Tsukumo

The nature of recent posts hardly belies the fact that they are not at all interesting to construct. While they could easily be construed as a form of showing off, they were also motivated by my interest in analyzing the game in a more simpler way than just hand-waving about shit like everyone else. To me, it juts makes a lot more sense to deal with averages, which are a nice way to ignore variability in both damage and attack frequency and really simplify quantitative comparisons. Sometimes you just have to do the boring shit yourself since few others are capable and even fewer willing.

Aside from the posts concerning samurai weapons, everything else I had some degree of "personal" interest in, including this one about Tsukumo. Should I even bother trying to get a Tsukumo? I attempted to assess the viability of Tsukumo as a replacement for Senjuinrikio in the main hand.

Could Tsukumo with DMG +5 alone supplant Senjuinrikio in the main hand? The way I'm currently (not) using ninja, 190 delay and a decent damage rating on the main hand would be enough to let Senju collect dust, but all the hand-wringers can't seem to let go of the 6% crit rate and 38 base damage, never mind that you'd be better off with Fudo if you want higher average damage in the fantasy land of high pDIF.

Whatever your idea of high pDIF is for ninja, there is a way to show quantitatively whether Tsukumo/Perdu Blade is relatively less (or more) efficient (I'm starting to hate this term) than Senjuinrikio/Perdu in terms of spamming Blade: Jin. The case of dual wielding requires just a little more work than single weapons.

From the standpoint of spamming weapon skills, TP return from the previous WS looms large in terms of determining how many hits, on average, it will take to get to 100 TP. The fact that the off-hand weapon contributes a full-TP hit to Blade: Jin's TP return makes it more difficult to determine the "true" average number of hits to 100 TP after a Blade: Jin, but there is a way to calculate it.

Given the following...

• 95% hit rate
  
• 15% double attack rate
  
• 5 Store TP (Rajas Ring)
  
• 40% delay reduction from Dual Wield

... what is the probability distribution of the required number of hits to 100 after a Blade: Jin (with TP return being a random variable)? This information is necessary to calculate exactly the average number of hits to 100 TP along with the average number of rounds to 100 TP.

So far, I have gotten away with assuming there is always sufficient TP return from the previous WS to get to 100 TP in n - 1 hits for a n-hit setup. Ignoring the 5% of the time that there isn't sufficient TP return is not really necessary, but it is convenient.

While this simplification may be tolerated for two-handed weapons, this is not acceptable for the dual-wield situation. Nominally speaking, both Tsukumo/Perdu (4.6 TP) and Senjuinrikio/Perdu (4.7 TP) require 22 hits to 100 TP starting from 0 TP. (I hope these TP values are correct as they are the linchpin of this "analysis.") After a Blade: Jin, which can take on any of a finite set of TP values, the required number of hits to 100 TP is broken out as follows:

Comparison of probability distributions for required number of hits to 100 TP after Blade: Jin

Weapon	22 hits	21 hits	20 hits	19 hits
Senjuinrikio/Perdu (4.7 TP)	.0002	.0092	.1533	.8373
Tsukumo/Perdu (4.6 TP)	.0025	.0933	.8877	.0165

It shouldn't be surprising that even a 0.1-TP difference results in dissimilar distributions. Most of the time, the Senjuinrikio/Perdu combination requires 19 hits to reach 100 TP. In contrast, the Tsukumo/Perdu combination requires 20 hits to reach 100 TP most of the time. We can use these probabilities to obtain a weighted average of the average number of hits to 100 TP after Blade: Jin.

Average time to 100 TP in the long run

Weapons	Average no. of rounds	Average no. of hits	Average time (s)
Senjuinrikio/Perdu	9.081	19.842	37.84
Tsukumo/Perdu	9.497	20.752	36.09

These figures are based on spamming weapon skills continuously, showing that Tsukumo/Perdu doesn't have much of an advantage. Note that this a different viewpoint than just looking at the rate of TP gain (Tsukumo/Perdu being the obvious "winner"), which is not very meaningful for assessing spamming efficiency because, from this point of view, TP return from the previous WS is meaningless (like in Campaign).

If you've read this far, congratulations! I posted a spreadsheet that calculates the average number of rounds to 100 TP and average number of hits to 100 TP based on hit rate, DA rate, and whether you're dual wielding or not. While making a comprehensive, user-friendly spreadsheet for melee damage calculations is not very interesting to me, I can see where these calculations can be incorporated into one.

(Note: simulation was used to validate these averages.)

Calculating average damage to 100 TP

Weapons	No. hits to 100 TP	AA dmg	Hits/WS (main/sub)	WS dmg	Total dmg
Senjuinrikio/Perdu	19.842	691.708 + 571.463	2.9925/1.0925	701.261	1964.433
Tsukumo/Perdu	20.752	1195.305	4.085	652.783	1809.689
Tsukumo/Perdu (5% crit)	20.752	616.329 + 597.652	2.9925/1.0925	666.847	1880.829

Now that the average time to 100 TP has been taken care of, all that's left is to calculate average damage per hit and damage per WS. Hey, why not consider Tsukumo with 5% critical hit rate, too?

Here, I am assuming an average of 1.6 pDIF given 20% base critical hit rate across the board (still delving in fantasy, obviously) except where modified by weapon properties, 4 fSTR for auto-attack, and 9 fSTR for weapon skills. Given Blade: Jin, I used a WSC value of 53.

As I understand it, during a weapon skill double attack procs once for the main weapon and one for the sub, so that there are up to 6 hits possible for Blade: Jin. Therefore, it is necessary to split the average number of hits for Blade: Jin to account for any base damage (or expected damage) differences.

Another assumption I made with absolutely no concrete evidence is that that there is a critical hit rate bonus of +10% at 100 TP (analogous to Evisceration) on top of the 20% base rate and weapon crit rates, and that it applies to all hits. Assuming there is even a bonus, does it even apply to the off-hand hit, or does the off-hand hit crit at the normal rate? Is the second potential double attack from the off-hand swing? Obviously, I never closely examined these subtleties. Anyway, these details aren't terribly important.

Damage per second

Weapons	AA prop. total dmg	DPS
Senjuinrikio/Perdu	.643	51.916
Tsukumo/Perdu	.647	51.207
Tsukumo/Perdu (5% crit)	.646	52.114

The auto-attack proportion of total damage is just under 2/3 for WS spamming, which seems rather low. Maybe the assumption of a critical hit bonus at 100 TP is wrong. Tsukumo/Perdu with 5% crit rate barely edges Senju/Perdu, which is similar to Fudo barely edging Senju given high pDIF.

Final thoughts

Since Tsukumo is really only acceptable in the main hand if at all, I would consider Tsukumo with DMG +5 (any other augments being gravy) for both TP-holding (Campaign) and weapon-skill spamming. Frankly, if ninja users actually cared about optimality, why weren't they using Fudo for high pDIF?