Katanas from Trial of the Magians

This post is patterned after "great axes from Trial of the Magians," but with a minimum of tedious commentary. These are explicit damage calculations that should match up closely with simplified, one-minute "paper napkin" analysis when WS damage is dropped as a damage component. It should be obvious what katanas are of interest (Kuina with STR and attack bonuses, for example). See FFXIclopedia entry for final forms of katanas.

Givens, assumptions, and simplifications for analysis

• Basic rates: 95% hit rate, 15% double attack rate, 0% haste, 40% dual wield delay reduction, 24% critical hit rate
• Store TP +5
• Blade: Jin used as the WS of interest
• At 100 TP, a critical hit rate bonus of +10% (added to base critical hit rate) exists for Blade: Jin (questionable assumption by analogy: Evisceration shown to have a critical hit rate bonus at 100 TP)
• All hits in Blade: Jin can critical hit (unfounded assumption)
  
• For WS, double attack can occur once for main hand and once for off hand (unfounded assumption)
  
• 40% "occasionally attacks twice" OAT rate for Isatu
• Effective double attack rate is the sum of the OAT and DA rates (unfounded assumption)
  

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

TP per hit	22 hits	21	20	19	18
4.6 TP	.00245	.09330	.88770	.01654	-
4.7	.00018	.00919	.15338	.83725	-
4.8	-	.00245	.09330	.88770	.01654

Remarks: these are required to account for variability of TP return to determine average time to 100 TP. 4.6 TP (201/190 delay combo), 4.7 TP (227/190, 227/201, 232/190, 232/201), and 4.8 TP (227/232) cover all katana combinations presented in this post.

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	37.87
Mozu/Perdu	9.081	19.842	37.87
Mozu/Isatu	7.780	19.955	35.71
Mozu/Kuina	9.081	19.842	38.87
Isatu/Perdu	7.815	20.045	32.98
Isatu/Kuina	7.815	20.045	33.84
Kuina/Perdu	9.497	20.752	37.13

fSTR and average pDIF (both auto-attack and WS)

Used baseline fSTR 4 and 9 for auto-attack and weapon skill, respectively (5 and 10 for Kuina), and +53 to Blade: Jin base damage from secondary modifiers (+54 for Kuina).

Used baseline average pDIF 1.452 (from 450/300 attack to defense... yes, I know that equals 1.5) and 2.552 for non-critical and critical hits, respectively. Average critical pDIF is taken to be 1.1 plus average pDIF (very rough estimate that can slightly overestimate the effect of critical hits).

Weapon	Phase	Average pDIF (no critical)	Average pDIF (critical)
Senjuinrikio/Perdu	TP	1.491	2.591
	WS	1.571	2.671
Mozu/Perdu	TP	1.491	2.591
	WS	1.571	2.671
Mozu/Isatu	TP	1.452	2.552
	WS	1.533	2.633
Mozu/Kuina	TP	1.506	2.606
	WS	1.586	2.686
Isatu/Perdu	TP	1.491	2.591
	WS	1.571	2.671
Isatu/Kuina	TP	1.506	2.606
	WS	1.586	2.686
Kuina/Perdu	TP	1.544	2.644
	WS	1.624	2.724

Average damage in a single cycle

Weapons	Avg. hits	Avg. TP dmg.	Avg. WS hits	Avg. WS dmg.	Avg. total dmg.
Senjuinrikio/ Perdu	19.842	758.796 + 626.823	2.9925 + 1.0925	820.638	2206.258
Mozu/Perdu	19.842	818.353 + 626.823	2.9925 + 1.0925	829.362	2274.540
Mozu/Isatu	8.499 + 11.455	685.489 + 746.999	2.9925 + 1.0925	817.325	2249.815
Mozu/Kuina	19.842	825.347 + 719.984	2.9925 + 1.0925	848.606	2393.939
Isatu/Perdu	11.507 + 8.538	767.446 + 539.427	2.9925 + 1.0925	775.131	2082.006
Kuina/Isatu	8.538 + 11.507	619.599 + 774.006	2.9925 + 1.0925	810.714	2204.320
Kuina/Perdu	20.751	769.145 + 675.347	2.9925 + 1.0925	822.067	2266.560

Remarks: Isatu effective DA rate is taken to be (40 + 15)% = 55%, which is subject to verification. Isatu's OAT rate is thought not to affect weapon skills.

Damage per second

Weapons	Proportion of total dmg. in auto-attack phase	Damage per second
Senjuinrikio/Perdu	.628	58.260
Mozu/Perdu	.635	60.063
Mozu/Isatu	.636	63.004
Mozu/Kuina	.645	61.592
Isatu/Perdu	.627	63.130
Kuina/Isatu	.632	65.141
Kuina/Perdu	.637	61.036

Remarks: Auto-attack damage proportions may be lower than what should be expected (closer to 2/3)

Some comments

It should have already been obvious that Mozu/Perdu would generally be better than Senjuinrikio/Perdu, especially in a max pDIF context. Fudo was already (barely) better than Senjuinrikio (for auto-attack damage alone)... Mozu/Kuina is the best of the non-Isatu pairings (OAT rate still in question; take with a grain of salt), particularly better than Kuina/Perdu because 4.7 TP per hit is better than 4.6 TP per hit. Kuina/Isatu still gives 4.7 TP per hit, making it a formidable combination on paper (again pending OAT rate verification).