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So what is the actual defense cap?

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Re: So what is the actual defense cap?

Postby rokkon » Mon Jun 22, 2009 9:52 am

Arcand wrote:If we were talking about a continuous function the asymptote description would make more sense - but if we assume that avoidance values are rounded off to two decimal places as they appear on the character sheet, does that not help to nail down the "maximum useful defense" number?


Yeah I thought about that (I mentioned in an earlier post, it's a brick up there in one of my walls of text). It could be found that way fairly easily if we were going for the theoretical maximum. I'll see if I can do it when I get back to my own computer.
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Re: So what is the actual defense cap?

Postby jere » Mon Jun 22, 2009 12:36 pm

Arcand wrote:If we were talking about a continuous function the asymptote description would make more sense - but if we assume that avoidance values are rounded off to two decimal places as they appear on the character sheet, does that not help to nail down the "maximum useful defense" number?


It would depend. Typically the number of decimal places is different in the display than it is in the math. It would depend on how they did the random number generation code. I don't think we can assume they stop at 2 decimal places. Displays are typically easier to set when looking at number of decimal places. Numbers in code are typically either floats or whole numbers. And functions are typically carried out in a continuous manner for things like the DR equation, etc.

In addition, the caps that have been derived are at least to 6 decimal places, or the DR function starts to give erroneous values for certain inputs, so it would make sense that the actual avoidance values are also at least 6 decimal places for consistency.

My guess is that avoidance values are not set in terms of number of decimal places. That would make agilty conversion and rating conversion code more convoluted than necessary.
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Re: So what is the actual defense cap?

Postby Arcand » Mon Jun 22, 2009 12:43 pm

jere wrote:In addition, the caps that have been derived are at least to 6 decimal places, or the DR function starts to give erroneous values for certain inputs, so it would make sense that the actual avoidance values are also at least 6 decimal places for consistency.


Could you enlighten me about the 'erroneous values for certain inputs' thing? I've read the above half a dozen times, the only interpretation I'm seeing is "theorycrafters decided to round off at six decimal places, therefore Blizzard must use six decimal places" and I'm pretty sure that's not what you meant.
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Re: So what is the actual defense cap?

Postby jere » Mon Jun 22, 2009 1:49 pm

Meaning, if you use less decimal places, you can end up with a result that is off from your character sheet in game sometimes. The more decimal places you use the less often it tends to happen. The theory crafters carried them out to that number (maybe further?) because that is how many they needed to get as much accuracy in the results as possible.

For example, if you simply used 88 as your dodge cap, eventually you are going to run into a situation where calculating your dodge after DR is somewhat off of what you see ingame. The difference between using 88.13 and 88.129021 is probably small, but it is there. Reducing precision gives less precise results.

Now if you don't think the caps are accurate to those decimal places, that is a different thing. I can only go off my own experiences. Back when I was first playing with the equation, I was occasionally seeing differences in my results versus the character sheet. Fixing the precision fixed my results (i.e. the calculation matched ingame). If they are off, I haven't seen it yet, but there is no reason why they couldn't be off some.

I was saying was that if you truncate at 2 decimal places on your avoidance, then you might see some deviations from your numbers. If the actual internal to the game dodge cap is truly 88.129021 etc. as theorized, then capping avoidance at 2 decimal places wouldn't make sense (plus it would be unnecessary code to add).
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Re: So what is the actual defense cap?

Postby Arcand » Mon Jun 22, 2009 1:57 pm

If they really wanted to nail that down they'd have to experiment with various internal-rounding schemes, in case there are a couple functions each doing their own rounding...and I wonder if they considered that the numbers could be rounded/truncated in a binary form, not a decimal one.

(I'm not trying to be argumentative, mostly just thinking out loud. I do worry that the chain of assumptions is getting a tad long, though, starting from "my n-decimal-place model didn't work perfectly therefore...")
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Re: So what is the actual defense cap?

Postby jere » Mon Jun 22, 2009 3:24 pm

I guess my only concern with that line of thinking though is that multiple rounding schemes would have put a lot of discontinuities or slope changes, so you would have seen a bunch of scenarios where the equation gave incorrect results. So far, I have found zero cases where the equation gave the wrong result with respect to the character sheet, whether they be mine or someone else's. You would kind of expect the equation to fail a lot statistically, especially if you were using multiple functions with different rounding schemes. I have seen people put in the avoidance incorrectly before, which leads to wrong results, but once you show them how to do it, the result comes out nicely. Granted, I am by no means an authority on it, but all I have to go on here is personal experience.

That's not to say you are wrong, but it's hard to swallow numerically given how nice the curve fits. You would expect to have a more scatterplot like effect if there were multiple functions all rounding differently, or at least edges forming somewhere, or a changing slope or something.

Even working with the derivatives of the proposed function really comes out nicely. If the function did change repeatedly, that should fail because you can't take the derivative of a discontinuity without noticing it, so it should show up there.

