Applying Tailored Mathematics to recreational gaming

 “How to Maximize Sa/Ta Damage

Sorry for anyone who was waiting for this to be finished. It took longer than expected, work and life and all that. Plus I ran into some snags with excel. Looking at the excel I made it looks pretty professional, but I really am by far not an expert at it. I also heavily underestimated this task I’d set for myself. I really, really did not enjoy writing this. Yet it was something I felt I needed to finish. Big thanks go out to Kornemuz from Asura and Ceiyne from Bahamut, for helping me figure out ‘if functions.’ I’d like to credit Releena of Seraph and Searain of Garuda, as well as the KI Thief Forums for providing a lot of the basis for this.

Ready for (another) ridiculous wall-of-text? Good.

For those who want to cut the crap and see conclusions,
-Summary, Formula, Conclusions, Stats, Rankings (link)
-Stat Comparison
-Gear Comparison

For those who want an in-depth reading,
In-Depth Explanation (link)
-Background Info
-Test Settings
-Explanation, w/out math
-In Closing,

Download the Excel Spreadsheets here: 
(1), (2), (3), (4)
(math has been reworked; above files not current)


Relative Stat Values
(updated Sep.25th, 2009)
I used my formula and an adapted excel spreadsheet to find the ultimate SA set for the given settings, including double march, haste spell, and 20% in TP set haste. Then I found the raw damage increase from adding a single point of the following given stats. Using a single point of Double-Attack as the standard of comparison, the following ratios were found.
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.)
1Slow(1xMarch,Haste) = -2.22 (d.a.)
1Slow(NoMarch,Haste) = -1.84 (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.)

1Dbl.Atk = 1
1TripleAtk = 2.51 (d.a.)
1Agi = 3.35 (d.a.)
1Dex = 0.39 (d.a.)
1Str = 1.29 (d.a.)
1Attack = 1.26 (d.a.)
1Slow(2xMarch,Haste) = -3.50 (d.a.)
1Slow(1xMarch,Haste) = -2.88 (d.a.)
1Slow(NoMarch,Haste) = -2.43 (d.a.)
1D.Wield(2xMarch,Haste) = 2.59 (d.a.)
1Haste(2xMarch,Haste) = 3.50(d.a.)
1Haste(1xMarch,Haste) = 2.89 (d.a.)
1Haste(NoMarch,Haste) = 2.43 (d.a.)

I wasn’t originally going to search for stat ratios, but now I’m glad I did. It’s probably the easiest and most effective way that players can use the data I’ve got here. I chose double attack as the base, with a value of 1, because it improved damage by the smallest amount (without negating).

We can draw some interesting and important knowledge from these ratios. For example, a single point of haste is, as probably expected, the most important stat in a double-march/haste-spell setting. But we can see it’s not very far ahead of Dex in importance. Intuitively we could predict that haste would be much less more important in lower-haste situations, but I did the math anyway. Just by removing the lesser march, 1dex is now more important than 1haste.

It’s also interesting to see how 1 single pt of attack does almost as much as 1str. This is due to the high base damage of SA/TA’s, and the corresponding lack of importance of fStr. Also interesting is how a single unit of Str and Atk do more for sa/ta than double attack. I did not expect this, and it also means that by these numbers Brutal Earring would be obsolete, Pixie and Merman’s earring being superior. Also from this, we can get that for SA, 2Str and 2Atk are roughly almost = to 1Dex. These numbers also confirm suppanomimi as being a superior choice for Sa, easily trumping Pixie and other options. Also it may be interesting to see that 1 triple attack is easily more valuable t han 2 double attack. This is because, since double attack proc is assumed to check before triple attack, adding double attack essentially nerfs some of our triple attack potential. Meanwhile, we can say generally that 3 pts of Dex and 5 pts of Slow roughly cancel each other out.

