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truculent
04-21-2011, 12:09 PM
Hey everyone,

I have an interest in the value of parry/parry rating for warrior tanks, however before i can address them ( which will take place in another thread *hint hint*) I have some questions about DR. This is an effort to better understand what diminishing returns are, how the effect of dr functions, and its practical application to theorycrafting.... specifically on parry.

below is the basic formula Ive been using.. is this correct?

1 1 k
- = - + -
x' c x

x' is avoidance after diminishing returns
x is avoidance before diminishing returns
c is the dodge/parry cap (65.631440% for warriors, paladins and DKs, 116.890707 for druids)
k is a constant equal to 0.9560 for warriors, paladins and DKs, 0.9720 for druids

Assuming this is the correct approach, I was planning on working out the DR on graph paper, and recalculating at intervals of 100, starting at an initial value of 1000.

so ..

1000
1100
1200

and so on, all the way thru 4800.

In this approach, Im assuming that the value of parry rating BEFORE dr is consistent. That is, that the slope will remain consistent and the value of parry increases exponentially as the amount of parry rating increases.

My goal here is to understand the before-and-after-dr value of parry, and compile as much information regarding the slope of each as the amount of parry rating increases.

Is this the right approach for what im trying to do?

HOW DOTH THOU CHECK THE ARITHMETIC?!?!?!?!?!?!?!?

Quinafoi
04-21-2011, 02:06 PM
http://www.wowpedia.org/Melee_diminishing_returns

Quinafoi
04-21-2011, 02:12 PM
The value of Parry Rating for a warrior is more variable than its impact on Parry alone because Parry has other interactions with the warrior class though Hold the Line.

You use a lot of "Parry" and not enough "Parry Rating" in your questions. You don't get Parry, you get Parry Rating which is converted into Parry.

Your comment about exponential growth is actually invalid. It would be linear. If the value of Parry Rating is not subject to deminishing returns, then the value in terms of Parry that you gain from one point of Parry Rating to the next is constant. It's only when you consider other factors such as Hold the Line would you introduce additional variability into it's value. It's because Parry is subject to deminishing returns that the function is logrithmic (the opposite of exponential growth). Simply removing the deminishing returns though turns the function linear, not exponential.

Quinafoi
04-21-2011, 02:21 PM

below is the basic formula Ive been using.. is this correct?
Yes, that is the formula for deminishing returns on the combat table events of dodge and parry. The source you copied it from is correct.

My goal here is to understand the before-and-after-dr value of the stat, and compile as much information regarding the slope of each as the amount of parry increases.

Is this the right approach for what im trying to do?
Why would you care about the value before deminishing returns? It isn't like you would make a decision to get or ignore a stat based on what it would be worth if a core game mechanic didn't exist.

HOW DOTH THOU CHECK THE ARITHMETIC?!?!?!?!?!?!?!?
1+1=2 in any base notation other than binary.
Rules of arithmetic are pretty universal.

jere
04-21-2011, 03:15 PM
If it helps, I write the equation in a slightly mixed around format (via algebra):

cx
Y(x) = ------
x + ck

NOTE: Y(x) is parry after DR and x is parry before DR (and only parry that is affected by DR. Base parry, for example won't be factored into the equation, but parry rating and parry from strength will).

What this form lets you see is how the waveform will end up. It will be asymptotic and converge at Y(x) = c if you let X go to infinity.

You're interested in knowing how much parry you get out of each "step" of parry you get, you can actually see that via the derivative (slope of the line) if you know calculus, which would be:

dY(x) (c^2)k
----- = ----------
dx (x + ck)^2

This tells you how "efficient" your current level of parry DR is. If dY(x)/dx = 0.56, then your next bit of parry (infinitesimally small bit) will only net 56% of it's value.

Back in WotLK, I plotted these values against the old linear non DR parry for an example:
http://img87.imageshack.us/img87/4827/dodgedr.jpg

The Y axis is in units of the ratio, since you can compare the DR curve to the non DR curve easily.

