Maximizing Sneak/Trick Attack Dmg (mathy)

[Shamaya]

This is something I would have posted in Standard, but there is only Advanced now. I wasn't originally going to post it because imo BG adv isn't usually the place you go for detailed job specifics. But sometimes you do see people interested in job specifics, and this is new material that applies to anyone who has thief leveled and bothers to make an SA/TA build (without a weaponskill attached to it).

The article in my blog is How to Maximize Sa/Ta Damage and if this topic interests you, I would go there because there is far too much to post here. The following is a much, much abridged version.

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 the formula in the LJ as well as how I came up with it. 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.

These stat ratios are by all means not going to hold for every single situation in the game, simply due to the wide range of enemies, equip sets, and other conditions. The gear rankings should generally hold pretty well for most situations though, I think.

For the bored and weary forum traveler who is not entertained by Thf discussion, there is also a writeup right below that LJ entry on how I funded my relic through gardening and precise step-by-step instructions on how to copy that method, and this may interest some more so.

This was one hell of an annoying project to do and I do hope it serves as a convenient reference for people that have Thief leveled ^.^
(edited 9-25-09, to fix critical error with haste calc, as well as many other smaller updates)

[Chisato]

Thanks a million for sharing your results, this is a really nice guide and I'll be able to make some improvements to my current builds using it.

If you ever feel taking it on, I don't think I've ever seen a guide like this relating to stacked and un-stacked THF weapon skills, particularly de/evi/sb/ms.

Anyway, thanks again, great job!

[stewie]

Where's homam place on feet?

[Shamaya]

NP, Chisato. No there's no such detailed guide for WS's, but one reason is because the math for that is a lot easier and many of the forum veterans just do the math for themselves or answer the questions of others on the fly. Whereas sa/ta unstacked has been more difficult, one of the complications being the opportunity cost of lost melee strikes as the delay of an sa/ta set increases (this is not an issue for WS's).



As for feet, thank you for that question. My pleasure to answer it. I didn't focus too much on it because I consider Skadi/Striders to be the end-all-be-all for sa/ta feet due to my stress on maximizing movement speed (can't be gotten into mathematically), so I neglected the feet secion.

However, if you are interested in where homam feet would place, my advice is to simply use the ratio references I've outlined above. Like so,

For example, Homam Gambieras,
6 acc, 3% haste. 6acc is of no concern to us since the sa/ta round will have 100% accuracy.

If you're rocking double march and haste spell, use the assigned haste stat value and multiply by 3 (since homam feet have 3% haste on them), like
3 * 2.86 (1Haste(2xMarch,HasteSpell),for SA) = 8.58

So compare that with other options. For example, leaping boots have 3dex on them. So look up the value for dex and multiply like so:
3 * 2.55 = 7.65

By this math, Homam Gambieras > Leaping Boots for SA (double march).

Looking at Dragon Leggings, they boost SA with 3dex and 2attack,
(3*2.55) + (2*1.14) = 9.93

By this math, Dragon Leggings > Homam Gambieras for SA, even where double march is concerned.


This is an example of how the stat values can be used as a reference for any individual to easily solve for themselves which pieces to pick for their Sneak/Trick sets.

[Liquidedust]

I assume your math disregards multi-hit SA/TA WS in this case, and just focus on regular main-hand/off-hand SA/TA hits.

But in a G.Colibri situation wouldn't you be better off with coupling a WS with SA and TA every 25-30 seconds to get the most out of your SA/TAs?

[hagun]

Hm. During merits, where your calculations put damage with time into consideration, there should be no instance where you are using SA or TA without a WS unless it's the final hit in which case delay is of no consequence. That occassion is pretty rare as you should be getting 100TP at a rate where neither SA nor TA can keep up alone. That would result in alternating SA WS and TA WS every fight as it should be.

There really shouldn't be a reason to use SA or TA unstacked with a WS outside the initial battle in merits. At least from my experience, that is the case. Under practical application, what is your justification for using SA or TA unstacked with a WS? I ask because I am always at the threshold where using SA/TA without TP would be a large loss in damage not to mention that using SA unstacked with a WS is a comedy of horror in a dynamic setting.

[Raen Ryong]

Thanks for the writeup Shamaya; I've been juggling things like this in my head for ages now so it's nice to see it all in a mathematical form.

[Kaope]

What about Chuculain's Mantle?

[Tubbers]

Those attack values are definitely not static. In fact you are treating several dynamically changing variables as if they had static or semi-static increases. This may give a decent rough estimate, but it's far from a working model. Nonetheless it's nice to see some real progress in this area.

[Shamaya]

Thx tubbers and all. For the record, unfortunately, there will never be such a "working model," tubbers. As mentioned in the OP and a couple times in the blog, there far too many interdependent variables and widely varying conditions to make any sort of universal prescriptions. This is simply my best attempt at it and will serve to satisfy me for now, though I'll probably never touch it again except for necessary edits.

I agree with you that attack->pDif is one of the bigger problems with accuracy in these results. This becomes particularly obvious if you look at the results I've got for Trick Attack. The value of a single point of Atk is very low, but if I were to add a bundle of attack, the increase is larger than expected (play around with the excel spreadsheet: TA, stat summary--you'll see what I mean). This is because my TA set, in those specific settings, is just riding the border of higher marginal pDif increases.

Cuchulain's Mantle, I forgot to add along with the Homam Gambieras. I'll probably edit this in later but for now if anyone's interested, they can compare it using the stat ratios, as that is their intention.

