Cutting corners with Store TP and weapon skills

Edit: Another table appended.

Last week I referred to "minimum store TP" to achieve so-called n-hit builds from the standpoint of going from 0 to 100 TP in n hits or reaching 100 TP in n - 1 hits starting with sufficient TP return from the previous weapon skill, but practically speaking I should have called it "worst-case scenario store TP if you're using a multi-hit WS." With all the TP you'll get after the first hit (and when was the last time you saw only the first hit land when your WS didn't kill your target?), there aren't too many compelling reasons to maintain "true" store TP totals if it means using equipment you wouldn't touch otherwise. The question is how much store TP to drop while still maintaining a "virtual" n-hit.

As you might have guessed, you can turn to probability to answer this. Consider first the case of a 5-hit polearm with a 5-hit weapon skill. After calculating the probabilities for obtaining sufficient TP returns from a single WS (no need to present such clutter, but I hope I didn't screw up), we can see the relationship between dropping store TP and the lowered probability that you will be able to get 100 TP in n - 1 hits of the next TP-generating "cycle." Of course, these probability calculations are based on the assumption that DA can proc only twice on a multi-hit weapon skill (fewer than seven hits).

I am assuming 95% hit rate for the first WS hit. Since (lack of) accuracy does affect TP return, I thought it would be useful to show the effect of a lower hit rate.

Table 1. Probability of getting 100 TP in 4 hits (after a WS) for a 5-hit polearm (480 delay, 17% double attack rate)

Minimum hits after 1st WS hit	Store TP	95% hit rate		80% hit rate
0	54	.95		.95
1	53	.949996		.948865
1	52	.949996		.948865
2	51	.949677		.930353
2	50	.949677		.930353
3	49	.940513		.815681
3	48	.940513		.815681
4	47	.822485		.490462
4	46	.822485		.490462
5	45	.233998		.105841

You can see there is not much of a drop by shedding up to 6 store TP and still being pretty close to a true 5-hit. Remember that the first hit of a WS can still miss.

The probabilities shown are cumulative probabilities in the sense that, given some amount of store TP, what is the probability that I will be able to get 100 TP in 4 hits after a weapon skill? More specifically, given some amount of store TP, what is the least amount of hits I need to land to be able to get 100 TP in 4 hits with an acceptable probability? Remember that .95 is pretty much as good as it gets.

If you have 95% hit rate, 48 store TP gives you a 94% chance of generating 100 TP in 4 hits, requiring at least a 4-hit return from the previous WS (1st hit TP and TP from at least 3 other hits). If you have a "true" 5-hit build, shedding 6 store TP may be a good trade-off. For example, I've seen 5-hit polearm builds with 49 store TP (including merits), suggesting awareness that 54 store TP is rather superfluous.

If you have 80% hit rate, 48 store TP gives you a 82% chance of generating 100 TP in 4 hits, so you might want at least 50 store TP if being around 80% hit rate is more realistic for whatever you are doing.

This exercise can be repeated for both 6-hit polearm and 6-hit great axe.

Table 2. Probability of getting 100 TP in 5 hits (after a WS) for a 6-hit polearm (480 delay, 21% double attack rate)

Minimum hits after 1st WS hit	Store TP	95% hit rate		80% hit rate
0	29	.95		.95
1	28	.949996		.948948
1	27	.949996		.948948
2	26	.949705		.931688
3	25	.941320		.823837
3	24	.941320		.823837
4	23	.832807		.513000
5	22	.284425		.130744

29 store TP not all that easy to obtain as a warrior (maybe you want to use Aurum Cuirass), but 24 is possible with a bunch of ticky-tack pieces. 15 from /SAM, 5 from Rajas, 1 from Brutal, 1 from Chivalrous Chain, 1 from Ecphoria Ring, and 1 from Engetsuto gives 24 total. Then again, if you're spamming crab sushi, some of these may not be very optimal for Penta Thrust.

Table 3. Probability of getting 100 TP in 5 hits (after a WS) for a 6-hit great axe (504 delay, 21% double attack rate)

Minimum hits after 1st WS hit	Store TP	95% hit rate		80% hit rate
0	22	.95		.95
1	21	.948478		.923695
2	20	.889887		.702636
2	19	.889887		.702636
3	18	.034124		.017160

I have only 6 store TP on equipment for warrior anyway. I can live with 21 store TP if I actually am using /SAM for some reason. What about the likes of 6-hit scythe and 6-hit polearm, both with four-hit weapon skills (like Guillotine and Drakesbane)? The following table compares the minimum TP for a "true" 6-hit build to the minimum TP for a "virtual" 6-hit build.

Table 4. Minimum Store TP requirements for 6-hit builds with 4-hit weapon skills

		Minimum Store TP
Delay	Base TP	True	Virtual
528	14.4	16	14
513	13.9	21	18
501	13.6	23	20
492	13.3	26	23
480	13.0	29	26

With "virtual" store TP builds, the corresponding probability is .9449 given 95% hit rate. (Of course, lower hit rate will lower this probability.) If that .0051-difference in probability really troubles you and is unacceptable, by all means be hyper-conservative.

Dumb thread(s) of the day

Here's a new feature where I talk briefly about crappy replies to decent questions. It would be a lot easier just to take pot-shots all day at shitty FFXI forum threads, which I might just do rather than play with numbers all the time.

Apparently, there is a thread on BG discussing why Allakhazam is so maligned, which usually is done by repeatedly knocking down the straw man that anyone actively endorses TPing in STR or DEX rings. When talking about a signal-to-noise ratio, the noise component is rather substantial on Allakhazam but the signal is pretty small in absolute terms for any FFXI forum, really. Even BG has threads like this, where bald-faced assertions are made without referencing sources and people can say they get 8-hit Drakesbanes with a straight face.

As another example, if you were talking about the relative efficiency of a 6-hit polearm build, you would pretty much get the same content-free, inane answers whether you posited this question on Allakhazam or Blue Gartr. Apparently, it is so difficult to use an average auto-attack damage, use an average WS damage, estimate the time between weapon skills, and use all this information to estimate roughly the relative efficiency of a 6-hit build. (Hint: a 6-hit is not even close to being 20% more efficient than a 7-hit). Instead, you have a reasonable OP followed mostly by dumb-fuck snark and drivel.

A comparison of Fortitude Axe, Perdu Voulge, and Engetsuto for Greater Colibri

I thought this would be a fun exercise using properties of expectation (probability theory) to compare the performance of Fortitude Axe, Perdu Voulge, and Engetsuto on a level 82 Greater Colibri (67 VIT, 327 defense) in terms of (approximate) average ideal damage. My idea of "average ideal damage" is based on a so-called "cycle" of TP generation to reach 100 TP followed immediately by a weapon skill.

Why compare the expected damage resulting from a "cycle" of auto-attack damage and WS damage? While this implies an unattainable ideal (along with generally uncontrollable factors "in the field," such as Pecking Flurry and the like, it is practically impossible to WS as soon as possible and still get the maximum "realized" damage from that WS because of overkill), it is a concise representation of efficiency in the long run that includes damage from both auto-attack and WS "phases." Talking about the long run means considering the variability of auto-attack and weapon skill damage.

Some motivation: arguments based on a wall of arithmetic tend to be annoying. Those who present these walls of arithmetic seem to labor under the pretense of precision (why calculate anything if you don't want to be as precise you possibly can?) yet their lack of clarity obscures "typical" mistakes like using cRatio as a stand-in for pDIF. This obviously underestimates the relative effect of attack where percent changes are involved. Another example is adding or subtracting percent changes. While the propagation of error may be slight because percent changes tend to be based on values near 1, it's still error.