Mind you the actual values of that chart are no longer valid (based off the old parry DR constants before CATA), but the trends are the same. What you'll see at X as it goes towards infinity is the DR curve will converge on the value of C, meaning the highest amount of parry you could ever have is 65.63% + whatever your base parry is. The "k" constant affects how quickly it converges to that 65.63% point.

truculent
04-21-2011, 03:16 PM
The value of Parry Rating for a warrior is more variable than its impact on Parry alone because Parry has other interactions with the warrior class though Hold the Line. [QUOTE=Quinafoi;504141]You use a lot of "Parry" and not enough "Parry Rating" in your questions. You don't get Parry, you get Parry Rating which is converted into Parry.

agreed. I will adjust the op.

Your comment about exponential growth is actually invalid. It would be linear. If the value of Parry Rating is not subject to deminishing returns, then the value in terms of Parry that you gain from one point of Parry Rating to the next is constant. It's only when you consider other factors such as Hold the Line would you introduce additional variability into it's value. It's because Parry is subject to deminishing returns that the function is logrithmic (the opposite of exponential growth). Simply removing the deminishing returns though turns the function linear, not exponential.

Yea, again, ill correct my OP so that my questions are more clear to the reader, But correct me if im wrong.. considering HTL, dosnt the value of parry ( not parry rating, but parry itself) grow exponentially? That is, the singular event on the combat table x the uptime of HTL ?

jere
04-21-2011, 03:21 PM
Just to re-inforce, remember that the DR equation does NOT count base parry (or dodge if doing dodge)

truculent
04-21-2011, 03:23 PM

Yes, that is the formula for deminishing returns on the combat table events of dodge and parry. The source you copied it from is correct.

Why would you care about the value before deminishing returns? It isn't like you would make a decision to get or ignore a stat based on what it would be worth if a core game mechanic didn't exist.

1+1=2 in any base notation other than binary.
Rules of arithmetic are pretty universal.

Im interested in its pre-dr value so that i have a base line to compare the diminished value. In other words, Im most interested in the loss of value parry rating suffers per 100 point interval.

yes, i understand 1+1=2 .. but please understand that as Im sure this is all elementary to you, this degree of crafting is fairly new to me.. so im trying to measure twice cut once .

truculent
04-21-2011, 03:36 PM
If it helps, I write the equation in a slightly mixed around format (via algebra):

cx
Y(x) = ------
x + ck

NOTE: Y(x) is parry after DR and x is parry before DR (and only parry that is affected by DR. Base parry, for example won't be factored into the equation, but parry rating and parry from strength will).

What this form lets you see is how the waveform will end up. It will be asymptotic and converge at Y(x) = c if you let X go to infinity.

You're interested in knowing how much parry you get out of each "step" of parry you get, you can actually see that via the derivative (slope of the line) if you know calculus, which would be:

dY(x) (c^2)k
----- = ----------
dx (x + ck)^2

This tells you how "efficient" your current level of parry DR is. If dY(x)/dx = 0.56, then your next bit of parry (infinitesimally small bit) will only net 56% of it's value.

Back in WotLK, I plotted these values against the old linear non DR parry for an example:
http://img87.imageshack.us/img87/4827/dodgedr.jpg

The Y axis is in units of the ratio, since you can compare the DR curve to the non DR curve easily.

Mind you the actual values of that chart are no longer valid (based off the old parry DR constants before CATA), but the trends are the same. What you'll see at X as it goes towards infinity is the DR curve will converge on the value of C, meaning the highest amount of parry you could ever have is 65.63% + whatever your base parry is. The "k" constant affects how quickly it converges to that 65.63% point.

EDIT: as a side note, back in WotLK, the "c" constant for parry was like 47 or 48 something, so you'll see that chart asymptotically approach 47 or 48% ish. In today's world it would approach 65.63%.

this is pretty much EXACTLY what i was trying to find out for the current situation, just a few steps ahead of my op. . .So any parry gained via strength does NOT effect the DR slope of the parry gained from rating? is that correct? of did i miss understand?

truculent
04-21-2011, 03:40 PM
Just to re-inforce, remember that the DR equation does NOT count base parry (or dodge if doing dodge)

Why would dodge be important? you lost me.

Insahnity
04-21-2011, 03:40 PM
this is pretty much EXACTLY what i was trying to find out for the current situation, just a few steps ahead of my op. . .So any parry gained via strength does NOT effect the DR slope of the parry gained from rating? is that correct? of did i miss understand?

