Earlier, I blabbed about the consequences of delay associated with the use of weapon skills in terms of modeling damage output mathematically, but did not justify how much delay should be specified because I didn't know how much the following attack round (after a WS) is delayed. Fortunately, I came across this presentation of results and discussion quantifying the amount of delay that is effectively added to the attack round following the use of a job ability (or weapon skill). The results of "stacking" job abilities aside (read for yourself), it is obvious that a two-second delay for the use of a weapon skill must be accounted for, at the minimum, when attempting to model theoretical damage output. (Using other job abilities while engaging an enemy would also have an effect on damage output, but the use of weapon skills, if spammed, is the dominant factor contributing to job ability delay. Consequently, many of my previous posts, which ignored this delay, likely have led to incorrect conclusions.)
For now, though, I think it would be instructive to show how much a weapon skill delay of two seconds obviously hampers the modeling of damage output. But I don't want to waste my time doing the "before" analysis, so I base my "after" analysis based on the conditions set forth in this comparison of great katanas (covering Hagun, Soboro Sukehiro, Kurodachi, and Radennotachi). There are some problems with it, especially with the implied use of /DRG (low DA rates but not accounting for the effect of Jumps, wut). Therefore, I do not merely reuse the computed figures given but provide my own in some cases. In any case, it may help to review that comparison and mine side by side as I wish not to waste my time rehashing said conditions.
Calculating WS frequency: Zanshin is relevant for main job SAM?
The effect of Zanshin on weapon skill frequency is something I had not considered in my previous posts, and I am kind of surprised the activation rate is apparently rather high for samurai as the main job. Recall that in the October, 19, 2006 version update, "the hit rate of the extra attack [was] increased." Moreover, there is very good evidence the Zanshin activation rate can be considered 45% for main job and 25% for subjob, with the hit rate bonus the result of +35 accuracy (source). Unfortunately, it is more difficult to furnish evidence as to how Zanshin interacts with double attack for auto-attack purposes, but it seems likely that Zanshin has a lower "priority" than double attack (if double attack processes, Zanshin doesn't, and if it doesn't, Zanshin can), so I'll just run with that. This means that accounting for Zanshin doesn't really matter all that much for multi-hit weapons, but since I do it for Hagun and Radennotachi, I might as well do it for the other two.To start off with my "after" analysis (remember I want to show the effect of weapon skill delay not previously considered on an analysis that incorrectly ignores it), going back to the "before" analysis I cited previously, I should first point out that pDIF is apparently ignored in favor of a bogus assumption of a "baseline" 35:65 ratio of melee damage to WS damage for Hagun.
Since we are talking about theoretical damage output, it is nonsense to assume such a ratio. The baseline assumption is bogus, not that 35:65 may be observed in practice. If 35:65 is observed, surely average auto-attack damage and average WS damage are also observed (from parser output)! Use those values instead to back-calculate an "average" pDIF for both auto-attack and WS damage that should be fixed across all great katanas. The differences in WS frequency and weapon base damage will then account for the differences in the ratio of melee damage to WS damage, holding pDIF constant.
Anyway, I will return to the pDIF issue later. After accounting for the effect of Zanshin, I obtain the following averages for attack rounds from WS use to 100 TP, auto-attack hits in the process of getting to 100 TP after WS use, and the "effective" hit rate (landed hits per attack round), which encompasses the effects of accuracy, double attack, and Zanshin.
| Weapon | Average no. of rounds | Average no. of hits | Effective hit rate |
| Hagun | 5.05945 | 5.10742 | 1.00948 |
| Soboro Sukehiro | 3.11051 | 5.58467 | 1.79542 |
| Kurodachi | 3.99375 | 5.32642 | 1.33369 |
| Radennotachi | 5.05945 | 5.10742 | 1.00948 |
I am aware of the apparent absence of Brutal Earring (5% DA) for Soboro (but why use a Pole Grip then, implied with the stated 2% DA?), replaced by a mysterious source of accuracy +5, and accounted for those differences. I gave the benefit of the doubt, so to speak, with Soboro (94% hit rate after accuracy +5), even though it could easily be argued that, across all merit mobs encountered, the average hit rate could actually be closer to 93.5%.
