A Samurai confused about Hagakure usage

From what I've read, Hagakure should be used pretty much on cooldown. I'm confused as to the reason though, because based on the math, Hagakure actually looks like a DPS loss. Meant only to fix undesired combinations of Sen (like running into an AoE fight with 3 Sen, or a boss fight with 2).
A Midare (3 Sen) has a potency of 720.
A Hagakure (3 Sen) grants 60 Kenki.
Shinten is the main converter of Kenki > DPS.
60 Kenki is 80% of the way to 3 Shinten, which would have a combined potency of 900.
80% of 900 is 720, identical to a Midare.
Except that Midare has a cast time of 2.5s, and 3 Shinten would occupy 3s, making it slower and thus less DPS.
As far as other uses of Kenki, the normal combo rotation grants enough to use Kaiten on every Iajutsu anyway, plus the occasional Shinten.

Am I missing something here?

You're not factoring in time correctly. Shinten is an ogcd so has a zero time cost. Midare has a cast time something like 3s

midare is 720 potency with kaiten at 20 kenki its 1080 potency

that same 80 kenki is effectively 3 shintens at 900 potency. so looks like midare is better.

factoring time though

hakaza (150) > shifu (280) > kasha (400) > hakaza (150) > jinpu (280) > gecko (400) > hakaza (150) > yukikaze (340) > kaiten midare (1080)
= 21 seconds (3,230 potency)
hakaza (150) > shifu (280) > kasha (400) > hakaza (150) > jinpu (280) > gecko (400) > hakaza (150) > yukikaze (340) > kaiten midare (1080)
= 21 seconds (3,230 potency)
total 42 seconds. (6,460 potency)

vs

hakaza (150) > shifu (280) > kasha (400) > hakaza (150) > jinpu (280) > gecko (400) > hakaza (150) > yukikaze (340) > hagakure
= 18 seconds (2,150 potency)
hakaza (150) > shinten (300) > shifu (280) > shinten (300) > kasha (400) > shinten (300) > hakaza (150) > jinpu (280) > gecko (400) > hakaza (150) > yukikaze (340) > kaiten midare (1080)
= 21 seconds (4,130 potency)
total 39 seconds. (6,280 potency)

Essentially you're losing 180 potency when you use hagakure but you're gaining 3 seconds.

However in that 3 seconds you can do roughly 1/3 of a 830 potency combo so a theoretical gain of 276.66 potency minus the 180 you lost from not using midare. results in a 96.66 potency gain.

This isn't 100% accurate though as the gains gets larger as your skill speed gets faster and your gcds get shorter. if can reach a point for example where your gcds are almost 2 seconds the midare casttime can be almost 1/2 of a 830 potency combo. so 415 - 180 = a 235 potency gain from using hagakure instead of midare.

and if you're able to use some of that kenki for seigens instead of shintens then the dps increase gets bigger still.

my numbers will be a bit off but the logic is about right I think it's also one of the things I like about sam as well because when you look at it. it's a bit more complex of a job than it originally seems.

Ah, thank you. That makes sense now. I was only looking over the numbers, and completely forgot that Shinten is oGCD.

Shinten is off the GCD - You can use it between weaponskills.
Midare is on the GCD - It is a weaponskill and shares CD with them.

Midare will thus delay all further weaponskills by 2,5 seconds, i.e. one GCD, i.e. the GCD you use for Midare. Shinten does not - You use it while your weaponskills are cooling down, which effectively puts you one GCD ahead in your rotation.

Put short: Using Hagakure/Shinten, you deliver the same damage without spending a GCD for it. That's where the gain lies.


Edit: Too late! <.<'

Another point of confusion I've seen argued a lot is whether Hagakure should always be used immediately with at least 1 Sen, or wait until you build 3 Sen.
If we say that Hagakure is worth 720p every 40s when used on cooldown with 3 Sen, that would be 18 DPS.
Let's give the most extreme case, and say the cooldown comes up when you have 1 Sen from Yukikaze, and no Skill Speed.
You should always have Shifu, putting you at 2.25s recast.
It would take 13.5 seconds (2.25x6) to get up to 3 Sen, costing 243p (13.5x18) compared to if you already had 3 Sen.
If you used Hagakure at 1 Sen, it would have had 240p. A net loss of only 3 potency in THE most extreme case.
Let's be more reasonable, and say that you have 2 Sen, and can use Yukikaze.
It would take 4.5 seconds (2.25x2) to reach 3 Sen, costing 81p (4.5x18), but with a gain of 240p on Hagakure. A net gain of 159p.

Even a tiny amount of Skill Speed should cause them to break even on the worst case.
Mathematically, you should always build 3. Does this look right?

Generally yeah this is what i believe.

there is however an exception in my opinion which is if waiting to build to 3 sen will interfere with reapplying Higabana.
then it's often better to use hagakure with less sen. otherwise you either let higabana drop off or end up clipping it too early. both of which result in lost potency from dot ticks

so if you took your worst case example for instance and in the process of doing that you let higabana drop off for 9 seconds. then you're effectively down 108 potency instead of just 3.

Yeah, I usually always build 3 Sen myself, unless certain circumstances arise due to mechanics that throws the rotation off horribly or the above as Dzian said.