On the other hand, this kind of junk tends to be done in an off-hand manner for quick and dirty comparison of what's better (or worse), which is understandable. Yet where putatively non-trivial comparisons are concerned, why not answer the question of how much better (or worse)? This is what I attempt to do with a comparison of Fortitude Axe and Perdu Voulge by outlining the steps I take to make the necessary calculations.

As for the specific example, I wish to mount a counter-argument against the "hype" that Fortitude Axe and a polearm (Engetsuto being a typical polearm for warrior to use) are meaningfully superior to Perdu Voulge. To me it's not at all obvious that the increased WS frequency associated with Fortitude Axe should overcome the base damage discrepancy despite facile intuition-based arguments that are biased toward Fortitude.

But before starting, why not make some preliminary assumptions?

Some general assumptions

• 95% hit rate.
  
• Meat mithkabobs for great axes and crab sushi for Engetsuto (the latter to ensure 95% hit rate especially without merits and high-end accuracy equipment).
  
• 19% double attack rate. It is known that the explicitly named Double Attack trait "stacks" with the virtue weapon property. Therefore, it is possible to attack up to four times in a single round (supposedly).
  
• Sufficient TP to achieve 6 hits from 0 to 100 TP for all weapons (also considering the 7-hit case for the polearm).
• Assume sufficient TP return from a previous WS to be able to reach 100 TP in 5 hits (or 6 hits in the case of the polearm) for the single "cycle" described earlier. In the "long run," which is what expectation is all about in a sense, the extra hit needed to attain 100 TP to begin with makes a slight contribution to the expected value.
  
• Berserk active only. This is merely for my own convenience.
• fSTR 6 for TP, 11 for WS.
• Average pDIF based on assumption of symmetry of pDIF distribution, which seems to hold for cRatio above 1.5. This assumption ignores behavior of pDIF at the extremes.
  
• 18% critical hit rate. This is completely arbitrary and corresponds to some level of DEX that I choose not to specify at this time.
• WS damage always assumed to be at 100 TP. The expected TP per WS for Fortitude Axe would obviously be higher than that for Perdu Voulge (where damage or crit rate varies with TP). This may be worth keeping in mind.
  

Some of the jargon and terminology (pDIF, cRatio) is explained in this FFXIclopedia article and immediate links to other articles.

I will also explain briefly how I derive all the computations that follow and state any further assumptions, if not justify them due to lack of verification through data or resources/comments "officially" sanctioned by SE.

1. Expected number of attack rounds to 100 TP

Given 100% hit rate and 0% double attack trait, the expected number of attack rounds to 100 TP for Fortitude Axe is 3.5625 given sufficient TP return from the previous WS, compared to 5 for Perdu Voulge (obviously) and 6 for Engetsuto. The 3.5625 value can be computed using conditional expectation and can be verified through simulation.

Of course, I assumed 95% hit rate and 19% DA rate to begin with, so the expected values of the number of rounds to 100 TP are different. Here is a table for the expected number of attack rounds for some values of hit rate to give some sense of the trend. As one should expect, the rate of change of the number of attack rounds increases as hit rate decreases for any weapon.

Table 1. Expected number of attack rounds to 100 TP for various values of hit rate.

	Hit rate
Weapon	95%	90%	85%	80%
Fortitude Axe	3.259	3.423	3.606	3.812
Perdu Voulge/ Engetsuto (6 hit)	4.557	4.803	5.077	5.386
Engetsuto (7 hit)	5.442	5.736	6.066	6.437

2. Expected pDIF for auto-attacking and WS (including the effect of critical hits)

I am basing pDIF and fSTR values (fSTR values of 6 and 11 stated earlier) loosely on my own equipment but do not assert complete fidelity to that.

With Berserk, a Meat Mithkabob, and 18% critical hit rate, the attack ratings, cRatios, and expected pDIF are as follows for both auto-attack and WS. The pDIF without critical hit contributions is necessary for the WS damage calculations done in a later step.

Table 2. Computed values for obtaining expected pDIF

Weapon	Attack	cRatio	pDIF (no crit)	pDIF (w/ crit)
Fortitude Axe (auto-attack)	576	1.411	1.346	1.526
Fortitude Axe (WS)	595	1.469	1.381	1.561
Perdu Voulge (auto-attack)	596	1.472	1.383	1.563
Perdu Voulge (WS)	607	1.506	1.407	1.587
Engetsuto (auto-attack)	445	1.010	0.963	1.143
Engetsuto (WS)	468	1.081	1.047	1.227

3. Expected number of hits in a 3-hit and 5-hit WS

Double attack is known to process twice on multi-hit weapon skills for two-handed weapons, but is it possible to double attack three times (or more) where applicable? While this may be an unsatisfying explanation, given the only data set (for Penta Thrust TP return) I have actually seen that attempts to answer this question, it seems very unlikely that DA can proc three times or more. Therefore, based on common experience, DA can proc only two times on a WS.

(This issue could merit its own post at a later date. For now, you could review my comments on DA and multi-hit weapon skills under the "double attack" tag, one of which addresses the Penta Thrust data set just mentioned.)

Based on the above, it is possible to obtain the probability distribution for the number of hits in the 3-hit and 5-hit WS cases. Since the first hit of a WS can have a different fTP (gorget effects or intrinsic property) and therefore different damage than the successive hits, these probabilities must be broken out by whether the first hit occurs in order to computed the expected damage. The total number of hits for a n-hit weapon skill is described using the notation "x+y," where x = 0, 1 are for the first hit and y = 0, 1, ..., n + 1 are for the rest.

Table 3. Probabilities for the number of hits in a 3-hit WS with 19% DA

No. hits	Probability
0+0	.0000919133
0+1	.0035232531
0+2	.0343440735
0+3	.0111244407
0+4	.0009163196
1+0	.0017463527
1+1	.0669418089
1+2	.6525373956
1+3	.2113643724
1+4	.0174100715

Table 4. Probabilities for the number of hits in a 5-hit WS with 19% DA

No. hits	Probability
0+0	.0000002099
0+1	.0000160425
0+2	.0004616123
0+3	.0059589813
0+4	.0299088222
0+5	.0123274910
0+6	.0013268409
1+0	.0000039875
1+1	.0003048071
1+2	.0087706328
1+3	.1132206449
1+4	.5682676222
1+5	.2342223291
1+6	.0252099764

4. Expected WS damage for King's Justice and Penta Thrust

I chose these weapon skills because neither can crit and I'm not sure what the critical hit rate for Raging Rush is at 100 TP. The properties of the alleged "damage spike" of King's Justice are not well known, so I do not account for this in the calculations.

Again, it is assumed that weapon skill damage is based on 100 TP. While this is an unrealistic assumption given the presence of double attack, it may be worth keeping in mind.

For the "effective" base damage for King's Justice, I used D + 11 + 42 = D + 53, where D is the base damage of the great axe. Here, the first hit is under the effect of an appropriate "sea" gorget (+0.1 fTP). For Penta Thrust, I used D + 11 + 32 = D + 43 and did not incorporate a gorget effect, but multiplied the damage by 1.25 to account for the piercing bonus on Colibri.