For TA, I’m a bit surprised at the difference. I’m fairly surprised that Agi is so high up in the ratios, even though I know one reason why it is the case. And that is because of the AF+1 hands’ +15% agi bonus effect. But it’s still quite a bit high. Str and attack are skewed farther apart for TA, and the benefit of attack is surprisingly low–less than the benefit of a single point of double attack in this case. (Looking further into the reason of the low attack benefit value, I found that it’s due to pDif tier. Before an atk/def ratio of 0.833, attack gives significantly less of a boost to pDif than after 0.833, at least until nearing the pDif cap). Slow and haste show similar value relationships for TA as for SA, though.

Relative Rankings, by Gear
The following gear comparisons have been made via the statistical ratios shown above.  Slow/Haste values used are for double-march.
(updated Sep.25th, 2009)

(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) > DH nq (27.38) = Skadi (26.59) > Anatares Harness (20.64) > Enkidu’s Harness (17.9) > 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)

(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) > Enkidu’s Harness (35.8) > 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)

edit: *Movement Speed*
I’ve been criticized (constructively) quite a few times, or bafflingly questioned at my prescription for Striders/Skadi for sa/ta, or for my hating of dusk.  Since I can’t quantify the benefit of these foot pieces, I’ve taken them out of the table above.  But I stand by my stance that:

Strider Boots / Skadi’s Jambeaux are, essentially, the best Sa/Ta feet you can wear at almost all times.
Suppanomimi likewise seemed quite counterintuitive for Sa, and yet it easily comes out as the top ear piece.  And people have been questioning my use of it for years.  Quantify it and people will be convinced.  It’s too bad these pieces can’t be quantified in though.  I am willing to admit though, that if you can’t see how these would help you at all for Thf, you may just not be playing the job to its max potential.  These will only help people who already understand how movement speed will affect your play.  And similarly, dusk shouldn’t ever be used for sa/ta for the very same reasons (this is coming from someone who used dusk himself for years before switching).

Playing around with the spreadsheet, I also spotted a few interesting things. I’d wondered sometimes if the slow on heca+1 made it so that the NQ heca was actually better than the HQ for sa/ta. It doesn’t seem so; HQ still appears to be better. I also found it interesting that Dusk NQ was better than Heca+1 with double march. This is probably counter-intuitive to what most people would think. This doesn’t mean, however, that homam hands are better than heca+1; it’s the attack that helps push dusk ahead. Either way, this is anecdotal and unimportant, since dusk slows down movement speed and therefore I wouldn’t use it for sa/ta anyway. So I’ve italicized it to point out that it’s arbitrary, same with Skadi and Striders since conversely they trump all.

Some of this stuff ran counter to what I’d expect as well. The idea of an adroit/hollow doing as much as a coral earring or brutal feels a bit odd. I find the back pieces interesting, since Cerb+1 is rare and thought to be the end all be all of backs, and nobody goes out of their way to buy a Charger’s. But I remember in a thread long ago I was discussing how I thought that Chrarger’s was the best. Seems so, but I was surprised to find AF2 so low in the rankings, even below commander’s which is kind of funny.

Shocking is how Love Torque is virtually equal to justice torque which is also virtual equal to agile gorget and barely above tiger stole, for TA. It goes in that order, but the numbers are pretty close. I find it interesting that Genin Earring came decisively above brutal for ta, as did even drone. I’d been under the impression that both were very ‘lol’ compared to brutal (for ta) for a long time. Meanwhile, while coral/merman’s more closely rivaled brutal for SA, brutal seems to come ahead for TA given the difference in pDif tier. Also, I was going to include Rapp vs Denali for TA in the spreadsheet but it became obvious that denali destroyed it, so it wasn’t worth looking much further into. Unlike for SA, Skadi decisively won over DH nq for TA. DH nq came barely above antares harness though, which was shocking to me given that it was a comparison of 10 attack versus only 2 agi. Again, that lower pDif tier makes a very big difference. For backpieces for TA, the values came out differently. Again due to pDif tier, Cerb+1 pulled ahead of charger’s. The rest of the back pieces came pretty close together, with commander’s surprisingly above Amemet+1 in this case. For waists, swordbelt+1 came out high, but this was because in my comparison, it’d just breached the pDif tier. So it seems that tier may be skewing the results a bit. Perhaps most shocking of all was the leg pieces for ta. Hideous dusk came out on top (though it technically can’t due to the decreased movement speed). Surprisingly barbarossa’s was equivalent to af pants, and this gave a bigger boost even than heca nq, which funny enough was ahead of heca hq. This has to do with the attack value not really overcoming the slow value on the piece.

