Diminishing Returns. Do some maths for me.

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Diminishing Returns. Do some maths for me.

Postby Invisusira » Sun May 10, 2009 7:17 am

With my dodge creeping higher and higher, I figured it was time to address this.

What is the percentage at which you start losing significant amounts of dodge % due to diminishing returns? I had originally thought it was around 25%, but have heard anywhere from 20% to 60%. After spending the last couple days searching here, Wowwiki, EJ, and the end credits to Star Trek, all I have to show is a whole lot of overly complex formulas and Excel spreadsheet stuff that I can't get to work for didly instead of any sort of straight answer in this regard.

Given the standard L80 prot paladin with 5% dodge from talents, when does dodge (and parry for that matter) start becoming a concern?
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Re: Diminishing Returns. Do some maths for me.

Postby Panzerdin » Sun May 10, 2009 7:32 am

It depends how much concerns you. What % efficacy do you want? By this, I mean that for every 1% dodge you 'get', how much do you want it to be actually giving you before it becomes important? If you tell me that, I'll have a go at doing the equations backwards to tell you the base dodge you'd need for that.

Alternatively, it never really becomes a concern because the gains from Avoidance are exponential, so the fact that you get progressively less of it is offset.
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Re: Diminishing Returns. Do some maths for me.

Postby Invisusira » Sun May 10, 2009 10:35 am

I'm just looking for, like, a graph. How much % do you lose when you're at X%.
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Re: Diminishing Returns. Do some maths for me.

Postby Panzerdin » Sun May 10, 2009 10:43 am

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Re: Diminishing Returns. Do some maths for me.

Postby Foolosophy » Sun May 10, 2009 10:44 am

I thought the rule of thumb was:
700 defense rating
700 dodge rating
start stacking parry.

I'm at 601 rating atm, that's 15,27 dodge for a total of 28,59. So I'll probably wait a bit more before I start looking into parry.

Links:
viewtopic.php?t=16737

With graphics:
http://www.failsafedesign.com/maintanka ... hp?t=17390
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Re: Diminishing Returns. Do some maths for me.

Postby Panzerdin » Sun May 10, 2009 10:46 am

The best method is to stack Defence and Dodge in a ratio between 3:2 and 2:1 (I can't recall it exactly) until Dodge DRs make stacking parry a better idea. In other words, you don't want Def = Dodge.
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Re: Diminishing Returns. Do some maths for me.

Postby arilink » Sun May 10, 2009 8:37 pm

A concern regarding what to gem/enchant/choose gear for the most avoidance?

My tip:
1. Get RAWR.
2. Load your character from the armory.
3. Check under "Comparisons" -> "Slot: Relative Stat Values".
4. ??
5. Profit.
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Re: Diminishing Returns. Do some maths for me.

Postby agnara » Mon May 11, 2009 12:16 am

Foolosophy wrote:I thought the rule of thumb was:
700 defense rating
700 dodge rating
start stacking parry.

I'm at 601 rating atm, that's 15,27 dodge for a total of 28,59. So I'll probably wait a bit more before I start looking into parry.

Links:
viewtopic.php?t=16737

With graphics:
http://www.failsafedesign.com/maintanka ... hp?t=17390

From the 2nd thread you linked
harlekin wrote:1) Stack ~700 defense rating (uncrittable)
2) Stack defense rating and block rating until 102.4% (Paladins only, maybe warriors)
3) Stack dodge rating until dodge rating = defense rating
4) Stack parry rating until 200 rating (assuming dodge = defense = ~700)
5) Add dodge, defense, and parry ratings at about a 10:10:2 ratio (at very high values the parry contribution will grow somewhat)


Most tanks got higher parry rating than what is optimal, because quite a lot of gear have some amount of parry rating on it. So stacking extra parry rating is unlikely to be the optimal choice.