Table 5. WS damage (King's Justice for great axe, Penta Thrust for polearm) by hit

	Before pDIF		After pDIF
Weapon	1st hit	others	1st hit	others
Fortitude Axe	128	117	176.863	161.664
Perdu Voulge	163	149	229.426	209.721
Engetsuto	160	160	167.588	167.588

Finally, we can calculate the expected WS damage based on the probability distributions in part 3:

Table 6. Expected WS damage

Weapon	Damage
Fortitude Axe	521.256
Perdu Voulge	676.195
Engetsuto	856.547

5. Expected number of auto-attack hits per "cycle"

The expected number of rounds to 100 TP (with TP return from the previous WS) is related to the frequency of WS while the expected number of auto-attack hits to 100 TP (also with TP return from the previous WS) corresponds to the damage dealt during the auto-attack phase. Using conditional expectation, the number of hits to 100 TP is summarized as follows:

Table 7. Expected number of auto-attack hits to 100 TP for various values of hit rate

	Hit rate
Weapon	95%	90%	85%	80%
Fortitude Axe	5.527	5.499	5.472	5.444
Perdu Voulge/ Engetsuto (6 hit)	5.151	5.143	5.135	5.127
Engetsuto (7 hit)	6.151	6.143	6.135	6.127

Unlike the expected number of rounds to 100 TP, which approaches infinity as hit rate tends to zero, the expected number of hits to 100 TP approaches 5 for a 6-hit setup and 6 for a 7-hit setup as hit rate tends to zero. It is easy to see that TP for WS often exceeds 100 for Fortitude Axe.

6. Expected total damage per "cycle" (auto-attack and weapon skill damage)

Finally, by combining the results of steps 1-5, I obtain the expected total damage per "cycle" of auto-attack damage that concludes with WS use immediately upon attaining 100 TP.

Table 8. Expected total damage per "cycle"

Weapon	Auto-attack	Weapon skill	Total in cycle
Fortitude Axe	590.767	521.256	1117.073
Perdu Voulge	821.619	676.195	1497.815
Engetsuto (6-hit)	669.821	856.547	1526.368
Engetsuto (7-hit)	799.837	856.547	1656.384

Total damage per cycle is a rate of damage. However, the duration of the cycle is different for each of these cases. To compare the efficiency of each of these, it is easier to convert damage per cycle into a damage per unit time.

At this point it I should see if these calculations do not flagrantly disagree with parsing of merit parties with both Fortitude Axe and Engetsuto. Informally speaking:

"REALITY" CHECK with Fortitude Axe:

• Auto-attack damage: The expected damage in this exercise is 106.8817 and accounts for critical hits. From a short merit party (27 mobs), I have an average damage of 126.069 without Dia II (174 hits). However, this party had 2x Minuet for what it's worth.
  
• Weapon skill damage: The sample mean of King's Justice damage (12 attempts) was 662.50. The expected value is 521.256 and the standard deviation is just under 102. Since the sample mean is approximately normal for sample size 12 (I checked this with simulation), it is obvious that 662.50 is not at all consistent with the estimated mean. Then again, a mere ~100-attack increase from 2x Minuet would raise the expected value to 652.810. This doesn't account for the alleged spikes in KJ damage.
  
• Auto-attack damage as a proportion of total damage: The expected proportion for Fortitude Axe is .5289, which compares favorably with the observed proportion of .5326.
• CONCLUSION: The calculations so far seem reasonable. There is no compelling reason to question the validity of the calculations.
  

"REALITY" CHECK with Engetsuto:

• Auto-attack damage: The expected damage in this exercise is 130.019 and accounts for critical hits. From a short merit party (128 mobs), I have an average damage of 178.6634 without Dia II (621 hits). Adding 100 more attack (approximating the effect of 2x Minuet) brings the expected damage up to 167.212, which is still lower than the observed. (Remember that I've been assuming Berserk always active.)
  
• Weapon skill damage: The sample mean of Penta Thrust damage (84 attempts) was 984.61. The expected value is 856.547 and the standard deviation is about 122.39. An additional 100 attack increases the expected value to 1046.136 and standard deviation to 153.
  
• Auto-attack damage as a proportion of total damage: The expected proportion for Engetsuto is .4829, which is a bit lower than the observed .5327.
  
• CONCLUSION: There don't appear to be any egregious discrepancies...

(I note that the Perdu Voulge latent bonuses are inactive above 100 TP but do not account for this in the calculations.)

7. How long is a "cycle"?

The answer is based on the expected number of attack rounds to 100 TP, which was computed in step 1.

Without any delay reduction whatsoever, and letting the first attack round occur at x delay after 0 delay, where x is the delay of the weapon of interest, one can approximate the time duration (in seconds) of the cycle by using the conversion 60 delay = 1 second.

Table 9. Cycle duration in terms of delay and seconds

Weapon	Delay	Time (s)
Fortitude Axe	1643	27.38
Perdu Voulge	2297	38.28
Engetsuto (6 hit)	2187	36.46
Engetsuto (7 hit)	2612	43.53

Finally, damage per second for a single cycle can be computed from the results of step 6 and the current step.

Table 10. Damage per second in a single cycle

Weapon	DPS
Fortitude Axe	40.614
Perdu Voulge	39.129
Engetsuto (6 hit)	41.868
Engetsuto (7 hit)	38.049

After all that work, it turns out that Fortitude Axe does edge Perdu Voulge. It is worth mentioning that I tried to minimize any rounding except where called for by game mechanics. Intuitively speaking, the effect of excess TP above 100 will have a very minor effect on these DPS values, but for the sake of comprehensiveness, excess TP can be considered in section 8.

No combat skill merits are considered for the polearm cases. With that in mind, it seems futile to use polearm on Colibri without spamming crab sushi to achieve capped hit rate (or getting a Madrigal). Without meat mithkabobs and the high hit rate, the piercing bonus can't overcome the attack deficit.

8. Can we account for the excess TP beyond 100 that contributes to WS damage?

This is a bit troublesome because I have been assuming "sufficient TP return from the previous WS to get to 100 TP in x number of hits." Actually, I can calculate expected TP return from the results of step 3, assuming the minimum Store TP for a "true" n-hit build.

Table 11. Expected TP return from a weapon skill (5-hit polearm WS, 3-hit great axe WS)

Enough Store TP for a ...	TP return
Great axe 6-hit (504 delay)	18.487
Polearm 6-hit (480 delay)	20.8582
Polearm 7-hit (480 delay)	18.1621

From here on, excess TP is relevant only for King's Justice.

One way to think about this problem is conditioning the expected number of hits beyond 100 TP on the previous number of hits attained (before 100 TP). Unfortunately, I do not see an easy way to calculate, say, the probability that the previous number of hits is 3. It is just easier to estimate the expected TP per WS by simulation of the required probabilities. Note that there will be excess TP even in the case of only 5 hits to 100, based on the expected TP return.

Table 12. Estimated probabilities of obtaining excess TP over 100 TP

Weapon	+1.9 TP	+18.6 TP	+35.3 TP	+52.0 TP
Fortitude Axe	.5795	.3239	.0883	.0083
Perdu Voulge	.848	.152	N/A	N/A

The expected King's Justice TP, fTP values, and WS damage (applicable only to the first hit) are as follows. (I assumed linearity of the fTP function with TP between 1.0 and 1.25.)

Table 13. Estimated expected TP and fTP for King's Justice (with sea gorget effect)

Weapon	Estimated expected TP	Est. fTP (1st hit)	Est. damage (1st hit)
Fortitude Axe	110.7612	1.126903	182.1795846
Perdu Voulge	104.5254	1.1113135	233.0656868

Recall that the expected damage on the first hit at exactly 100 TP was 176.863 for Fortitude Axe and 229.426 with the Perdu Voulge.

After all the intermediate calculations (results not shown), the updated DPS values for the great axes are obtained.

Table 14. Damage per second in a single cycle accounting for excess TP above 100

Weapon	DPS
Fortitude Axe	40.800
Perdu Voulge	39.219

The difference still favors Fortitude Axe, but again, it is slight. People seem to like percent changes, so it's about 3.194% better.