There is no difference between Parry rating gained from strength vs Parry rating gained from rating. There is only parry rating. The only difference is where it comes from, it all diminishes the same way at the end.

THERE IS ONLY ZUL.
THERE IS NO SPOON! *warps the spoon*

truculent
04-21-2011, 03:43 PM
nvm

Ion
04-21-2011, 03:44 PM
Yeah, you gain parry rating at the rate of 1 parry rating per 4 strength (so, for example, if you had 3200 strength, you'd get 800 parry rating from it).

Fetzie
04-21-2011, 04:21 PM
Why would dodge be important? you lost me.

The diminishing return on dodge chance from dodge rating and agility, and parry chance from parry rating is determined by the same expression. Or in other words, the benefit from the two ratings decreases at the same rate when you add the same amount of rating.

To elaborate on the "base parry and dodge" bit:

Your base dodge and base parry chances are different, this becomes obvious if you remove your character's armor so that you have no ratings - your dodge chance is lower than your parry chance when naked. Your bonuses to dodge and parry chance are added on to these values after the DR has been calculated.

While you are not interested in dodge chance as you want to calculate HtL uptime maximisation and this is based on your parry chance, don't forget that both avoidance types work off the same expressions.

jere
04-21-2011, 04:35 PM
As stated by those above, parry from STR does count (as long as it isn't base STR).

Real world example:

Take the warrior Truculent on the Dark Iron realm (might be you).

He has the Following:

2647 STR (192 Base and 2455 from gear, enchants, gems, etc)
11.67% parry chance (after DR)

The parry tooltip reads he has 1255 parry rating which would give 7.10% parry (before DR sets in)

I can tell you that if you take his STR from gear, etc (the 2455 number), you get 2455*.25=613.75 parry rating from STR (notice the 192 didn't come into effect). If you add that to the parry rating on his gear/enchants/etc and round, you will get a total of 1255 parry rating.

Now let's run the 7.10% parry into the DR equation:

y(x) = (65.631440*7.10)/(7.10 + 65.631440*0.956) = 6.67% (after DR)
Add that to the 5% base parry you get and:

6.67 + 5.00 = 11.67%, which is what your character sheet shows.

Quinafoi
04-21-2011, 05:11 PM
Deminishing returns is only applied to the change in Parry or Dodge (or Miss, but since Defense Rating is no longer in the game this isn't a factor so much anymore). This is the net difference caused by all the Parry Rating you gain from either Strength or Parry Rating directly. Note that Strength does not convert to Parry directly, it converts to Parry Rating and then is converted to Parry. So functionally, you only need to consider one variable in the case of Parry, what the Parry Rating is from the combined sources. In the case of Dodge however, Agility is in fact converted directly into Dodge, not Dodge Rating as a intermediate conversion. Because Dodge has two variables which contribute to the net change it is slightly more complicated of a formula.

If your base dodge was say 5% and base parry say 6%. Then the amount of DR you suffer at 6% dodge and 7% parry (difference from base value of 1%) is identical. Meaning the value of 1 Dodge Rating = 1 Parry Rating at the base values of 5% and 6%, but also when the delta is the same the ratio of values from DR remain constant. So at 6% and 7%, 1 Dodge Rating is still equal to 1 Parry Rating in terms of DR (this wouldn't be true if the constants for dodge and parry were different).

Airowird
04-22-2011, 05:43 AM
In the case of Dodge however, Agility is in fact converted directly into Dodge, not Dodge Rating as a intermediate conversion. Because Dodge has two variables which contribute to the net change it is slightly more complicated of a formula.
Actually, while Agility does not directly add dodge rating, it DOES count directly into the DR formula (at a value of ~0.41 Dodge Rating per Agility). This is why you need to consider buffs when comparing stats, as an equal amount of Strength & Agility pushes Dodge further into DR than Parry.

@OP:
If you want a complete math base, I suggest checking out my spreadsheet (in sig). It has formulas to calculate all your dodge & parry, as well as a derivate on the last page, which shows the gain in avoidance from Dodge/Parry Rating as a result of DR. If you don't understand, feel free to PM me about the spreadsheet, I'll try & explain it as best as I can untill you understand :)

Quinafoi
04-22-2011, 07:14 AM
WarTotem, that's what I said in my first paragraph.

