + 15 [41]

fstr = 3
cratio = 1.197
Acc% = 88.5
Base Damage = (34 + 3) && (33+3)

Main: X's Knife
Sub: Blau Dolch
Range: -
Ammo: Bomb Core
Head: Hecatomb Cap +1
Neck: Love Torque
Ear1: Brutal Earring
Ear2: Pixie Earring
Body: Skadi's Cuirie
Hands: Hecatomb Mittens +1
Ring1: Rajas Ring
Ring2: Thunder Ring
Back: Cuchulain's Mantle
Waist: Warwolf Belt
Legs: Hecatomb Subligar
Feet: Hecatomb Leggings +1

Level 82: Defense 327, Evasion 339, VIT 67, AGI 67
Coeurl Sub: Str+5 Agi+1 Attack+20(75)
1BRD: Attack+66 Haste+11%

Str: 62 + 41 + 5 [108]
Dex: 80 + 58 [138]
Attack: 8 + 269 + 16 + 7 + 16 + 12 + 5 + 20 + 54 + 66 + 75 [548]
Slow: 9 + 7 + 12 + 6 [34]

fstr = 11
cratio = 2.325
Base Damage = (34 + 11 + 138) + (33 + 11)


44.289 + 43.092 -> 90

425.475 + 58.3 -> 480


Main: X's Knife
Sub: Blau Dolch [Attack +16]
Range: -
Ammo: Bomb Core [Attack +12]
Head: Assassin's Bonnet +1 [Dex+6]
Neck: Love Torque [Dex+5 Dagger+7]
Ear1: Brutal Earring
Ear2: Pixie Earring [Dex+3]
Body: Skadi's Cuirie [Dex+8 Attack+5]
Hands: Enkidu Mittens [Str+4 Dex+4]
Ring1: Rajas Ring [Str+5 Dex+5]
Ring2: Thunder Ring [Dex+5]
Back: Cuchulain's Mantle [Str+4 Dex+4]
Waist: Warwolf Belt [Str+5 Dex+5]
Legs: Dragon Subligar +1 [Dex+5]
Feet: Dragon Leggings +1 [Dex+4 Attack+3]

Level 82: Defense 327, Evasion 339, VIT 67, AGI 67
Coeurl Sub: Str+5 Agi+1 Attack+20(75)
1BRD: Attack+66 Haste+11%

Str: 62 + 18 + 5 [85]
Dex: 80 + 54 [134]
Attack: 8 + 269 + 16 + 7 + 16 + 12 + 5 + 3 + 66 + 75 [477]
Slow: 0

fstr = 5
cratio = 2.108
Base Damage = (34 + 5 + 134) + (33 + 5)

364.684 + 42.104 -> 410

70 decrease; 30 gain

Inbeforelolnapkinmath. Most of the stuff I that wasn't exact was done in favor of the not-slow situation. I didn't even apply the accuracy for the normal attack round, which would have lower the damage gained by getting rid of slow even more, etc.

Edited, Aug 4th 2009 1:14am by Deadgye

FIrst off, thanks for the fixes. :3 Second, I having difficulty seeing how 34% slow can cause a delay difference of a whole round. Extrapolate!

The comparison isn't between the TP gear and the Slow Gear though, it's between the replacement gear and the heca gear. The difference is only 34% slow, there's 0% difference in haste.

@Deadgye: this is not what Shamaya meant with his OP. Shamaya is suggesting to balance gears. Use heca where you get the most bang for your buck. Example: use Hecatomb Subligar +1 instead of Dragon Subligar+1.
And use other options when heca does not offer as much. Example: ANNM Dragon Mitts > Enkidu's mitts > Heca +1 mitts.

You should do the math again but now with the gear options Shamaya gave. Except Skadi Feet.

Edited, Aug 4th 2009 5:08pm by Breaze

So Sword Belt > Forest Belt huh?

mmm and my sword belt +1 has a +1 dex mod :D


however, I don't understand the whole striders/trotters deal... even after reading the LJ


There a similar article for "With weaponskills"?

Edited, Aug 5th 2009 10:58am by PyroElf

Ah there's my problem, I was dividing by the delay of the nonslow equipment instead of the tp equipment for some reason. Although, I remember reading somewhere that you took your attack round and multiplied it by the haste you had, and then multiplied it by the slow you had. I could be wrong as I can't seem to find it again, but meh.



The difference in attack rounds is actually exactly the same using Blau/Sirocco and etc, since the delay difference between the heca set and nonslow set decreases proportionally do the decrease in the regular round delay. Since blau/sirocco will turn out less damage per attack round than X's/blau, it's actually more in favor of the heca scenario with blau/sirocco.

I plan to redo the napkin math, and then turn it into full math using the top gear that shamaya said. But that'll have to wait for after my 20k ding, which will be after I get back from this 2~3 day camping trip I'm going on tomorrow. :p (I agree with most of Shamaya's findings, but I can't let myself listen to them without testing them myself to make sure. )

Honestly if I knew how to make graphical interfaces for programs I could whip something up in a day or two that would do any and all of these comparisons between two pieces of gear pretty easily.. (Not counting skadi/trotter boots, lolmovementspeed.)

Edited, Aug 5th 2009 5:15pm by Deadgye

This. I was referring to the bonus damage x's gives when you critical, not its attack speed.