9. Why exactly are polearm and Fortitude Axe played up for Greater Colibri?

Good question, considering the inconvenience of farming virtue stones (even though soloing xzomits is simple). Using a weapon with inferior combat skill is also pretty inconvenient when you have a A+ weapon with 8/8 combat merits. In my own experience, I never felt that Fortitude Axe was that much better than Perdu Voulge, but "all things being equal" rarely applies when experience is discussed.

As for an informal argument as to why Fortitude Axe might be superior, here seem to be the main points, with rudimentary supporting calculations that someone might perform for a forum post:

• "Fortitude Axe provides 50% more damage, going from 0% DA to 50% DA, compared to a featureless 64-damage, 504-delay great axe." Of course, no warrior has 0% DA. In the presence of 19% DA, Fortitude Axe's WS frequency is expected to be about 1.40 times that of a generic great axe (based on time per cycle).
• "The double attack property of Fortitude Axe compensates for the low base damage." This is not really a self-evident statement. A 32-point difference in base damage from 64 to 96, given 11 fSTR, is approximately a 43% increase in damage. Yet from the standpoint of damage in the auto-attack phase, Fortitude Axe is still better roughly by about [(70*5.527/27.38)/(102*5.151/38.28) - 1]*100 = 2.941%, ignoring attack differences.
• From the standpoint of WS damage per unit time, where virtue weapon DA does not apply, Fortitude Axe is better by about [117/27.38/(149/38.28) - 1]*100 = 9.781%, again ignoring attack differences.
  
• A naive person would incorrectly add these percent changes, but in reality the calculation of difference is more like [(70*5.527+117*3.135)/27.38/(102*5.151+149*3.135)*38.28 - 1]*100 = 6.160% in favor of Fortitude Axe, yet again ignoring attack differences. (3.135 is the expected number of hits of a 3-hit WS.) This should not be counter-intuitive because TP damage is slightly more influential than WS damage.
  

Practically speaking, the percent difference is closer to 3.194% in favor of Fortitude because attack differences still exist, even for Greater Colibri.

As for polearms, I can see where it can be pretty effective with sufficient Store TP for a 6-hit, appropriate support, and meat mithkabobs. I wouldn't say it's particularly efficient or easy to implement though.

10. Conclusion

Fortitude Axe is better than Perdu Blade "on paper" against a Greater Colibri by about 1.04 damage/second or, in terms of percent difference, about 3.194%.

If you had polearm merits and enough accuracy (whether from equipment or a Madrigal), a combination of polearm and meat mithkabob spamming could be more "efficient" (more so for 6-hit) if your idea of efficiency is wasting a bard song on Madrigal or spending millions on the scarce accuracy equipment (basically Toreador's Rings or Sniper Rings +1 and Cuchulain's Mantle) to eke out more accuracy. Without sufficient accuracy and support though, meriting with polearm seems to be a waste of time.

Tomahawk for dummies

(Motivation for entry: Not surprised that Tomahawk properties are not well known among those who actually use warrior, which makes sense because those who play up warrior are mostly oblivious shit-for-brains who take pride in playing a one-trick pony. Also, this will be the last of my filler posts for a while—until well after the July version update if at all—as I am scraping the bottom of the barrel for new things to talk b.s. about.)

The in-game descriptions of abilities and traits are renowned for their clarity, specificity, and transparency, and that for Tomahawk, a Group 2 warrior ability, is no exception.

Tomahawk "expends a throwing tomahawk to inflict a special defense down effect on an enemy," with "special defense down" being understood as a temporary reduction of any "direct" damage mitigation properties the enemy may have. Note that this is different from defense rating. For example, any blunt damage on slimes is reduced by 3/4, to 1/4 of the full physical damage, and Tomahawk reduces this 3/4 factor by some amount. Similarly, any magic damage on ahrimans is reduced by 1/4, to 3/4 of full magic damage), with Tomahawk reducing this 1/4 factor by some amount.

According to the wiki.fo.jp article entry, Tomahawk provides a 25-percent reduction of the direct damage mitigation factor. This seems to make sense given experiences with Tomahawk in SE Apollyon, where mobs have low defense ratings but immunity to a specific damage type that seems to be "damage taken -100%," to use the in-game descriptions of damage-reduction properties, yet Tomahawk does not remove the "immunity" completely.

Similarly, elementals in Temenos apparently exhibit a 25% reduction in physical and magic damage, which itself is reduced to 18.75% in the presence of the Tomahawk effect. Consequently, the observed percent increase in damage is only 8.33%.

Finally, Jailer of Temperance is yet another example of Tomahawk having some effect. Given that Tomahawk (supposedly) works on the likes of Ouryu ("Ouryu Cometh"), which normally takes a 50% cut to magic damage, it would have been very helpful to me to have someone test Tomahawk on the T4 ZNMs for possible direct magic damage reduction.

To compare the Tomahawk effect for various monster types known to exhibit a so-called resistance to certain physical damage types, a table of damage reduction factors for slashing-type damage modified by Tomahawk is presented.

Damage penalty multipliers for slashing

Family	Before Tomahawk	After Tomahawk
Elementals	.250	.4375
Flans (normal)	.875	.90625
Flans (spiked)	.375	.53125
Ghosts	.750	.8125
Hecteyes	N/A	N/A
Leeches	N/A	N/A
Mimics	.500	.625
Skeletons	.875	.90625
Slimes	.500	.625

Consequently, the relative increase in damage from Tomahawk increases with the magnitude of the original reduction.

Physical damage increase (%) for slashing under the effect of Tomahawk

Family	Dmg increase (%)
Elementals	75.00%
Flans (normal)	3.57%
Flans(spiked)	41.60%
Ghosts	8.33%
Hecteyes	N/A
Leeches	N/A
Mimics	25.00%
Skeletons	3.57%
Slimes	25.00%

As OCD types are mainly preoccupied with percent changes (even relative increases based on crap), the following table of may be a useful summary for them.

Physical damage increase (%) under the effect of Tomahawk

Family	H2H (blunt)	Impact (blunt)	Slashing	Piercing
Elementals	75.00%	75.00%	75.00%	75.00%
Flans (normal)	8.33%	8.33%	3.57%	N/A
Flans (spiked)	75.00%	75.00%	41.66%	25.00%
Ghosts	25.00%	25.00%	8.33%	8.33%
Hecteyes	8.33%	8.33%	N/A	N/A
Leeches	8.33%	8.33%	N/A	N/A
Mimics	25.00%	25.00%	25.00%	25.00%
Skeletons	N/A	N/A	3.57%	25.00%
Slimes	75.00%	75.00%	25.00%	25.00%

I could do the same for magic damage, but you get the idea. A quick inspection of the above table shows that using Tomahawk on flans (normal mode) and skeletons yields a relatively small increase in slashing-type damage.

Accommodating Samurai Roll with two-handed weapons

Regardless of what you think about Samurai Roll compared to other types of offensive rolls, I was kind of interested in whether it actually removes a hit from a "n-hit setup" for various delay values. A "n-hit setup" is usually understood to be an equipment/food configuration for a two-handed weapon (because no one seems to care too much about Store TP for one-handed weapons) with enough Store TP to achieve at least 100 TP in n (landed) hits starting from 0 TP. Of course, in practice one starts from 0 TP only after zoning or upon TP reset because weapon skills do give TP if they don't miss completely, but I am keeping this general to avoid accounting for whether a WS is multi-hit or not.

To satisfy my curiosity, I looked up some typical delay values for two-handed weapons and computed the minimum Store TP to achieve a 7-hit, 6-hit, and 5-hit setup for each of the delay values. Assuming that I have attained a n-hit setup for some arbitrary delay, if someone is going to use Samurai Roll effectively (this means not stopping at 6 for the most part), at least I will know if I am taking advantage of the Store TP bonus.