My effective hit rate figures agree with the previous analysis more or less, but I do not compute effective hit rate directly. Instead, I compute it, as a kind of check on my calculations, after computing the average number of attack rounds and average number of hits (example: 5.10742/5.05945 = 1.00948) to make sure I didn't make any errors calculating the average number of attack rounds.
As always, the average number of rounds can be converted to the average time to accumulate 100 TP, but now the time between weapon skills must also account for the two-second weapon skill delay discussed previously. (This will be done at the end of the post.)
Accounting for average TP for the use of Tachi: Gekko
The previous analysis assumes maximum fSTR for each of the weapons (16, 12, 15, and 17 for Hagun, Soboro, Kurodachi, and Radennotachi, respectively), which would appear to be reasonable given the implied high STR modifier bonus used for Tachi: Gekko (152*.75*.83 = 94.62, which is close to the given 94). As mentioned previously, pDIF is completely ignored, but based on the attack bonus of Tachi: Gekko, it is reasonable to assume an average pDIF of 2.3 (based on a symmetric pDIF distribution between 1.9 and 2.7).The only thing left is calculating the fTP bonus of the first hit for Tachi: Gekko, which requires calculation of average TP for each weapon when a one-hit weapon skill is used, accounting for double attack. This, in turn, requires knowledge of the probability distribution of TP return from a one-hit WS and the corresponding TP values, which is the same regardless of weapon.
This would seem straightforward except for the observation of 2-TP return with one-hit weapon skills (source), which would suggest that for weapon skills, Zanshin can occur on the first hit independent of the double attack (Zanshin still can't occur for the double attack hit, presumably). The presence of Zanshin effectively "reallocates" the probability of missing the first hit (and losing the full TP return of 16.7), which is 5% most likely, so ignoring the Zanshin effect for a one-hit weapon skill results in negligible error for TP return (but not necessarily WS damage).
| Weapon | Average TP per WS (my calculation) | fTP bonus of 1st hit (with Gorget effect) |
| Hagun | 101.27806 | 1.9829879 |
| Soboro Sukehiro | 109.24816 | 1.6914005 |
| Kurodachi | 104.93533 | 1.6779229 |
| Radennotachi | 101.27806 | 1.6664939 |
Note that average TP shouldn't be truncated because these averages are themselves based on the actual truncated TP figures to begin with (assumed 16.7 TP per main WS hit and auto-attack hits and 1.4 TP for off-hand WS hit).
Accounting for average Tachi: Gekko damage: ignore Zanshin?
Given 91% hit rate for any double attack hits (7% DA rate) for Tachi: Gekko (95% otherwise), the average number of hits per weapon skill is .95 + (.91)(.07) = 1.0137. Accounting for the 45% Zanshin rate, this average rises to 1.035075, of which .95 still corresponds to the first hit (which receives the fTP bonus), so 0.085075 of the hits in the average WS have an fTP = 1. The effect of Zanshin is, therefore, like adding 2.345% DA, which, for the purposes of Tachi: Gekko, constitutes approximately a 1.1-1.3% increase in average WS damage. (This is given the conditions stated in the "before" analysis). Whether or not this is accounted for (I will account for it), the effect of Zanshin very slightly "favors" weapons with worse WS "secondary" hit damage (compared to other factors), so it can be ignored for convenience.A "fatal" flaw: consequences of the effect of haste with weapon skill delay
Because weapon skill delay, which is a fixed value (consider it two seconds), exists, the relative benefit of haste (or other forms of delay reduction) is higher for weapons with lower weapon-skill frequency compared to weapons with higher weapon-skill frequency. It follows that a weapon with higher weapon skill frequency CAN actually be "worse," on average, than a weapon with lower weapon skill frequency depending on the level of haste!One way to think of this is to consider an arbitrary time frame during which weapon skills occur. The time associated with the WS frequency might be reduced with haste, but there is always an absolute weapon skill delay tacked on. Even if haste goes to 100% (meaning the time associated with WS frequency goes to 0) and you still decide to use WS for some reason, the sum of the absolute weapon skill delay for the weapon with higher WS frequency will be
A "practical" consequence is that for "zerging" situations where maximum haste is involved, low-damage, multi-hit weapons (on average) can be worse than standard weapons. Similarly, multi-hit weapons may not be that good for meriting situations.