DR is applied to the change in Dodge or Parry from it's base value, not to the stats which contribute to it. However from a formula standpoint in determining your non-DR Dodge or Parry, the formula is different in that Agility converts directly into Dodge where as Strength converts to Parry Rating before converting to Parry. I was discussing the differences in the formulas, but at no point do I say Dodge from Agility isn't subject to deminishing returns. In fact I say the exact opposite in the first sentance of that post.

Deminishing returns is only applied to the change in Parry or Dodge
That doesn't say Dodge from Agility isn't subject to deminishing returns.

Note that at no point in that post is "Dodge" used where "Dodge Rating" was meant and the same for "Parry" and "Parry Rating". I was very deliberate in my word selection to avoid confusion however I believe you may have misinterpreted it. If I don't say "Rating", I don't mean rating.

truculent
04-22-2011, 07:29 AM
The diminishing return on dodge chance from dodge rating and agility, and parry chance from parry rating is determined by the same expression. Or in other words, the benefit from the two ratings decreases at the same rate when you add the same amount of rating.

To elaborate on the "base parry and dodge" bit:

Your base dodge and base parry chances are different, this becomes obvious if you remove your character's armor so that you have no ratings - your dodge chance is lower than your parry chance when naked. Your bonuses to dodge and parry chance are added on to these values after the DR has been calculated.

While you are not interested in dodge chance as you want to calculate HtL uptime maximisation and this is based on your parry chance, don't forget that both avoidance types work off the same expressions.

thank you sir. much clearer now.

jere
04-22-2011, 07:49 AM
WarTotem, that's what I said in my first paragraph.

DR is applied to the change in Dodge or Parry from it's base value, not to the stats which contribute to it. However from a formula standpoint in determining your non-DR Dodge or Parry, the formula is different in that Agility converts directly into Dodge where as Strength converts to Parry Rating before converting to Parry. I was discussing the differences in the formulas, but at no point do I say Dodge from Agility isn't subject to deminishing returns. In fact I say the exact opposite in the first sentance of that post.

I think some confusion may have just came from the way you stated it earlier in the thread. It almost read as if you were saying the DR formulas were different for dodge and parry (which they are not, they are exactly the same). However, from this quote it looks like you are more talking about formulas for calculating avoidance percent, which would then be input into the DR equations. I think yall are talking about two different "formulas" and thinking yall are talking about the same one. Easy to get mixed up in all this stuff.

I'll be honest, I read your earlier posts as implying that you need to put rating values into the DR equations, but I think (correct me if I am wrong) you really didn't mean it that way. The DR formulas specifically take in avoidance percentage values as inputs. You can convert ratings into those percentage values, but not all avoidance come from rating (well for parry it does, but not for dodge as you stated).

truculent
04-22-2011, 08:05 AM
As stated by those above, parry from STR does count (as long as it isn't base STR).

Real world example:

Take the warrior Truculent on the Dark Iron realm (might be you).

He has the Following:

2647 STR (192 Base and 2455 from gear, enchants, gems, etc)
11.67% parry chance (after DR)

The parry tooltip reads he has 1255 parry rating which would give 7.10% parry (before DR sets in)

I can tell you that if you take his STR from gear, etc (the 2455 number), you get 2455*.25=613.75 parry rating from STR (notice the 192 didn't come into effect). If you add that to the parry rating on his gear/enchants/etc and round, you will get a total of 1255 parry rating.

Now let's run the 7.10% parry into the DR equation:

y(x) = (65.631440*7.10)/(7.10 + 65.631440*0.956) = 6.67% (after DR)
Add that to the 5% base parry you get and:

6.67 + 5.00 = 11.67%, which is what your character sheet shows.

so in my own case, whereas I have 3460 str, and 2397 parry raiting :

3460 - 189 = 3271
3271 *.25 = 817.75
2397 - 818(str) = 1579

y(x) = (65.631440 * 8.935)/(8.935 + 65.631440 * 0.956) = 7.693741......?