Why don't you just install tankpoints or ratingbuster? They both factor in DR, and it is both faster, and easier than most of the other options
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Re: Diminishing Returns. Do some maths for me.

Postby jere » Mon May 11, 2009 1:11 pm

To add to Panzerdin's chart, this one also plots out the DR ratio (BLUE line):
Image

The blue line here basically tells you how effective adding more dodge percent is

Key points (all rough estimates):
06.5% dodge => you are going to be about 90% efficient at this point
12.0% dodge => you are going to be about 80% efficient at this point
15.0% dodge => you are going to be about 75% efficient at this point
18.5% dodge => you are going to be about 70% efficient at this point
27.0% dodge => you are going to be about 60% efficient at this point
37.5% dodge => you are going to be about 50% efficient at this point
52.0% dodge => you are going to be about 40% efficient at this point
73.0% dodge => you are going to be about 30% efficient at this point
88.0% dodge => you are going to be about 25% efficient at this point

******THESE VALUES DO NOT INCLUDE BASE OR TALENTED DODGE (ABOUT 10% TOTAL)***********

What that means is when you get to 27.0% dodge (before DR) from defense/dodge/agility, your next 1% from those sources will really only net you about an additional 0.6% dodge due to DR.

Most paladins hover around 25%-30% dodge in their tanking gear at Ulduar levels. That's 15%-20% after DR from dodge/def/agil that isn't talented or base, which would be 17.5%-25.0% roughly before DR. So at current levels, we are looking at our dodge being just above 60% efficient (1% gives about 0.6% after DR).

In this example, 25% dodge before DR gives 20.17% after DR and adding 1% to make it 26% before DR increases it to 20.78% after DR. That's a difference of 0.61% after DR, roughly, or 61% efficiency, which is close to what the line predicts.

Remember, each bit of dodge rating you add reduces the efficiency of the next bit.
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Re: Diminishing Returns. Do some maths for me.

Postby Gamingdevil » Mon May 11, 2009 1:34 pm

I thought base or talented avoidance wasn't taken into account for DR?
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Re: Diminishing Returns. Do some maths for me.

Postby jere » Mon May 11, 2009 1:47 pm

Gamingdevil wrote:I thought base or talented avoidance wasn't taken into account for DR?


It's not, that's why I didn't include them (notice, I subtracted 10% in my example...that's 5% from talents and 5% base for humans). DR only affects avoidance from dodge/def/agily after base or talents.
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Re: Diminishing Returns. Do some maths for me.

Postby neokai » Mon May 11, 2009 1:49 pm

Gamingdevil wrote:I thought base or talented avoidance wasn't taken into account for DR?


You are right, which is also explicitly mentioned by jere.
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Re: Diminishing Returns. Do some maths for me.

Postby Foolosophy » Tue May 12, 2009 8:08 am

jere wrote:*lots of lovely information*

Do you have a similiar one for parry and defense rating? Then I can do some simple calculations and say: "after X amount of dodge, parry is cheaper" etc.

jere wrote:15.0% dodge => you are going to be about 75% efficient at this point

If Diminishing returns only count for the % of dodge taken from the mouse over of the character screen, then stacking parry now is cheaper for me. I'm at 15,26 dodge from dodge rating.

Assuming that:
- 1% dodge = 39,35 rating (http://elitistjerks.com/f76/t37172-prot ... _3_0_wotlk)
- 1% parry = 49,18 rating (http://elitistjerks.com/f76/t37172-prot ... _3_0_wotlk)

39,35 | ??
------- | -------
0,750 | 1

-->
39,35 x 1 / 0,75 = 52,46 dodge rating needed for the next 1% of dodge. Then I can better go for parry rating (when I have no parry rating already). To know the break even point for sure, I need some more values ^^



Yes, I do miss lots of information right now. So it's not complete yet, but if we expand this a bit more, we can easily make some formula's that can say: you should now stack Parry / Dodge / Defense Rating. ;)
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Re: Diminishing Returns. Do some maths for me.