The "fatal flaw" with the "before" analysis is the unstated assumption that the haste level doesn't matter across weapons, so that the "pecking order" of great katanas always holds. Because weapon skill delay is not accounted for, the analysis does not hew to what is experienced in practice.
Repeat the analysis instead with ~65% haste (Hasso, Haste spell, double March, 20% equipment haste) along with the weapon skill delay of two seconds. The following figures are the result of a "per weapon skill" perspective, using average auto-attack pDIF 1.15 and average WS pDIF of 2.3. (Overwhelm 5/5 also used.)
| Weapon | Avg. TP dmg | Avg. WS dmg | Time per WS | Dmg/sec | TP:WS dmg |
| Hagun | 510.99763 | 910.7053192 | 15.281 s | 93.04 | 36:64 |
| Soboro Sukehiro | 333.96349 | 619.4514917 | 10.165 s | 93.79 | 35:65 |
| Kurodachi | 490.03068 | 744.1553438 | 12.810 s | 96.35 | 397:603 |
| Radennotachi | 593.22713 | 835.6201688 | 15.281 s | 93.50 | 415:585 |
Given 65% haste, relative to Hagun, Kurodachi is about (96.3474/93.0370 - 1)100% = 3.56% more efficient, and Soboro, about (93.7931/93.0370 - 1)100% = 0.81% more efficient. Radennotachi is about 0.5% more efficient. This jibes with the observation that Soboro is not really any better than Hagun in a typical merit situation.
Now, what happens given 80% haste?
| Weapon | Avg. TP dmg | Avg. WS dmg | Time per WS | Dmg/sec | TP:WS dmg |
| Hagun | 510.99763 | 910.7053192 | 9.589 s | 148.26 | 36:64 |
| Soboro Sukehiro | 333.96349 | 619.4514917 | 6.666 s | 143.03 | 35:65 |
| Kurodachi | 490.03068 | 744.1553438 | 8.177 s | 150.93 | 397:603 |
| Radennotachi | 593.22713 | 835.6201688 | 9.589 s | 149.01 | 415:585 |
Obviously, the damage figures (other than rate of damage) shouldn't change with haste. As they are fixed, changes in relative efficiency calculations (relative to 65% haste) involve only changes in time per WS (where applicable). The effect of 15% more haste benefits Hagun relatively more than it does Soboro because of the presence of the fixed two-second weapon skill delay. The result here shows that Hagun is more efficient than Soboro in a max-haste situation when spamming WS, and you should be. 910 damage, on average, in exchange for 2 seconds is better than 511 damage, on average, over 7.589 seconds.
(Correction: 06/13/2010) Incidentally, given 9% DA (the stated condition), Kurodachi is still better than Hagun even with maximum haste,
Conclusion
Weapon skill delay, which exists and can be considered to be two seconds, should be considered when doing a theoretical comparison of things related to doing damage.A major consequence of weapon skill delay is that, as haste increases, weapons with lower WS frequency benefit relatively more than weapons with higher WS frequency. This affects the "correct" choice of weapon for situations where high levels of haste are achieved. For example, even though Soboro Sukehiro may be better than Hagun at low levels of haste, it is inferior at high levels of haste (on average, since there is some inherent variability of WS frequency associated with multi-hit weapons).
(Correction: 06/13/2010) However, it can be shown that Kurodachi is superior to Hagun when WS frequency is a relevant factor (e.g., not relying only on Meditate to generate TP). "Actually better" in theory, however, is contingent on how much base DA is present.
The effects of Zanshin on WS frequency, WS damage (fTP bonus and Zanshin hits), and TP return can be quantified. While the effects of Zanshin given low hit rate were not discussed, the effect of Zanshin can "safely" be ignored for relative comparisons given high hit rates.