Formula Breakdown
Sa/Ta “Act” Dmg =

(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

In-Depth Explanation

The purpose of this inquiry is to help people choose which stats and gear to use for unstacked SA / TA.

What’s best for SA/TA: dex/agi, attack, or haste? Do str and slow herein matter much either? Just like everything else in FF, the answers to give are not so easy because the game is situational. All of these elements and more play roles in sa/ta effectiveness. Sometimes it’s almost impossible to say what’s better/worse generally. Denali or skadi head for ta? Rapp or DH? Heca+1 hands or enkidu’s? Many options come really close.

In order to answer this question I chose to make an excel document ((1), (2), (3), (4)) (these files are outdated as of 9-25-09) which ranks gear sets based on the formula that I crafted. I’m not an excel expert so I didn’t include everything thief can/might equip. Instead I wanted to create a spreasheet of the equips that I thought were best.

Things to consider:
-Mob Target
-The quality of your other SA/TA gear
-The quality of your TP gear (yes, even this)

From these settings you will find pDif, crit pDif, hit rate, crit rate, fStr, and delay for both SA and TP equip sets. Also important will be double and triple attack rate, but these are constants for our mathematical adventure. All of these elements will go into our formula.

These values all have a huge effect on the answer of “what sa/ta gear is optimal.” The equip set that works best for the person who’s eating meat with double march vs trolls and has a really shotty TP set is not the same set that works best for the person farming inner sea with one march, no food, and fantastic TP gear.

Given how hard it is just tell everyone what gear to use, I’ll limit my aims instead. So my aims are:
1. To use my own stats and gear so I can at least know how to best gear myself,
2. To use the standard “merit settings” ruler that people are familiar with, so I can gear myself optimally in at least one situation,
3. To thusly try to work out the “best of the best” for SA/TA sets,
4. In conclusion, to rank stat options based on these specific example settings,
5. In conclusion, to rank gear options based on these specific example settings,
6. To offer some closing prescriptive advice.

Background Info
About a year ago there was a really nice thread on the KI Thief Forums as well as a followup thread on Allah’ about this subject. Slightly before that time Releena of Seraph also began looking into this subject. In the thread, some people stated that they really didn’t switch out of TP gear at all, or at least not the pieces with haste on them. Others were appalled by this counterintuitivity, but yet others could see the merit behind these ideas given the growing haste-worship in ‘XI these days. The thread died on a rather unfinished note, not quite fulfilling the nagging desires of people wanting to know for sure what to equip. This was frustrating, as it’s generally much easier to say what we should equip in most other situations.

Sa/Ta gear concerns didn’t begin just there though. People’ve been wondering about this for years. Some people don’t swap. Some go very heavy on dex/agi while others go heavy on attack. Some balance between attributes/attack. Others balance in haste vs slow as well. Some, like myself, have been questioned before over seemingly odd gear choices, i.e. that I sa/ta in striders and suppanomimi.

The debate used to be mainly dex/agi vs attack. Then after awhile it was found how awesome haste was and haste stacking became more common, so this became a concern. Then, prompted by some of Kirschy‘s haste research, Releena covered in in her LJ entry that slow5 was =/= (not) -%haste. Actually, once again it has been confirmed (by Krischy) that gear slow% is actually -haste%. This is not the case for magic slow, which is actually a separate function.