As for liquid's concern, there's definitely nothing to do with WS's here; that much should be pretty apparent.


The matter of whether or not to do unstacked SA/TA's of course doesn't change our math but is of course fundamental since if there's never any reason to do this, then none of this matters. However, I can say after having Thf as my main since I started the game shortly after NA release, that there's nothing to even debate on this subject. Every Thf who wants to improve their damage above a very mid-range or low level, should have unstacked SA/TA sets.

I'm a mandau thief, and even I do unstacked SA/TA's, though I must admit I do them quite a bit less than I used to pre-mandau. This is because after a time, it became traditional that the pretty pro thing to do for dmg on Thf (in burn situations at least where DE/EV are still good) is to not worry so much about stacking, but WS when you have TP and SA/TA when they're up. I switched to this style a few years ago, and definitely noticed increases in damage over time while finding the style more enjoyable. The correct answer when it comes to stacking SA/TA and WS is to stack selectively. If your sa/ta is up and you're a few seconds from having TP, wait on your TP. Conversely, if you've got TP and your sa/ta is a few seconds away, wait on it. If you're something like 7+ seconds away, just unstack. If you wait to stack too often, you lose total sa/ta/ws volume.

A last word on that, the "get tp in at least 30 seconds = you can always stack" mantra began very a long time ago when gaining tp in 30 seconds was almost a dream. Just a single experience in a merit party or in other burn situations like nyzul, dynamis, limbus, and many others will allow you to see this philosophy broken down to being meaningless. If you've killed all mobs in your area and there's no spawns, hit sa/ta so you have it up and the timer's already counted way down by the time you actually do have a mob. Mob's HP too low to sustain a full stacked WS? Just ja or WS and save the other half for the next mob, rather than build excess TP or keep your timers unproductively at 0. There are too many examples to show that this philosophy is dated. Colibri stole your TP. There's another one. It just doesn't work. And fortunately (for non-mandau) it is not the secret to maximizing dps.


Thx for your comments all, keep em comin (though I'd like more on my LJ rather than here )

[Tubbers]

It's definitely not impossible to have an actual working model, but I'll more or less agree with you that nobody will ever make one, lol.

[Mistress Stowastiq]

Thank you for taking the time to do this. Need to sit down and have my husband translate it into pretty pictures and colorful words so I can understand it . Also very interested in your blog about the gardening to fund relic.

[Baha]

I didn't focus too much on it because I consider Skadi/Striders to be the end-all-be-all for sa/ta feet due to my stress on maximizing movement speed (can't be gotten into mathematically), so I neglected the feet secion.

I understand strider's/trotters for TA (only lose 1-2AGI and some attack, movement speed may come in handy when repositioning), but for SA it doesn't really compute. Maybe when you ready it between mobs it's helpful, but otherwise there's usually no reason to not be on a mob's ass *before* your SA timer is up.

Interesting stuff, much more thorough and informative than the usual KI flavor of the month SA/TA gear wisdom (keep on tp gear! haste > all! wearing slow+ gear? lol!).

[DancingEdge]

I <3 Sham.

Good shit dude, I'll actually read this in more detail when I'm not on vacation.

[Kukuk]

Awesome, some of the gear you listed as top SA or TA gear really surprised me. Who would have thought that AF2 back would be so low on the list lol.

Great guide and thx again for all your hard work :D.

[jupeeh]

Great post! There are often times I have SA or TA up without TP during merits, especially with 5/5 SA merits. I sloppily put together gear sets for unstacked SA/TA, but you've motivated me to get something better going. Thanks!

I enjoyed your other posts on your blog as well. I'm really interested in how cuchulain's mantle stacks as well - I'll be refreshing for an update hopefully :D

[Franzer]

this might be the first math thread i've read that wasn't attacked in the first page

[jimbobsonofgod]

Just Curious on why rapp made the list but not enkidu harness ?

[Eaglestrike]

Hm. During merits, where your calculations put damage with time into consideration, there should be no instance where you are using SA or TA without a WS unless it's the final hit in which case delay is of no consequence. That occassion is pretty rare as you should be getting 100TP at a rate where neither SA nor TA can keep up alone. That would result in alternating SA WS and TA WS every fight as it should be.

There really shouldn't be a reason to use SA or TA unstacked with a WS outside the initial battle in merits. At least from my experience, that is the case. Under practical application, what is your justification for using SA or TA unstacked with a WS? I ask because I am always at the threshold where using SA/TA without TP would be a large loss in damage not to mention that using SA unstacked with a WS is a comedy of horror in a dynamic setting.

Some WS's gain very little coupled with SA/TA. The first hit is a critical and the offhand hit will also hit are the things gained by stacking a WS with the ability, but for something like Dancing Edge which only gets a 1.18 fTP bonus that's not a huge increase in damage. As well, the gear you use, depending on your ws set, could have more accuracy than your tp set and thus not need the accuracy from SA/TA. Whereas your tp set will benefit from 100% accuracy on an unstacked SA/TA.

It really is a judgement call though. If your tp gain and timers line up perfectly, then stack them, it doesn't hurt. But there's little reason to wait 10-15s on timers to do so. There are times I gain tp in 15s and times it takes closer to 30s. There are times a colibri takes tp from me 3 times in a row and SA/TA is just sitting there.

[Chen]

how does cuch mantle not make the list? (assuming you've counted it, as cuch belt was listed)

surely cuch > amemet+1 (and most/all others)?