7.693741 + 5 = 12.693741........?

but for some reason thats not adding p to whats on my character sheet. ( 13.56 parry chance gained from rating and a total of 16.67 parry chance)

truculent
04-22-2011, 08:10 AM
Now going back to the OP, assume im trying to understand the avoidence vaule after DR, is this a different ball o wax all together? the last few posts have kinda lost me.

Quinafoi
04-22-2011, 08:43 AM
I hope you aren't copying your Parry Rating from the tooltip for Parry, cause that includes Parry Rating from Strength in it. You need to go through all your items and total up the Parry Rating you have on your gear. 2400 Parry Rating seems a bit high for someone that would prioritize Mastery very heavily. Around 1600 seems more reasonable for a lower priority secondary stat which would be what it would be without the Parry Rating from Strength.

truculent
04-22-2011, 08:49 AM
I hope you aren't copying your Parry Rating from the tooltip for Parry, cause that includes Parry Rating from Strength in it. You need to go through all your items and total up the Parry Rating you have on your gear. 2400 Parry Rating seems a bit high for someone that would prioritize Mastery very heavily. Around 1600 seems more reasonable for a lower priority secondary stat which would be what it would be without the Parry Rating from Strength.

No, im not copying from the tooltip, But i think I goofed. I edited the last post. I stack parry pretty heavily at the moment. hense why Ive set out on this endeavor.I have a theory, one that may be usefull to teh tnakspot community. However, before I go on a rant about a very abstract idea, I'm trying to see if any portion of the theory makes sense. my current stats as listed in the tooltip are

8.40% dodge (766 rating)
50.12% block
11.78% mastery ( 2112 rating)

if i screwed somthing up in the math thats one thing. but to answer your question, yes.. i have a lot of parry.

But Im dont understand your question.... i did back out the parry from str.

Airowird
04-22-2011, 09:37 AM
@Quinafoi: I actually read your post as saying "Dodge receives DR from Dodge Rating, and then a separate DR from Agility added to the total". I just wanted to make clear that both add to the same DR formula, thus 1 Agility always gives you Dodge% equal to ~0.41 Dodge Rating.
Back on topic:
3271 strength is 817 Parry Rating (3272 would be 818, you always round DOWN to the integer)

Also, remember that the "Parry chance gained from Rating" the tooltip indicates is the raw chance BEFORE Diminishing Returns.
Basicly, you can take that into the formula and see if it works :)

Quinafoi
04-22-2011, 10:01 AM
You don't need to subtract the Parry Rating gained from Strength. I was just worried that you may have double counted the value of Strength by figuring out how much Parry Rating it was and adding it to a number which already included it.

jere
04-22-2011, 04:33 PM
so in my own case, whereas I have 3460 str, and 2397 parry raiting :

3460 - 189 = 3271
3271 *.25 = 817.75
2397 - 818(str) = 1579

y(x) = (65.631440 * 8.935)/(8.935 + 65.631440 * 0.956) = 7.693741......?

7.693741 + 5 = 12.693741........?

but for some reason thats not adding p to whats on my character sheet. ( 13.56 parry chance gained from rating and a total of 16.67 parry chance)

In your example, take the parry rating displayed in the tooltip, 2397, and divide it by 176.7189, the amount of parry rating for 1% parry:
2397/176.7189 = 13.5639 parry %.

That is before DR. Now lets use that number in the DR equation:

y(x) = c*13.5639/(13.5639 + c*k) = 11.67% parry after DR.

Now add the 5% base, and you should get 16.67% chance to parry (which reflects your character sheet).

Aside:
---------------
Going back to what Quinafoi said, the 2397 is your total parry rating. It is comprised of both the parry rating on your gear and the parry rating from your strength. You calculated the parry rating from STR correctly as 818 parry rating. That means 1579 parry rating comes from gear, enchants, and gems. There is really nothing more than academics in calculating these values. They only serve to give you an idea of where your parry rating comes from. For the DR calculations, use the total parry rating, 2397, convert it to percent, and plug it into the DR equation.
---------------

Now, back to your opening post. Given that your parry rating (2397) gives 13.5639% before DR, lets see how efficient your DR is:
dy(x)/dx = c*c*k/((13.5639 + c*k)*(13.5639 + c*k)) = 0.7072

So at your current level of parry, you are at 70.72% efficiency, meaning your next 0.1% parry (before DR) will net slightly less than 0.071% extra parry after DR.