For those that don’t understand why it’s difficult to calculate what’s best, I suppose I could say a little more. Dex/Agi are great, but as you stack more the marginal gains are less and less. Dex/Agi is chiefly what you’re looking to improve upon, but sometimes there’s a choice between a mediocre amount of dex/agi and a lot of attack. A good example of this is AF2 cape (4dex/4agi) vs AmemetMantle+1, a question we’ve seen on the Thf forums a few times in the past. Further, attack also decreases in benefit as you add more of it. Also sa/ta are criticals, which make attack less important than if they were non-critical melee strikes. As for haste and slow, the haste/slow you have on at the time you sa/ta affects the delay until your next attack round. The difference in added delay often means the loss of an extra melee attack before the mob dies, which would generate damage as well as TP.

Test Settings
So I mentioned earlier that very specific settings would have to be chosen for any sort of comparison. Here are the settings used:
-75 Mithra Thf/Nin
-5Str Merits and merits capped otherwise

SA Set
Bomb Core
–head unchosen–
Love Torque
Brutal Earring
–ear2 unchosen–
–body unchosen–
–hands unchosen–

Rajas Ring
Any +5Dex Ring
Cerberus Mantle +1
–waist unchosen–
–legs unchosen–

Strider Boots

Variable equips chosen for my excel spreadsheet comparison:
(head) Walahra Turban, Hecatomb Cap +1, Skadi’s Visor, Maat’s Cap, Gnadbhod’s Helm
(ear2) Suppanomimi, Pixie Earring
(body) Dragon Harness +1, Rapparee Harness
(hands) Dusk Gloves +1, Hecatomb Mittens +1, ANNM Dragon Mittens (7dex,2atk), Enkidu’s Mittens
(waist) Cuchulain’s Belt, Speed Belt, Swift Belt
(legs) Barbarossa’s Zerechs, Enkidu’s Subligar, Hecatomb Subligar +1, Homam Cosciales

TA Set
Bomb Core
–head unchosen–
Hope Torque
–ear2 unchosen–
Denali Jacket
Any +5Agi Ring
Any +5Agi Ring
Cerberus Mantle +1
–waist unchosen–
–legs unchosen–

Strider Boots

Variable equips chosen for my excel spreadsheet comparison:
(head) Maat’s Cap, Denali Bonnet, Skadi’s Visor, Walahra Turban
(ear2) Genin Earring, Brutal Earring, Merman’s
(waist) Speed Belt, Swordbelt+1, Scouter’s Rope
(legs) Barbarossa’s Zerechs, War Brais +1, Hecatomb Subligar +1

TP Set
Fire Bomblet
Walahra Turban
Love Torque
Brutal Earring
ACP Body (10acc,3%DW)
Homam Manopolas
Rajas Ring
Toreador’s Ring
Cerberus Mantle +1
Speed Belt
Homam Cosciales
Homam Gambieras

-Lvl82G.Colibri w/ totDef327 and totEva339
-No food
-Double March & Haste (Spell)
-Madrigal-level accuracy buff
(this could also be viewed as close to Hunter’s Roll, Crab Sushi, or other Sushi)

Next, we must have a formula that can accurately describe the real damage contributed by the action of an sa/ta. Base game mechanics can be found on wiki, but applied math such as this is something for freelancing. I had to think for a little while while on what formula I should use, what elements to include, and how to calculate the various elements. A lot goes into it that would probably not occur to most people, and even then the formula is still not perfect but is merely a best (though probably pretty good) attempt. If I hadn’t participated in forums so much in the past years, my making of this formula would not have been possible.

