Apex Arrow Maths

Howdy. I am making a transition to Bard as a main for Endwalker. I have a simple question for anyone here that knows Bard stuff. I am trying to pin down my rotation priorities and I am making good progress, but all the guides seem wrong on Apex Arrow. They all say to use it when you are at 100 Soul Guage, but that cannot be right.

Does anybody know the damage formula for Apex Arrow's potency? I tried looking online, but I can only find information that reflects what the tooltip says: at 20 Soul Guage, the potency is 120 and at 100 it is 600. That seems like a linear growth pattern to me, 30 potency for every 5 Soul Guage. If that is the case, then it would be logical to fire Apex Arrow any time after around 45 Soul Guage and before you reach 100. If you always waited until 100 Soul Guage to use it, then there is a small window during the time you reach 100 and before you use Apex Arrow that you might earn Repertoire that goes to waste, because you are at 100 Soul Guage.

You always would want your abilities to deal as much damage as possible. That's why you should use Apex Arrow at 100. It's a finicky skill, due to how Repertoire is gained, but you would still use it at full power either way.

So here's the catch - Apex Arrow is a GCD (global cooldown).

In order to use Apex Arrow, you have to forgo using a Burst Shot, to use Apex in that slot instead.

This means that Apex is not actually worth up to 600 potency. In reality, we are only dealing 326.67 more potency at full gauge than we would have if we never put the button on our hotbar. (the avg filler gcd for Bard is 273.33p)

If we use it at 95, that's 296.67 potency, or 3.123 potency per gauge, vs. 3.267 ppg to use it at 100. That means we lose 13.68 potency to inefficiency.

The odds of getting a double proc on a given DoT tick are 16%, vs. 48% for a single proc. So by waiting on 100, we are introducing a 1 in 4 chance of losing 5 gauge - which is, at best, worth 30p (it's actually less for some added reasons).

A 1 in 4 chance to lose 30p is -7.5p expected loss, which is not as bad as losing the 13.68 outright by using Apex at 95. So, we wait for 100.

I see what you are saying. I made an error in my original math by assuming Apex Arrow is just a dump that will always equal the same DPS in any window. But yeah, I whipped out a spreadsheet to check what you are saying, and I see the potency loss over time for every extra Apex Arrow action I take. Thank you :D