Postby jere » Tue May 12, 2009 11:08 am

Remember, when you are talking about dodge, you get some dodge from defense and agility (kings/MotW), not just dodge rating.

Well, the general equation for that blue line, regardless of avoidance type is:

Code: Select all
            (c^2)*k
DR_ratio = ---------
           (x+c*k)^2


Here, c is the cap of the avoidance type, k is the class constant, and x is the amount of avoidance pre DR (don't count talents/base)

The parry curve looks like this:
Image

Looking at your armory, it looks like you have 17.87% parry, which is 7.87% after DR if you subtract out 10% for talents/base. That's about 9% parry from parry rating and defense before DR. At that level, you have about a 72.6% efficiency for parry, meaning it costs 67.74248539 parry rating for your next 1%, so dodge is still better.

Here is a graph showing the two different DR ratio curves for dodge and parry:
Image

Notice how much more steep the parry curve is. So even IF you could find a point where stacking parry was more beneficial, it wouldn't take long for dodge to be better again, cause as soon as you add parry, you drop your efficiency more.
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Re: Diminishing Returns. Do some maths for me.

Postby jere » Tue May 12, 2009 11:57 am

If you are intersted in how to figure out when parry gives more avoidance per rating point, then take a look at the efficiency numbers. Basically, you want the point when the dodge efficiency is lower than the parry efficiency (or ratio), but then adjusted for the rating for each

Code: Select all
               (C_d^2)*k
dodge_ratio = -----------
              (d+C_d*k)^2


               (C_p^2)*k
parry_ratio = -----------
              (p+C_p*k)^2


You need to look at dodge_ratio < parry_ratio:

Code: Select all
   (C_d^2)*k     (C_p^2)*k
  ----------- < -----------
  (d+C_d*k)^2   (p+C_p*k)^2


(C_d^2)*(p+C_p*k)^2 < (C_p^2)*(d+C_d*k)^2

C_d*(p+C_p*k) < C_p*(d+C_d*k)


          C_d
d+C_d*k > ---*(p+C_p*k)
          C_p


Which simplifes to:
Code: Select all
    C_d
d > ---*p     == >    d > 1.875*p
    C_p


That's the cross over point in terms of dodge percent versus parry percent where parry becomes better to stack ***SEE NOTE BELOW***

Now if you want to consider the point where it becomes better to stack parry rating over dodge rating, that is a slightly different beast. You need to make an adjustment to the above equation. You are looking for the cross over where parry efficiency is greater than 1.25 times dodge efficiency (since you get 1.25 times more avoidance per rating point of dodge). I will lay the math out later, but his simplifies to:
Code: Select all
    C_d
d > ---*SQRT(1.25)*p + (SQRT(1.25) - 1)*C_d*k    ==>     d > 2.096252*p + 9.944522
    C_p


Those r values are the conversion values for getting percents out of ratings. Note that the "d" and "p" values are still percentages.

So as an example, if you have 9% parry BEFORE DR, then once you have more than 28.81% dodge BEFORE DR, parry rating will provide more avoidance ******SEE NOTE BELOW***********

SPECIAL NOTE:
Do not forget that parry rating degrades much much faster than dodge rating in terms of DR, so even if you get to a point where stacking parry rating is better, it is only good for probably half a percent (or even less).

As an example:

At 9% parry (BEFORE DR), you need more than 28.81% dodge (BEFORE DR) to make parry stacking better
At 10% parry (BEFORE DR), you need more than 30.91% dodge (BEFORE DR) to make parry stacking better

So if you reach 9% parry and have 29% dodge (all before DR and talents/base stats), you say to yourself "cool, stacking parry rating is better!!". Well as soon as you add 1% more parry, you are already back in the range where stacking dodge rating is better. So this is a very slippery slope to play with.
Last edited by jere on Wed May 13, 2009 4:04 pm, edited 1 time in total.
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