Here’s what it is. I’ll start simple and then expand it more to show more detail.
Actual SA/TA “act” damage=

(SA/TA round Dmg) – (TP round opportunity cost)
(Initial Critical Hit)+(Extra Swings) – (dDelay Function)*(TP round Dmg)
{(Mainhand +fStr’a +Dex/Agi)*(pDif’a +1) + [(Mainhand +fStr’a)*Dbl./TripleAttacks + (Offhand + fStr’a)*(1 + Dbl./TripleAttacks)]*(pDif’a function)}
– ((delayTP – delaySA)/delayTP)*(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
The above formula should suffice for showing all of the special elements that go into solving this. But for anyone who craves more detail, then the following is one way of showing most of the constants and variables that go into the calculation.

Actual SA/TA “act” damage =

{(39 +(totStr’a-67)/4 +totDex/Agi))
*(Atk’a/327def – 0.35cRatio)
->[IF(0.833 < a/d cRatio’a < 1.25),THEN(pDif’aAvg=(2.4*a/dcRatio’a -0.5)/2) ELSE etc..]
[((39 +(totStr’a-67)/4)*0.24 + (34 +(totStr’a-67)/4)*(1 + 0.24)]
*{IF((9 + (totDex – 20 -67)/2) > 24,Crit’a=24%, ELSE Crit’a=(9 + ( – 20 -67)/2)%)}
*[IF(0.833 < a/d cRatio’a < 1.25),THEN(CritpDif’aAvg=(2.4*a/dcRatio’a -0.5)/2)+1, ELSE etc..]
(1 – Crit’a)
*[IF(0.833 < a/d cRatio’a < 1.25),THEN(CritpDif’aAvg=(2.4*a/dcRatio’a -0.5)/2)+1, ELSE etc..]

((b.Delay*0.77dw*0.45haste – b.Delay*%dw*[%haste -%slow])/b.Delay*0.77dw*0.45haste )
[(39 + 34 +2(totStr’b-67)/4)
*{(381atk/327def – 0.35cRatio) -> [IF(0.5 < a/d cRatio’b < 0.833),THEN(pDif’bAvg+1=(1.2*a/dcRatio’b +0.5)/2 +1)}
+ 87%nonCrit’b
*{(381atk/327def – 0.35cRatio) -> [IF(0.5 < a/d cRatio’b < 0.833),THEN(pDif’bAvg=(1.2*a/dcRatio’b +0.5)/2)}
*1.24 d.a./t.a.Procs
*94.5 acc%

(the above is for SA. TA formula was slightly different, including the +15% agi bonus from af+1)

-This test doesn’t account for TP gained
-Nor how that TP might be used to contribute damage
-Does not account for the probability of meleeing in your sa/ta set for more than 1 melee round
-Of course, the test settings are rigid in that they assume only 1 mob of 1 given level, do not account for frequency of buffs or possible debuffs (dia/angon/feint/etc), and the equips chosen for settings are high-end.
-There are a couple errors in truncation steps, but they’re not very serious
-X’s Knife crit boost not taken into account. Relic 3xProc not taken into account
-Assumptions are made as to the mechanics of crit rate
-fStr is not truncated; I’m listing this here because some would view this as problematic. However, it actually isn’t since it allows for broader comparisons
-Hard min and Hard cap values are not set for pDif functions, but in reality we’re not herein concerned about these situations either

Understanding Actual SA/TA Damage, an Explanation for Non-robots
SA/TA produce spike damage. However, the attack round usually produces higher delay so some delay is lost. How do we find the damage lost due to that delay loss? Well, what would have happened during that delay?

I mean, if I SA and then it takes 6 seconds for my next attack round because SA slowed me down, and if my normal rounds of TP only take 3 seconds each, then what have I lost? Well, if I hadn’t switched to an SA set my delay would have been 3 seconds. So I lost 3 seconds. That means I lost a round of melee strikes in my TP set. So I just multiply the amount of delay lost (in this case enough for 1 round of attacks) by the damage dealt on average from my TP set.