Out of curiosity though, what method would you use to truncate them in a binary form though? Decimals are not directly stored in memory bit for bit, and most languages have no support for fixed number notation. You wouldn't even want to try to reliably modify IEEE 32 or 64 bit floating point (not to mention that is really really intricate stuff to mess with). Not that it is impossible, but you couldn't do it by simply chopping off bits. That has a different effect all together.

Sorry if this sounds all argue'ie (is that a word?). I don't mean it to be. I can drop the topic if you like. Has the function failed for you before? What assumptions do you think that it makes? It all kind of confuses me I guess more than anything.

EDIT: Sorry Arcand, my constant questions are probably out of line. I will just defer on this and not worry about it.
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Re: So what is the actual defense cap?

Postby Pizbit » Wed Jul 15, 2009 6:32 am

You could just sum it up with 'shit tons'?
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Re: So what is the actual defense cap?

Postby theckhd » Wed Jul 15, 2009 9:19 am

Veering back to the topic of the thread: While the DR equations prevent you from ever capping out parry, dodge, or miss individually, you could consider a "useful" defense cap where dodge+parry+miss=102.4%. At that point, you've pushed everything else off of the combat table, and adding defense rating won't make any change in the amount of damage you take from normal physical attacks (because you've hit 0).

Since you get 10% dodge and parry from base+talents, you would need 82.4% avoidance from sources subject to diminishing returns. Using avoid_dr.m:


Assuming you have 304 Agility from raid buffs, the crossover happens at 148495 defense rating (82.4001% avoidance).
If you pretend you aren't raid-buffed, then you get 149179 defense rating (82.4000% avoidance).

<edit> values incorrect, see below.
Last edited by theckhd on Tue Jul 21, 2009 10:02 am, edited 2 times in total.
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Re: So what is the actual defense cap?

Postby Rinanth » Tue Jul 21, 2009 5:44 am

theckhd wrote:Assuming you have 304 Agility from raid buffs, the crossover happens at 148495 defense rating (82.4001% avoidance).
If you pretend you aren't raid-buffed, then you get 149179 defense rating (82.4000% avoidance).


So what does that equate to in Defense skill?
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Re: So what is the actual defense cap?

Postby theckhd » Tue Jul 21, 2009 6:16 am

Rinanth wrote:So what does that equate to in Defense skill?

30,191 and 30,330 respectively.
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Re: So what is the actual defense cap?

Postby lythac » Tue Jul 21, 2009 8:54 am

theckhd wrote:you could consider a "useful" defense cap where dodge+parry+miss=102.4%.


101.8%

theckhd wrote:Since you get 10% dodge and parry from base+talents, you would need 82.4% avoidance from sources subject to diminishing returns.


I thought the 5% boss miss chance was also not subject to DR?
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Re: So what is the actual defense cap?

Postby theckhd » Tue Jul 21, 2009 10:01 am

Lythac wrote:
theckhd wrote:you could consider a "useful" defense cap where dodge+parry+miss=102.4%.


101.8%

theckhd wrote:Since you get 10% dodge and parry from base+talents, you would need 82.4% avoidance from sources subject to diminishing returns.


I thought the 5% boss miss chance was also not subject to DR?

You're right on both counts. So we need 101.8% - 10% parry - 10% dodge - 5% miss for 76.8% required post-DR avoidance.

While recalculating, I noticed I made a mistake. The values I was giving earlier are how much defense rating it takes to get 82.4% of dodge, not total avoidance. Using the new value of 76.8%, and looking at the correct output field of the function, I get 7491 defense rating unbuffed (1523 defense skill) and 7083 rating (1440 skill) if you're raid-buffed with 304 agility.
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Re: So what is the actual defense cap?

Postby Arcand » Tue Jul 21, 2009 10:18 am

theckhd wrote:While recalculating, I noticed I made a mistake. The values I was giving earlier are how much defense rating it takes to get 82.4% of dodge, not total avoidance. Using the new value of 76.8%, and looking at the correct output field of the function, I get 7491 defense rating unbuffed (1523 defense skill) and 7083 rating (1440 skill) if you're raid-buffed with 304 agility.


Dammit! Now I have to re-gem everything. Thanks a lot.
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Re: So what is the actual defense cap?

Postby Jonesy » Thu Aug 20, 2009 10:10 am

How about with scorpid sting(3%), frigid deathplate (3%) and rune of swordshattering (4%)?
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Re: So what is the actual defense cap?

Postby Isetnefret » Thu Aug 20, 2009 12:57 pm

What I'm MORE interested in is:

I have 778 defense rating (558 defense skill)
I have 600 dodge rating (28.84% chance)
I have 211 parry rating (18.38% chance)


My total avoidance, completely unbuffed (no self buff, no flask, nothing) is 56.30%.

What is the easiest way (itemization points-wise) to get to 65% total avoidance?
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