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Agility and Dodge in ICC

Warning: Theorycraft inside.

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Re: Agility and Dodge in ICC

Postby bashef » Fri Jan 22, 2010 7:28 am

Theck,

Thanks once again for the interesting analysis. Something that occurred to me reading this (although it's a largely academic interest in my case since in any practically available gear I'll take less avoidance for more armour, I don't believe the difference will be sufficient to force me into making that trade) is the statement "Agility is x as effective as Dodge for reducing incoming (avoidable) damage" depends on current armour and dodge rating, and I wonder how variable that is?

For example, the EH set I tank most bosses in (it's max armour but in all but one or two cases it's also max HP, and even then the difference is negligible) has me at 24.55% dodge and 31.5k armour unbuffed (that is, without Dev aura or libram up). This has me at close to 3k armour more than the gear you use for the calculations and 6% lower on dodge, both of which will make my absolute gains from agility over dodge in terms of damage reduction less pronounced than in that gearset. Now I suppose the issue is that it's not easy to characterise the break-even surface without some 3D plot style thing, which would probably be hard to view anyway, but it may be of interest at least to tabulate some values in those two dimensions in addition to the single-variable plots you have above.

One more thing that occurred to me, and spologies that I'm not able to formulate any clear impressions about this til I think about it some more, but here goes: the reason I was careful to say absolute damage reduction from agility is that while each point of armour does not give a linear increase in absolute damage reduction, it does give a linear increase in TTL or relative damage reduction. This means in the case of armour, each point of agi is equally valuable regardless of how much armour you already have. While it's not linear, there's also a distinction between the absolute gain in avoidance for each point of dodge (which diminishes) and the relative gain, which I believe someone showed was roughly linear before things got messed up in 3.2. My question is, is there a way of incorporating this into the consideration as to which to gem? Is that a useful thing to do? Or am I just being pointlessly obscure?
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Re: Agility and Dodge in ICC

Postby theckhd » Fri Jan 22, 2010 8:46 am

bashef wrote:Thanks once again for the interesting analysis. Something that occurred to me reading this (although it's a largely academic interest in my case since in any practically available gear I'll take less avoidance for more armour, I don't believe the difference will be sufficient to force me into making that trade) is the statement "Agility is x as effective as Dodge for reducing incoming (avoidable) damage" depends on current armour and dodge rating, and I wonder how variable that is?

For example, the EH set I tank most bosses in (it's max armour but in all but one or two cases it's also max HP, and even then the difference is negligible) has me at 24.55% dodge and 31.5k armour unbuffed (that is, without Dev aura or libram up). This has me at close to 3k armour more than the gear you use for the calculations and 6% lower on dodge, both of which will make my absolute gains from agility over dodge in terms of damage reduction less pronounced than in that gearset. Now I suppose the issue is that it's not easy to characterise the break-even surface without some 3D plot style thing, which would probably be hard to view anyway, but it may be of interest at least to tabulate some values in those two dimensions in addition to the single-variable plots you have above.

It would be relatively easy to make a 3D or colormap plot to show the break-even line, much like I did with some of the seal analysis plots in the TPS thread. But I don't know that it's worth doing for two reasons.

1) It takes 200-300 dodge rating or 2k-3k armor to make a difference of around 1% in the effectiveness ratio. So you could estimate the effectiveness at 2-3% lower than my calculated one for your gear set. That sort of rough estimate is still enough to show that you aren't going to lose much, if anything, by using agility.

2) The 100% break-even point isn't the criterion for whether you use dodge or agility. The point of this calculation was to show that the two are roughly the same for total damage intake. Since most of us value EH over avoidance, and agility gives us some EH in the form of armor, we'd use an agi gem over a dodge gem even if it was slightly less efficient in total damage taken.

This might be a more difficult decision to make if agility was 50-70% as effective as dodge. But this calculation shows that they're very close up until the armor cap, so most tanks will be better off taking agility regardless of their exact armor and avoidance levels.

bashef wrote:One more thing that occurred to me, and spologies that I'm not able to formulate any clear impressions about this til I think about it some more, but here goes: the reason I was careful to say absolute damage reduction from agility is that while each point of armour does not give a linear increase in absolute damage reduction, it does give a linear increase in TTL or relative damage reduction. This means in the case of armour, each point of agi is equally valuable regardless of how much armour you already have. While it's not linear, there's also a distinction between the absolute gain in avoidance for each point of dodge (which diminishes) and the relative gain, which I believe someone showed was roughly linear before things got messed up in 3.2. My question is, is there a way of incorporating this into the consideration as to which to gem? Is that a useful thing to do? Or am I just being pointlessly obscure?

This is already accounted for in the calculation, basically. The linearity (or nonlinearity) of the effect the two stats have are fundamentally built into the calculation, since they're part of the equations for damage mitigation.

You could certainly consider TTL, but all you'd be doing is adding an extra unnecessary step. TTL is proportional to 1/DTPS (or 1/D for short). The current calculation determines DTPS with each type of gem, and calculates the result of (D2-D0)/(D1-D0). In other words, if agility gives you a bigger reduction of incoming DTPS than dodge does, it's more efficient than dodge and gives you a value > 1.

If you wanted to look at TTL, you'd want to plot (TTL2-TTL0)/(TTL1-TTL0), which can be rewritten as (H/D2-H/D0)/(H/D1-H/D0) = (D1/D2)*(D2-D0)/(D1-D0). So it's the same metric with a multiplicative factor of D1/D2 in front. In practice, this multiplicative factor is 1 (1.0001 for the numbers I gave in the OP), since our base mitigation is very high and we're only tweaking it very slightly.

I just plugged in the numbers, and the TTL metric comes out at 104.10% effectiveness where the DTPS metric gives us 104.09% So the TTL evaluation would give us the same result to within roughly 0.01% effectiveness, which is far less than the variations we're looking at from different gear configurations.
"Theck, Bringer of Numbers and Pounding Headaches," courtesy of Grehn|Skipjack.
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Re: Agility and Dodge in ICC

Postby theckhd » Fri Jan 22, 2010 8:53 am

Also, I fixed a typo in the OP. I wrote that damage was reduced by A1/A0 or A2/A0 * M2/M0, when really it's reduced by (1-A1)/(1-A0) (and so forth).

The matlab file was doing the correct calculations, so all the numbers were right. It was just a typo that occurred while posting the math.

If you're curious, the reason it happened is probably because in the code, I store the reduction values [ i.e. R1=(1-A1)/(1-A0), R2=(1-A2)/(1-A0)*(1-M2)/(1-M0) ] and then simply divide them. Somehow while typing it my brain must have thought "R1/R0" and typed "A1/A0". Oops.
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