Since the effect of Store TP is generally considered "discrete" in the sense that you want just enough TP to attain a n-hit setup (any excess Store TP trait having no effect and thus superfluous), the Store TP bonus from Samurai Roll will usually overshoot or fall short of the minimum requirement for a (n - 1)-hit setup.

Starting with a 7-hit setup, the following table summarizes the TP "surplus" or "deficit" with Samurai Roll in effect, without the +10 Store TP bonus from having a SAM in the party. Why should a SAM necessarily be present?

TP surplus/deficit with Samurai Roll going from 7 to 6 hits (5 hits with 11)

	Minimum	Roll total
Delay	Store TP	II	VII	VIII	IX	X	XI
528	0	+16	0	+4	+6	+8	+1
513	3	+14	-2	+2	+4	+6	-1
504	5	+15	-1	+3	+5	+7	-1
501	6	+15	-1	+3	+5	+7	-2
492	8	+14	-2	+2	+4	+6	-3
480	10	+13	-3	+1	+3	+5	-4
450	25	+11	-5	-1	+1	+3	-9

I omitted roll totals 1, 3, 4, 5, and 6 because those are generally not desirable. In general, Samurai Roll does shave a hit off 7-hit setup except when the roll total is 7. If the roll total is 11, the +40 Store TP bonus falls short of shaving two hits off a 7-hit setup. Of course, if a SAM is present the +10 Store TP bonus overcomes these deficits. Suppose you happen to be subbing /NIN and have sufficient TP for a 7-hit setup. In this situation, Samurai Roll would "work."

TP surplus/deficit with Samurai Roll going from 6 to 5 hits (4 hits with 11)

	Minimum	Roll total
Delay	Store TP	II	VII	VIII	IX	X	XI
528	16	+9	-7	-3	-1	+1	-18
513	21	+9	-7	-3	-1	+1	-19
504	22	+8	-8	-4	-2	0	-21
501	23	+7	-9	-5	-3	-1	-21
492	26	+7	-9	-5	-3	-1	-22
480	29	+7	-9	-5	-3	-1	-24
450	46	+4	-12	-8	-6	-4	-32

In the 6-hit scenario, however, Samurai Roll generally does not provide enough TP to achieve a 5-hit setup unless the roll total is 2 or 11. If a SAM is present, however, Samurai Roll generally does remove a hit. In either case, the 11 roll is not even close to providing enough TP to achieve a 4-hit setup.

TP surplus/deficit with Samurai Roll going from 5 to 4 hits

	Minimum	Roll total
Delay	Store TP	II	VII	VIII	IX	X	XI
528	39	-3	-19	-15	-13	-11	+5
513	44	-4	-20	-16	-14	-12	+4
504	46	-5	-21	-17	-15	-13	+3
501	48	-4	-20	-16	-14	-12	+4
492	51	-5	-21	-17	-15	-13	+3
480	54	-7	-23	-19	-17	-15	+1
450	74	-12	-28	-24	-22	-20	-4

Let us now turn to the fanciful situation of having a 5-hit setup before Samurai Roll, which is, practically speaking, reserved only for polearm-using samurai. A 4-hit setup with Samurai Roll is possible only by rolling a 11 (without SAM) or by rolling a 2 with a SAM present.

Another half-year in parses

While others hoard screenshots, I hoard parser files. Another six months, another excuse for a filler post based on parser "output." The point of this exercise is to show that parsing can be a useful summary of your activities and, in some cases, help to assess how well you are doing in aspects of the game other than mindless merit damage.

Edit (July 4): updated

An Affable Adamantking? (June 26)

Damage Summary
Player               Total Dmg   Damage %   Melee Dmg  WSkill Dmg   Spell Dmg
BLM (me)                     5     0.04 %           0           0           5
BLM                       1078     8.12 %           0           0        1078
DRK/DNC                   2109    15.88 %        1287         526         296
DRK/NIN                  10090    75.97 %        9756           0         334
Total                    13282   100.00 %       11043         526        1713

Melee Damage
Player            Melee Dmg   Melee %   Hit/Miss   M.Acc %  M.Low/Hi    M.Avg
DRK/DNC                1287   61.02 %       12/2   85.71 %    86/134   107.25
DRK/NIN                9756   96.69 %       83/6   93.26 %     5/187   120.43

Comments: I responded to a Whitegate shout for one of the "beastmen helm" quests that hardly anyone cares about. I had done this previously with NIN/WAR and the assistance of a RDM/WHM by zoning Diamond Quadav until it was isolated from its stooges, and I was interested if they would take a different tack. Actually, their approach called for a DRK-zerg of Diamond Quadav, leaving the BLMs to preoccupy (sleep) the others, which isn't a bad idea yet they still ran out of steam. As you can see, the damage output seemed to be decent enough to pull this off. (The DRK/DNC didn't 2-hour for some reason.) Diamond Quadav being a WHM, of course Benediction ruined this attempt, especially with no attempt to separate the boss from its minions.

Damage Summary
Player               Total Dmg   Damage %   Melee Dmg  WSkill Dmg   Spell Dmg
BLM (me)                  3347    19.23 %           0           0        3347
BLM                       5610    32.23 %           0           0        5583
DRK/DNC                    906     5.20 %         439           0         467
DRK/NIN                   7544    43.34 %        2843        2659        2042
Total                    17407   100.00 %        3282        2659       11439

Melee Damage
Player            Melee Dmg   Melee %   Hit/Miss   M.Acc %  M.Low/Hi    M.Avg
DRK/NIN                2843   37.69 %     198/74   72.79 %     0/167    13.44

Weaponskill Damage
Player                 WSkill Dmg   WSkill %  Hit/Miss   WS.Acc %   WS.Low/Hi   WS.Avg
DRK/NIN                      2659    35.25 %      12/0   100.00 %      38/525   221.58
- Vorpal Blade               2659   100.00 %      12/0   100.00 %      38/525   221.58

With Blood Weapon now unavailable, the only realistic tactic was to isolate Diamond Quadav and proceed to plink away at it with nukes and letting the DRK/NIN "tank." Unfortunately, the guy who wanted to "upgrade" the quadav barbut died without reraise and, in fact, Diamond Quadav is rather accurate for an easily-enfeebled NM, giving the DRK/NIN some trouble with shadows, so I just kited it with gravity and bind until the guy returned along with someone else on bard, making blink-tanking realistic. Meleeing was just terrible (not sure why there was a switch to 1-handed sword), but whatever gets the job done...

Farming Royal Jelly (May 7)

Experience Rates
Number of Fights : 234
Date             : 5/7/2009
Party Duration   : 14:14:40
Total Fight Time : 2:11:13
Avg Time/Fight   : 219.15 seconds
Avg Fight Length : 33.65 seconds

Item Drops
89 beehive chip
13 serving of royal jelly
22 insect wing
6 giant stinger

Comments: For those aspiring to level cooking to 100, it's either Red Curry or Cursed Soup, the latter requiring Royal Jelly, which was inexplicably flagged "exclusive" by some asshole on the "dev team." With a glut of 20 red curries languishing on a mule and sitting somewhere above 99 skill, I tried my hand at farming this shit.

Where do you farm Royal Jelly? You can risk dying to Final Sting while farming pephredos in Wajaom Woodlands (if you melee) or mow down all the Death Jackets, all on a 14-minute respawn timer in Crawler's Nest. 234 bees later, I got a 13th Royal Jelly and I still didn't get to 100 cooking.

