Impale + Bladestorm dps equation - check my maths?

Since Path of Building doesn't support impale, I'm trying to work it out myself, but I need a general equation so I can compare with other effects.

impale records 10% of a hit, and adds that to the next 5 hits that enemy receives.

Bladestorm creates an aoe each time you attack that hits as frequently as you do, at 50% damage. You can have max 3 storms at once.

s = Attack speed (aps)
d = base physical attack damage (not including bladestorms)
i = chance to impale
e = increased impale effect

dps without impale = s * d * 2.5 (bladestorms deal 50% damage and there's max 3)

total hits per second = s * 4

impales applied per second = s * 4 * i

average impale damage = 0.1 * e * d * 2.5 / 4 = d * e / 16

impale average dps = d * e / 16 * s * 4 * i * 5 = d * s * e * i * 1.25

(the 5 here accounts for the fact that each impale can trigger 5 times)


So, the increase to total physical dps for bladestorm from impale would be

d * s * e * i * 1.25 / (d * s * 2.5) = e * i / 2

I'm always suspicious when a PoE equation turns out to be remotely simple, which makes me suspicious that I've got something wrong haha.

I can't check your math, but you might be interested in a recent related post:

Impale Guide & Calculator
https://www.pathofexile.com/forum/view-thread/2680960

you don't really need to do anything complicated to calculate dps with impale you just work out the specific number for your build and apply it to your pure phys.

So if your a 5 stacker with 40% effect and 100% chance you just multiply your pure phys dps by 1.7 to get your total.

Basically work out your impale multiplier and slap it on your PoB dps.

Impale Formula
= Chance to Impale * Number of Impales * Damage per Impale
= Chance to Impale * Number of Impales * .1(1 + Increased Effect)

That will give you the more multiplier impale provides. You can simply multiply your s and d to that if you want more accurate readings; PoB also calculates the more portion of Impale Support. If using hybrid damage, multiply the percentage of physical damage dealt. Chance to impale reaches a hard cap at 100%.

Remember Dread Banner is an aura and can be increased via aura effect, including quality on the banner itself. DB contribution will need to be rounded down for its contribution to chance and effect. My current build for example reaches nearly 100% DB aura effect which will drastically affect its contribution.