If you need to look at it in terms of parry ratings, here is a chart I tossed together in excel:

Avoidance Percent Percent DR DR Avoidance Gained
Rating Before DR After DR Efficiency Eff (Percent) Per 100 Rating
600 3.395222582 3.369173319 0.941386782 94.13867821 0.53729997
700 3.961093013 3.897357231 0.925482564 92.54825644 0.528183912
800 4.526963443 4.416655135 0.909978008 90.99780081 0.519297904
900 5.092833873 4.927289402 0.894859833 89.48598334 0.510634268
1000 5.658704304 5.429475048 0.880115308 88.01153077 0.502185646
1100 6.224574734 5.923420031 0.865732219 86.57322187 0.493944982
1200 6.790445165 6.409325537 0.851698849 85.16988489 0.485905507
1300 7.356315595 6.88738626 0.838003952 83.80039516 0.478060723
1400 7.922186025 7.357790655 0.824636729 82.4636729 0.470404395
1500 8.488056456 7.82072119 0.81158681 81.15868101 0.462930535
1600 9.053926886 8.276354579 0.798844231 79.88442313 0.455633389
1700 9.619797317 8.724862011 0.786399417 78.63994168 0.448507432
1800 10.18566775 9.166409359 0.774243161 77.4243161 0.441547348
1900 10.75153818 9.601157389 0.762366611 76.23666112 0.43474803
2000 11.31740861 10.02926195 0.750761252 75.07612517 0.428104565
2100 11.88327904 10.45087418 0.739418888 73.94188884 0.421612225
2200 12.44914947 10.86614064 0.728331634 72.83316343 0.415266462
2300 13.0150199 11.27520354 0.717491896 71.74918959 0.409062895
2400 13.58089033 11.67820084 0.70689236 70.68923603 0.402997307
2500 14.14676076 12.07526648 0.696525982 69.65259824 0.397065638
2600 14.71263119 12.46653046 0.686385974 68.63859737 0.391263974
2700 15.27850162 12.852119 0.676465791 67.6465791 0.385588542
2800 15.84437205 13.2321547 0.666759126 66.67591256 0.380035708
2900 16.41024248 13.60675667 0.657259894 65.72598938 0.374601965
3000 16.97611291 13.9760406 0.647962227 64.79622268 0.369283932

truculent
04-22-2011, 04:42 PM
this information listed above is current?

Airowird
04-23-2011, 02:38 AM
It is as current as it can be. Whatever that means :)

04-23-2011, 06:11 AM
Jere would it be possible to make a column hold the line uptime increase per 100 rating? Would be nice to compare uptime increase versus loss through DR.

truculent
04-23-2011, 07:08 AM
Jere would it be possible to make a column hold the line uptime increase per 100 rating? Would be nice to compare uptime increase versus loss through DR.

actually, that was my plan. The reason I made this thread was to have a better understanding of dr before I did so.

jere
04-24-2011, 04:54 AM
I'll be honest, I only play my warrior as an alt nowadays. I don't know much about HtL mechanics. I would (off the cuff) think that it would require simulation to get an accurate uptime, which I am not experienced at. There are a lot of things I don't know about it. Such as:

1. Do HtL procs refresh or does one lock out the proc of another?
2. Does it have an ICD?

For example, if it refreshes, then looking for 6 procs a minute isn't going to give you 100%uptime, because some of those will overlap.
However, if the current proc locs the next one out, then it is easier to calculate. An ICD can also make it a bit easier to calculate.

From some cursory reading, it looks like it probably: new procs refresh/overwrite current ones, and does not have an ICD.

Also, wouldn't uptime also be a function of boss attack speed, since it triggers off of parries?

WarTotem may have looked into all of this for his spreadsheet, so you might peg him for some ideas on how to calculate it.

Dwarfisshort
04-24-2011, 11:49 AM
I am 48 and am a bit rusty on my math, can someone explain in plain english without all the math involved how bad the diminishing returns are?

04-24-2011, 12:12 PM
From some cursory reading, it looks like it probably: new procs refresh/overwrite current ones, and does not have an ICD.

Also, wouldn't uptime also be a function of boss attack speed, since it triggers off of parries?