More Aura Statues x58 (Jan 21)

Debuff     # Times   # Successful   # No Effect   % Successful
Aspir            2              2             0       100.00 %
Bind            60             43             0        71.67 %
Gravity        117            106             2        90.60 %
Sleep            5              4             0        80.00 %
Sleep II        17             17             0       100.00 %
Stun            37             37             0       100.00 %

Comments: Aura Statues are bothersome with relatively poor enfeebling skill as I showed last time. But at this point, I am pretty sure I had all the key enfeebling pieces, including Oracle's Gloves and Enfeebling Torque, but no Witch Sash, Enfeebling Earring, or corresponding elemental grip. Even so, Gravity outright resisted 9 of 115 times. I would imagine scholar with dark arts and the appropriate equipment and merits would have little trouble enfeebling statues.

Damage mitigation on WAR/SAM with Greater Colibri

Damage Taken Summary
Player         Total Dmg   Damage %   Melee Dmg   Abil. Dmg
WAR/SAM (me)        7727    50.27 %        5660        2067
WAR/NIN             3687    23.99 %        1885        1802
DRG/SAM             1944    12.65 %        1304         640
RDM/WHM              145     0.94 %         145           0
BRD/NIN             1432     9.32 %        1432           0
BRD/WHM              437     2.84 %         437           0
Total              15372   100.00 %       10863        4509

Passive Defenses
Player   Evasion  Evasion %   Parry  Parry %   Counter  Counter %
WAR/SAM        4     3.13 %       7   5.65 %        17    15.18 %
WAR/NIN        3     3.41 %       7   8.24 %         0     0.00 %

Active Defenses
Player   Shadow  Shadow %   Anticipate  Anticipate %
WAR/SAM       0    0.00 %           62       52.99 %
WAR/NIN      56   71.79 %            0        0.00 %
DRG/SAM       0    0.00 %            3       23.08 %
BRD/NIN      54   85.71 %            0        0.00 %

Comments: Where Utsusemi is involved, in KParser the "blink" rate is the number of absorbed attacks over the total number of attacks that weren't evaded or parried. The total number includes TP moves (but not their individual hits). From experience with Greater Colibri, my rate has ranged from 82% to 90%, which seems acceptable if not a sign of hyper-vigilance in recasting Utsusemi.

Similarly, a "Seigan rate" can be calculated by substituting the sum of counters and anticipates for the number of blinked attacks. To the extent that the Seigan rate, as a measure of "active" defensive efficiency, can be maximized with judicious use of Third Eye, it could help identify room for improvement. I have yet to see any discussion about what an optimal Seigan rate might be, though.

Unfortunately, my personal insight on WAR/SAM damage mitigation consists solely of two pickup parties. The parser output above is a partial record of a short (approximately 30 minutes) March 13 merit party where I was actually allowed to sub /SAM. My Seigan rate was 79/128 = .617.

Damage Taken Summary
Player        Total Dmg   Damage %   Melee Dmg   Range Dmg   Abil. Dmg
WAR/SAM (me)      16069    45.15 %       13888           0        2181
BRD/NIN            4669    13.12 %        4669           0           0
DRG/NIN            2780     7.81 %        1576           0        1204
BRD/WHM             176     0.49 %         176           0           0
WAR/SAM           11527    32.39 %        9227           0        2300
WHM/SCH             372     1.05 %         372           0           0
Total             35593   100.00 %       29908           0        5685

Passive Defenses
Player        Evasion  Evasion %   Parry  Parry %   Counter  Counter %
WAR/SAM (me)       10     3.02 %      10   3.12 %        40    13.11 %
BRD/NIN             9     4.39 %       0   0.00 %         0     0.00 %
DRG/NIN             4     2.37 %      10   6.06 %         0     0.00 %
WAR/SAM             9     4.84 %       9   5.08 %        16     9.94 %

Active Defenses
Player        Shadow  Shadow %   Anticipate  Anticipate %
WAR/SAM (me)       0    0.00 %          166       53.38 %
BRD/NIN          164   83.67 %            0        0.00 %
DRG/NIN          134   86.45 %            0        0.00 %
BRD/WHM            3   60.00 %            0        0.00 %
WAR/SAM            0    0.00 %           85       50.60 %

This parser output summarizes defensive efficiency from a June 17 polearm-only (hey, I was curious) merit party (82 minutes) where I was also allowed to sub /SAM. My Seigan rate was 206/311 = .662, a sign of personal improvement but also an indication that I could be more efficient as I was being rather lazy with Seigan renewal. The other WAR/SAM had a Seigan rate of 101/168 = .601. In contrast, the DRG/NIN actually outparsed both of us (draw your own conclusions) and was much more efficient defensively.

Innin could've come in handy here (April 16)

Damage Summary
Player    Total Dmg   Damage %   Melee Dmg   WSkill Dmg
NIN/WAR        4454   100.00 %        2854         1600

Melee Damage
Player    Melee Dmg   Melee %   Hit/Miss   M.Acc %  M.Low/Hi    M.Avg
NIN/WAR        2854   64.08 %      87/62   58.39 %     11/43    30.64

Comments: The reaction to the upcoming (July 2009) Ninja job adjustments, particularly Innin, a new ninja ability that "lowers enmity in exchange for reduced evasion" while conferring bonuses to accuracy, critical hit rate, and ninjutsu damage "when striking your target from behind," has been mixed to put it charitably.

This combination of lower enmity (sounds like this will have the effect of lower rate of enmity increase with Innin active) and increased damage-dealing capability seems peculiar, especially since these new abilities are subject to decay per "development" team fetish. I can imagine the enmity change doesn't "decay" while the damage-dealing part does. But it could be of use in low-number activities where ninjas can still melee, provide enfeebling support, and don't have to worry about positioning, but basically concede "tanking" to a far superior DD (like monk), possibly in conjunction with thieves being unaccountable for the damage they inflict. (Oh, you call that hate control?)

The above output from an "arena-style" fight from the quest "Bonds That Never Die," is a partial picture of how feeble (my) ninja was even with sushi. Being totally outclassed by 2-handers (samurai) who ended up tanking the latter half of the fight, Innin could've helped to speed up the fight.

Okay, this is a really weak argument for Innin, but at least it's something.

An example of NW Apollyon soloing failure (May 10)

Fight #   Enemy               Start Time   End Time   Fight Length
1         Bardha                11:55 AM   11:57 AM       00:02:27
3         Mountain Buffalo      12:00 PM   12:05 PM       00:05:03
4         Mountain Buffalo      12:05 PM   12:13 PM       00:07:32
5         Apollyon Scavenger    12:15 PM   12:17 PM       00:01:40
7         Gorynich              12:20 PM   12:22 PM       00:02:14
8         Gorynich              12:22 PM   12:24 PM       00:01:32
9         Gorynich              12:26 PM   12:28 PM       00:01:42
10        Gorynich              12:31 PM   12:33 PM       00:01:54
11        Gorynich              12:36 PM   12:37 PM       00:01:38
12        Kronprinz Behemoth    12:43 PM   12:47 PM       00:04:16
13        Kronprinz Behemoth    12:50 PM   12:52 PM       00:02:26
14        Kronprinz Behemoth    12:55 PM   12:58 PM       00:02:46
15        Kaiser Behemoth        1:01 PM    1:32 PM       00:31:11

Player          Spell Dmg   Spell %  #Spells  S.Low/Hi     S.Avg
- Aero IV             629    7.47 %        1   629/629    629.00
- Bio                   5    0.06 %        1       5/5      5.00
- Bio II              434    5.15 %        8     16/69     54.25
- Blizzard IV        6345   75.33 %        8   770/853    793.13
- Drain              1010   11.99 %        9    35/165    112.22

Comments: This output represents a wasted opportunity to clear NW Apollyon with ease on my first legitimate attempt. You can see where I wasted a lot of time even with only two buffaloes to kill. Also, I lost valuable time by dying to Kaiser Behemoth somehow. Aspir accuracy is indeed a rate-limiting step (NW Apollyon motivated my earlier posts on Aspir), so to speak, and for some reason I managed to cast Aspir only three times in a half-hour (47, 91, 81). It seems Kaiser Behemoth can be killed in 20 minutes solo (unless the video from some jackoff hume BLM I saw was subtly sped up), so this was very disappointing to me. It's one thing to know what to do, and another to execute actually.

