Point out where any of the math is wrong. I'll wait.
The issue isn't the math; It's that the math is incomplete or build on incorrect assumptions.
imbue dice scale linearly and exclusively with RP and do not crit or benefit from DS at all.
This is verifiably a false, and will impact the results.
- Whether imbues crit is orthogonal to the RP vs DS efficiency comparison
Using the term orthogonal here doesn't make any mathematical sense (neither of the terms is a vector), I assume you mean they're unrelated. They also aren't unrelated: if imbues could crit, it would increase the value of RP since the scaling is 150-200% compared to 100% for DS
Let:
- ID = number of imbue dice
- RP = Ranged Power (as % damage increase)
- DS = Doubleshot (as % projectile increase)
- p = crit chance (0–1)
- m = crit multiplier
Expected imbue damage per projectile:
Effective Imbue Damage (eID)=ID×(1+RP/100)×(1+DS/100)×[1+p(m−1)]
simplified: Imbue DMG = Imbue dice x RP scalar (though it's the incorrect scalar) x DS scalar x Crit scalar
You're claiming imbues can crit. This assumes the imbue dice scales 100% off ranged power, which most imbues don't. You also didn't include the base dice weight, as it can be anywhere from d6 to d10. I'm also not sure why you would have an equation that consist of only imbue dice, no weapon damage, no sneak. This equation fails to account for debuffs, as PRR debuffs go higher than MRR which would also impact the outcome. On most ranged builds, the DPS split is around 70-80% front number, 10-20% sneak, 10-20% imbue. The math here is calculating imbue damage in a vacuum, but you need a weapon to deal imbue damage. It isn't even right for imbue damage, as it factors crit chance into the imbue damage.
My point here is your math focuses on a single component that accounts for 10-20% of most DPS, and doesn't use realistic values for the scaling.
This conclusion is only true for builds using 100% RP scaling imbues, with 0 front+0 sneak DMG. None of which exist in ddo.
If you want the accurate formula for auto attacks with no shiradi mantle:
DMG = [1+ (DS/100)]x [(Imbue dmg x MRR scalar x (RP scalar for imbue- either 1.5 or 2)x(1+Rp/100) )+( sneak dmg x PRR scalar x 1.5 x (1+RP/100))+ (Weapon damage x PRR scalar x crit chance x multi x (1+Rp/100))+ (weapon dmg x PRR scalar x chance for non crit x (1+Rp/100))]
Because RP has multiple scalars, when you try to find the break point for the full DMG equation, you end up with a system that requires you to know: sneak damage, imbue damage, PRR and MRR debuffs, crit chance, crit multi, and weapon damage. Generally I combine crit multi, weapon dmg, crit chance into a single value I like to call expected weapon damage, but the result is still a 4 variable system (weapon DMG/sneak DMG/ imbue DMG/ Debuffs).
It depends on the build, but doubleshot is almost always worth more. The factors:
- Ranged power often scales things more than 100% (fate strike, shiradi mantle, sneak dmg, imbue)
- Doubleshot is often lower and harder to get than Ranged power
Generally, the first point matter less than the second point, as most of ranged dps is from front number (70-80% on current meta ranged dps)
Typical values for non-giga comp+ geared ranged DPS with a few AF stacks:
Inquis- 100 DS, 400 RP, DS is clearly the better choice here
Repeater- 120 DS, 380 RP, again DS is the clear choice
Shuri- 270 DS, 420 RP, This one is harder to figure out, but DS wins here as well
Bow- 130 DS, 400 RP, DS clearly wins
GXbow- 70 DS, 350 RP, DS wins
Dagger- 200 DS, 380 RP, DS still wins