What goes into calculating SA dmg and TP round dmg? A lot and a little. For SA, the SA big crit dmg = mainhand weapon dmg + fStr + total Dex. Also accuracy will be 100% in this case. Other little known fact, but every attack in that melee round will be 100% accuracy, including your offhand hit, or any double or triple attack procs that might go off on either hand during the SA attack round. Of course, these extra attacks are also modded by the same pDif that modified the big SA crit. And some of those additional hits may critical as well, so crit rate needs to be factored in. So this is all calculated and summed together as our “SA attack round Dmg.”

We the need to find TP round dmg. Since the variables in our formula will only be for our SA round, these values are all constants. To find TP round dmg we simply use base damage and multiply against pDif, crit, multi procs, and accuracy. Base damage is the base damage of the weapons + fStr. pDif is of course a function of player attack over mob defense. Crits are just pDif+1. But we also must factor in crit rate. Multi procs are just our triple attacks and brutal double attacks. Accuracy is accuracy.

So the big three are finding out (1) how much dmg our SA and it’s attack round do, (2) find out how much dmg our TP set does in a single round, and (3) find out what % of an attack round we’ve lost as a function of SA set delay and TP set delay. Multiply TP/round dmg against the delay function, and subtract that from the damage dealt in our single SA attack round, and we have our answer as to how much dmg we /actually gain/ by doing a Sneak Attack. Same thing goes for Trick Attack of course, only we use Agi instead of Dex as our primary attribute of course.

New Assumptions for Calculating Crit Rate
All the mechanics that go into this are already solidly accepted as true represenations of how the dmg is calculated in FFXI–with the exception of crit rate. For crit rate I used data on this very helpful article by Searain of Garuda. Based on the data in that thread and elsewhere, it seemed to me that the cap for melee crit rate is likely the assumed number of 50-points-of-dex above a target’s agi. There’s also a supposed “placebo region” where if you don’t achieve a certain level of dex above the targets agi, adding dex will not increase crit rate. For this test and for my own future reference, I’ve assumed this placebo region to be any point below 20-points-of-dex above a target’s agi. That is, if a target’s agi is 100 and your dex is 119, you will have the same floored crit rate as if you had 0dex. This leaves a spread between 20 and 50 points-of-dex above a target’s agi to account for the spread of 5%-20% floored/capped critical hit rate (or 9%-24% if fully merited). I stumbled into this accidentally but it turns out to be convenient that the spread of dex-agi for the area of efficacy is 30 points, and the spread of crit% is 15 points. So, we have an easy ratio of 2dex=1%crit or 1dex=0.5%crit. It’s my belief that this or something close to it is a correct representation of crit mechanics. I drew my assumptions based on looking for trends in Searain’s data, as well as additional anecdotal evidence seen elsewhere.

In Closing
I can honestly say that throughout most of my working on this, I did not enjoy it. Not in the least. I had the idea of finding the formula for showing actual marginal sa/ta damage, and adapting it, but I hadn’t predicted the amount of work that that would entail. So, some closing comments/conclusions:
*Suppanomimi is essential and trumps all for /nin sa/ta.
*Brutal earring isn’t king for sa/ta; In fact it can be easily outdone.
*The full haste idea for sa/ta does not produce the highest damage.
*Likewise, laziness and not swapping for sa/ta does decrease your damage output.
*Heca slow does make a difference, especially for TA, where you’re not gaining a real benefit from dex.
*Mid-range equips, with a combination of good stats, seem to be the best.
*It’s best to not follow any particular mantra when gearing, but look carefully at each option. The stat ratios laid out in the beginning can help out.
*I haven’t covered my stance on movement speed and sa/ta (striders/skadi > etc > dusk), but that can’t be gotten into with math.

I also have a feeling that the optimal sa/ta sets should cover a variety of situations. Given the way the stats work out, the relative values of haste, dex/agi, str, attack, etc, should hold nicely whether you’re farming low level mobs, fighting an HNM, are stacked with heavy buffs, or have no buffs on at all. Multiple, situational SA/TA sets is probably going to be excessive.

Now to find an ice pack for my head.

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