In later attempts, I also decided to cast three times in a "lap" around the fifth floor (Blizzard IV, Aspir, and Bio II or Drain where applicable) as opposed to the two times that others do, but this seemed counterproductive since I wasn't really inflicting damage at a faster rate with a "three-point" approach and I was exposing myself to higher risk.

Ninja, Marinara Pizza, and Temenos - Western Tower

Damage Summary
Player        Total Dmg   Damage %   Melee Dmg  WSkill Dmg   Spell Dmg  Other Dmg
PLD/NIN           32083    14.21 %       25625        5980           0        371
NIN/WAR (me)      79879    35.37 %       53089       26707           0         83
DRK/NIN           53584    23.73 %       28735       21994        1960        895
RDM/WHM            7327     3.24 %           0           0        7327          0
THF/NIN           51155    22.65 %       30764       19718           0        134
SC: Detonation      833     0.37 %           0           0           0          0
SC: Scission        965     0.43 %           0           0           0          0
Total            225826   100.00 %      138213       74399        9287       1483

Melee Damage
Player        Melee Dmg   Melee %   Hit/Miss   M.Acc %  M.Low/Hi    M.Avg  #Crit  C.Low/Hi   C.Avg     Crit%
PLD/NIN           25625   79.87 %    672/121   84.74 %      0/77    35.50     56    32/112   67.11    8.33 %
NIN/WAR (me)      53089   66.46 %   1069/145   88.06 %      0/90    43.69    181    32/139   78.98   16.93 %
DRK/NIN           28735   53.63 %     252/57   81.55 %     0/222   104.41     29   138/287  187.97   11.51 %
THF/NIN           30764   60.14 %     797/72   91.71 %      0/68    28.57    140    29/381   85.67   17.57 %

Weaponskill Damage
Player         WSkill Dmg   WSkill %  Hit/Miss   WS.Acc %   WS.Low/Hi   WS.Avg
NIN/WAR (me)        26707    33.43 %      46/0   100.00 %     159/901   580.59
- Blade: Jin        26078    97.64 %      44/0   100.00 %     268/901   592.68
- Blade: Kamu         629     2.36 %       2/0   100.00 %     159/470   314.50

Passive Defenses
Player             Evasion  Evasion %   Parry  Parry %
BRD/WHM                  1    11.11 %       0   0.00 %
PLD/NIN                 13     8.28 %       3   2.08 %
NIN/WAR (me)            25    11.26 %       6   3.05 %
THF/NIN                  3    15.00 %       0   0.00 %

Active Defenses
Player             Shadow  Shadow %
PLD/NIN                76   53.90 %
NIN/WAR (me)          152   79.58 %
DRK/NIN                 3   27.27 %
THF/NIN                 5   29.41 %

Comments: I had a chance to do Temenos West as NIN/WAR, so I took this opportunity to see how well I could do with Marinara Pizza (+1), which is kind of a boon for 1-handed melee since it overcomes the accuracy deficit that 1-handers face compared to 2-handers and also provides an attack bonus.

Even 44+ accuracy (estimated) wasn't enough to achieve maximum hit rate, though.

Damage Summary
Player               Total Dmg   Damage %   Melee Dmg  WSkill Dmg
RDM/WHM                   4133     1.07 %           0           0
WHM/SCH                   1395     0.36 %           0           0
THF/NIN                  62995    16.29 %       35352       26928
NIN/WAR                 110655    28.61 %       78434       32156
WAR/NIN (me)            113930    29.45 %       72330       41287
PLD/NIN                  49607    12.82 %       29385       19984
Diabolos                   231     0.06 %         231           0
Garuda                   34906     9.02 %        5926           0
Leviathan                   72     0.02 %          72           0
Shiva                     1615     0.42 %         166           0
SC: Detonation            2272     0.59 %           0           0
SC: Impaction              307     0.08 %           0           0
SC: Light                 2034     0.53 %           0           0
SC: Reverberation         1676     0.43 %           0           0
SC: Scission               978     0.25 %           0           0
Total                   386806   100.00 %      221896      120355

Melee Damage
Player         Melee Dmg   Melee %   Hit/Miss   M.Acc %  M.Low/Hi    M.Avg  #Crit  C.Low/Hi   C.Avg     Crit%
THF/NIN            35352   56.12 %    897/104   89.61 %     10/65    30.99    178    28/290   73.42   19.84 %
NIN/WAR            78434   70.88 %    1510/99   93.85 %     0/103    45.94    231    27/150   85.17   15.30 %
WAR/NIN (me)       72330   63.49 %     458/25   94.82 %    50/247   143.30     67   135/306  243.28   14.63 %
PLD/NIN            29385   59.24 %    797/204   79.62 %      0/88    35.23     32    42/128   76.13    4.02 %

Weaponskill Damage
Player             WSkill Dmg   WSkill %  Hit/Miss   WS.Acc %   WS.Low/Hi   WS.Avg
NIN/WAR                 32156    29.06 %      55/0   100.00 %    220/1023   584.65
- Blade: Jin            30307    94.25 %      50/0   100.00 %    220/1023   606.14
- Blade: Kamu            1849     5.75 %       5/0   100.00 %     259/490   369.80
WAR/NIN (me)            41287    36.24 %      56/0   100.00 %    161/1615   737.27
- King's Justice        35740    86.56 %      50/0   100.00 %    161/1291   714.80

Passive Defenses
Player             Evasion  Evasion %   Parry  Parry %
RDM/WHM                  1     7.14 %       0   0.00 %
THF/NIN                  4    50.00 %       0   0.00 %
NIN/WAR                 42    17.00 %       4   1.95 %
WAR/NIN (me)             4     5.13 %       2   2.70 %
PLD/NIN                 16    11.76 %       5   4.17 %

Active Defenses
Player             Shadow  Shadow %
THF/NIN                 3   75.00 %
NIN/WAR               165   82.09 %
WAR/NIN (me)           56   77.78 %
PLD/NIN                77   66.96 %

This other (successful) attempt to clear Temenos West involved a different NIN/WAR using Dorado Sushi. It was really annoying to see average melee and WS damage similar to mine when using Marinara +1, but this could be explained by other factors (birds have low defense, Usukane, more katana merits, more consistent application of Dia II, etc.).

Retaliation

The warrior job ability Retaliation (level 60) is something I rarely use outside Nyzul (for bosses), so I was curious about how frequently it activates. This is something I would probably have a good idea about just from doing Campaign... if I actually did Campaign. Of course, FFXIclopedia's article is not much help as to what actually affects this frequency (there seems to be variability based on something else other than neglecting to reactivate Retaliation), so I went looking for any sort of data elsewhere.

From wiki.ffo.jp, apparently it is thought that Retaliation rate is based on weapon delay, from 20% at 999 delay to 50% at 200 delay, subject to further verification. (At least this is what I gleaned from Google Translate.)

