[MENTION=10319]OrionTempest[/MENTION];
I worked through comparing rings last night. This is what I came up with.
Here is a function that computes the damage increase given new/old crit damage and new/old crit rate.
where c = average crit damage, cn = new average crit damage, r = crit rate, r = new crit rate
This is an abstract formula since it doesn't deal with your range directly. You need to unequip each of your rings one by one and multiply the calculated damage increase by your lowered range, then you can figure the difference between your current range and range if you had a specific sylph ring.
In your case:
f(1.61, 1.66, 1.0, 1.0) = 3.1% average increase in damage for CL + dSE + 10% min/max crit ring
f(1.735, 1.785, 1.0, 1.0) = 2.9% average increase in damage for CL + dSE + Ice Counters + 10% min/max crit ring
f(1.61, 1.61, 0.97, 1.0) = 1.1% increase for FO with dSE + 10% crit ring
f(1.61, 1.66, 0.97, 0.97) = 3.0% increase for FO with dSE + 10% min/max crit ring
f(1.735, 1.785, 0.97, 0.97) = 2.8% increase for FO with dSE + Ice Counters + 10% min/max crit ring
BUT! 10% boss damage is clearly the winner if you boss a lot, right? Actually there are diminishing returns. That is, if you have 10% BD and you add another 10% BD, your damage is not actually increasing by 10%. It's actually increasing by roughly 9%.
Adding a 10% ring to these existing BD amounts:
Important: You can essentially add 20% BD for skills that have reinforce hyper skills since reinforce stacks additively with BD. Therefore, the benefits you actually get from a BD ring can be less.
How does this stack up to crit rate/crit damage overall? Skip to the last bit of this post to see general numbers.
10% def ignore is a bit tougher to calculate since it varies by boss and current def ignore sources:
I don't think this is accurate, I will revisit it at a later time.
where pdr = the monster's pdr stat, ni = new ignore source, ei = existing ignore sources already multiplied together
General conclusions: min/max crit rings can add 5% average damage AT BEST. Other rings potentially add more than that depending on your existing stats.
1. A min/max crit ring will have varying amounts of effectiveness depending on how much crit damage you already have:
2. Crit rate rings add varying amounts of damage depending on your current crit rate and average crit damage:
3. Once you reach 150%+ BD you should start looking at crit rate and crit damage rings
4. Def ignore adds a varying amount and is hardly reliable as a source of damage output. I believe it is more effective to use almost any of the other rings since they add stats that are harder to get than def ignore.
5. The status resist ring is highly undervalued!
I worked through comparing rings last night. This is what I came up with.
Here is a function that computes the damage increase given new/old crit damage and new/old crit rate.
Code:
f(c, cn, r, rn) = ((rn * cn + (1 - rn)) - (r * c + (1 - r))) / (r * c + (1 - r))This is an abstract formula since it doesn't deal with your range directly. You need to unequip each of your rings one by one and multiply the calculated damage increase by your lowered range, then you can figure the difference between your current range and range if you had a specific sylph ring.
In your case:
f(1.61, 1.66, 1.0, 1.0) = 3.1% average increase in damage for CL + dSE + 10% min/max crit ring
f(1.735, 1.785, 1.0, 1.0) = 2.9% average increase in damage for CL + dSE + Ice Counters + 10% min/max crit ring
f(1.61, 1.61, 0.97, 1.0) = 1.1% increase for FO with dSE + 10% crit ring
f(1.61, 1.66, 0.97, 0.97) = 3.0% increase for FO with dSE + 10% min/max crit ring
f(1.735, 1.785, 0.97, 0.97) = 2.8% increase for FO with dSE + Ice Counters + 10% min/max crit ring
BUT! 10% boss damage is clearly the winner if you boss a lot, right? Actually there are diminishing returns. That is, if you have 10% BD and you add another 10% BD, your damage is not actually increasing by 10%. It's actually increasing by roughly 9%.
Adding a 10% ring to these existing BD amounts:
Spoiler
Important: You can essentially add 20% BD for skills that have reinforce hyper skills since reinforce stacks additively with BD. Therefore, the benefits you actually get from a BD ring can be less.
How does this stack up to crit rate/crit damage overall? Skip to the last bit of this post to see general numbers.
10% def ignore is a bit tougher to calculate since it varies by boss and current def ignore sources:
I don't think this is accurate, I will revisit it at a later time.
Code:
g(pdr, ni, ei) =
let a = 1 - pdr * (1 - ni) * (1 - ei)
b = 1 - pdr * (1 - ei)
a - b iff a >= 0
0 iff a < 0where pdr = the monster's pdr stat, ni = new ignore source, ei = existing ignore sources already multiplied together
Spoiler
General conclusions: min/max crit rings can add 5% average damage AT BEST. Other rings potentially add more than that depending on your existing stats.
1. A min/max crit ring will have varying amounts of effectiveness depending on how much crit damage you already have:
Spoiler
2. Crit rate rings add varying amounts of damage depending on your current crit rate and average crit damage:
Spoiler
3. Once you reach 150%+ BD you should start looking at crit rate and crit damage rings
4. Def ignore adds a varying amount and is hardly reliable as a source of damage output. I believe it is more effective to use almost any of the other rings since they add stats that are harder to get than def ignore.
5. The status resist ring is highly undervalued!