As for data to support that kind of trend, so far I found one source that describes the results of dual wielding Brass Jadagna +1 (334 delay) and Caduceus (216 delay). Indeed, it is not immediately obvious whether Retaliation, in a dual wield context, is dependent only on the main weapon or based on total delay. The results indicate that Retaliation rate depends only on the main weapon:

Brass Jadagna +1 (main)/Cauduceus (sub): 71/244 (.291) with 95% confidence interval (0.2347960, 0.3523304)

Caduceus (main)/Brass Jadagna +1 (sub): 110/241 (.456) with 95% confidence interval (0.3923515, 0.5215964)

I would assume the experiment was done with Retaliation constantly active, at maximum hit rate (95%), and the Retaliation rate is not dependent on mob's melee attack speed and level (to account for the possibility that there were different mobs involved). Even more important, I would assume the rates were estimated by taking the ratio of Retaliation procs over the number of times being hit.

If these assumptions actually hold, then Retaliation frequency does appear to depend on the main weapon delay only, not the total delay from both weapons. The higher delay weapon, Brass Jadagna +1, had a significantly lower rate than the lower delay weapon, Caduceus. It is not clear whether dual wielding would be any different from using a 2-handed weapon, but I don't see why there would be a difference.

Chocobo update: winning streak ended at 10; have won 12 of the last 13 (7 uncontested). Record is 111-79-24-15.

Phantom Roll and support for discretion to roll however you want

Before I discuss the optimality of several approaches to using Phantom Roll, I want to talk glibly about whether Phantom Roll even involves the use of a fair die in practice, which is the major assumption underlying Phantom Roll "strategies." I will use Pearson's chi-square test to check badness of fit of the following count data.

This is the only discussion I've seen so far (2006) that entertains the possibility that the outcome of Phantom Roll (I through VI inclusive) is not uniformly distributed. The point of the data collection was to find some evidence that the die becomes weighted in the presence of the optimal job associated with the specific roll (Bard with Choral Roll, etc.). You can read the thread for details.

The first example, with 700 uses of Corsair's Roll, did not yield compelling evidence against unbiasedness (p-value .0811).

The other eight examples involved sampling 100 times under varying conditions. At this point it bears reminding that the distribution of p-values under the null hypothesis of a fair die is (asymptotically) uniformly distributed (keeping in mind bin specification for the sake of generating histograms), as illustrated below with a bunch of simulated p-values sorted into histogram bins, given a sample size of 100.


I bring this up only as a reminder of what the possible p-values can be under the null hypothesis.

For the remaining eight data sets, tests for unbiasedness yield p-values of .4614, .2739, .3601, .007439, .7974, .3101, .09696, and .2763. Based on this crude analysis, only the data set for Healer's Roll with WHM present showed statistically significant evidence of biasedness (specifically 30/100 for a roll of I), but compared to the other non-significant results, it seems difficult to attribute this to something other than Type I error.

Of course, the primary question of interest was not whether Phantom Roll gives unbiased rolls regardless of situation, but whether the presence of the optimal job changes the "weight" of the roll. Tests for homogeneity for each specific roll (multiple testing duly noted) give p-values of .5402 (bard), .1077 (white mage), .6433 (ranger), and .1099 (thief).

Generally speaking, chi-square tests have pretty low power, and one tends not to "invert" these to (sets of) confidence intervals to get a good sense of how (in)adequate the sample sizes are. But considering this data as a whole there isn't a particularly good reason to think that the Phantom Roll die is biased.

Now, optimality of two Phantom Roll approaches

The following could basically be summarized as comparing the pros and cons of busting more versus busting less depending on how you go about doubling up.

There is a spreadsheet that provides a convenient summary of whether to Double-Up for various roll types, based on a criterion of conditional expectation (actual buff value), given the current roll total. Basically, consideration of (conditional) expected value is a formal way to make a decision that can be mostly carried out using common sense--you will never double up with a total of 11, as the expected value of the buff after Double-Up must be 0--but addressing borderline cases where it may not be obvious whether one should double-up, for example if your current roll is 6. I awkwardly call this the "expected value on double-up" (EVDU) approach.

The spreadsheet also gives an unconditional expected value of the roll after doubling up based on the expected value criterion, which could be useful for comparing different types of rolls on a "long-run" basis.

For wannabe nerds who can't even calculate the conditional expectations or understand probability, that is one way to go about it. Not unexpectedly, these min/maxing wannabe nerds frown upon conservative approaches that seek to minimize the probability of a Bust, with the implication that people who refuse to Double-Up on a 6 are "suboptimal." For the remainder of this post, I will call categorical refusal to Double-Up on 6 (unless 6 is unlucky), yet still Doubling-Up if one gets an "unlucky" total (therefore risking a Bust), as the "conservative" approach (and the only one I will consider in this post).

I am willing to bet that most of the people who advocate EVDU (implicitly or not) never actually bothered to compare EVDU with more conservative approaches quantitatively, especially for specific types of rolls. By quantitatively, I mean comparing (unconditional) expected values under each approach to see how much better in the long-run EVDU is, and also comparing the busting proportions under each approach to see how much riskier in the long-run EVDU is.

Personally, I don't really give a shit what rolling strategy a corsair actually uses, since to me it mostly falls under the purview of individual playing style.

Consider Corsair's Roll, for example. Under EVDU, the expected percentage increase in EXP is 15.66% while the conservative approach gives an expected increase of 15.55%, which to me is a really trivial difference. Moreover, the probability of busting under EVDU is .051 while the probability of busting "conservatively" is 0. If you are willing to assume an actual 5% (non-zero) chance of busting for a theoretical 0.11% long-run increase in EXP, fine. But here, the tradeoff between risk and reward is not all that good.

I also estimated the probabilities for the Corsair's Roll bonuses under each strategy (since I didn't want to waste even more time thinking about how to hand-calculate them) to make it easier to compare the strategies in probabilistic terms. (Relative frequencies may not add up to 1 due to rounding.)

COR Roll	EVDU	Conservative
Bust	.051	.000
8%	.134	.082
13%	.000	.309
15%	.193	.142
16%	.165	.114
17%	.095	.044
20%	.309	.309
24%	.052	.000

I colored the relevant probabilities one "side" might use to make a case against the other. Note that the probability of obtaining the "lucky" result (20% EXP increase) is the same regardless of approach. I also did the same for Hunter's Roll (melee and ranged accuracy) and Chaos Roll (melee and ranged attack) without the presence of the optimal job.

Again, the tradeoff between risk and reward is not so great. Whether you, as a corsair, want to make that tradeoff should be up to you and not to dumbasses who need to rely on mindless rules of thumb because they don't know any better. Personally, I would rather allocate all of my busting risk to another roll rather than to Corsair's Roll if the increased risk is actually worth it on another roll. But when is it worth it? I repeat the above exercise with both Hunter's Roll and Chaos Roll, rolls that are available early on.

For Hunter's Roll, the expected value under EVDU is 29.63 accuracy, and 28.09 taking the more conservative tack. Clearly, a 1.54-point difference in average accuracy is such a profound increase as to assume a greater risk of busting. The estimated probabilities are given below.

RNG Roll	EVDU	Conservative
Bust	.135	.057
20	.000	.3o9
25	.194	.142
27	.161	.101
30	.124	.063
40	.264	.264
50	.122	.064

For Chaos Roll, the expected value under EVDU is 18.6% attack increase (47.5/256), and 17.6% attack increase (45.0/256) playing it conservatively. Again, a 0.98% average difference in attack obviously warrants the increased risk of busting. The estimated probabilities are given below.

DRK Roll (xx/256)	EVDU	Conservative
Bust	.134	.058
32	.000	.3o8
40	.193	.142
44	.163	.101
48	.124	.063
64	.265	.265
80	.124	.063

Sure, a 1-point or 1% difference may be important enough to you, but 0.11%?

I spent time constructing this post while considering whether to level corsair to 75. (I won't but not based on what I found in this post. Ultimately I'd rather buy an account with a ready-to-play COR75 than waste time leveling another job to 75.) Take-home message: do whatever the hell you want as long as you can support it logically.