Aye this is correct. Would need to make an assumption of the attack speed and work of that some increase in the uptime. For gimmick fights like chimearon or fights with adds numbers would differ quite a bit, but most encounters the boss swings around every 2 secs?

@Dwarfisshort
Just look at the DR efficiency column from Jere. Before diminishing returns 176,7rating=1% dodge/parry. In that column you can see that the next 100 rating gets less efficient the more you have 88% efficiency at 1000 rating, 75% efficiency at 2000 rating etc.

Booi
04-25-2011, 01:05 AM
I am 48 and am a bit rusty on my math, can someone explain in plain english without all the math involved how bad the diminishing returns are?

In simple terms. The effect of diminishing returns is "not bad". We can't avoid its effects, and so the goal is simply to balance the dodge and parry DRs as well as you can. Every 500 rating the value of that rating tends to drop by ~10%.

As a general rule, parry can be a few percentage points higher because it increases hold the line uptime. Mastery rating tends to trump both as it has no diminishing returns.

Loganisis
05-02-2011, 03:05 PM
I've finally sat down and tried to work this out for myself (I need to do things to learn them) - my question is a bit down the way)

So, for example, if you have 2000 parry rating from all sources, you have:

X = (65.63144*11.31740861) / [ 11.31740861 + ( 65.6311 * .0956)]
X = 10.02926195

So pre-DR 2000 parry rating = 11.32% Parry
post-DR 2000 parry rating = 10.03% Parry

I think that math is correct. However the graphs don't help me much (which is weird because I'm usually a very visual person). So I'm trying to find a way to quantify it that makes sense to me. Are the following statements valid statements, without the need of qualifiers?

Because of diminishing returns, at the specific point of 2000 parry rating:
A) The real world impact is parry is 1.288147% lower than if DR did not exist;
B) Parry is only 88.618% as effective as in a world where DR does not exist; and
C) The effective rating per 1% of parry is 199.4165

I don't want to confuse people if this needs a lot of caveats, but this, for me, if I were to work out a full table (as opposed to a graph) makes more sense to me since it deals with the in-game actual effect more than a graph does to me.

Am I off base on this?

05-02-2011, 03:25 PM
Because of diminishing returns, at the specific point of 2000 parry rating:
A) The real world impact is parry is 1.288147% lower than if DR did not exist;
B) Parry is only 88.618% as effective as in a world where DR does not exist; and
C) The effective rating per 1% of parry is 199.4165
Am I off base on this?

All of the above is true but its not very useful information. Its much more useful to know how effective the last 100 rating was or how effective the next 100 rating will be instead of calculating the average effectiveness of the whole 2000 rating.
If you look at the table Jere made you will see 75% effectiveness at 2000 rating.

Hope this helps :)

Loganisis
05-02-2011, 03:41 PM
See, I don't understand how it's 75% as effective. That doesn't mean anything to me. The 199.4165 per 1% means a lot more to me now. It means I'm going to need more than 200 parry rating to grab another 1% parry because I know DR will continue to become larger.

I can compare the current amount per 1% against dodge and get an measurement in my head as to how good they are.

I can use that number to look at reforging.

I dunno, to me C especially means the most to me. Its what the real world impact is.

And I'm still confused as to the 75% effectiveness, that's looking at the next point, right? It just doesn't mean a whole lot to me. :-/

jere
05-02-2011, 04:10 PM
See, I don't understand how it's 75% as effective. That doesn't mean anything to me. The 199.4165 per 1% means a lot more to me now. It means I'm going to need more than 200 parry rating to grab another 1% parry because I know DR will continue to become larger.

I can compare the current amount per 1% against dodge and get an measurement in my head as to how good they are.

I can use that number to look at reforging.

I dunno, to me C especially means the most to me. Its what the real world impact is.

And I'm still confused as to the 75% effectiveness, that's looking at the next point, right? It just doesn't mean a whole lot to me. :-/

What the 75% means is that the next bit of parry you get will give you 75% of the parry percentage you calculate by dividing rating/conversion factor. So the next 0.10% parry you get from parry rating will really only net you 0.075% parry rating due to DR (actually a bit less because it is a continuous function and each step nets a lower value...talking infinitely small steps).

So if you were sitting at 2000 parry rating and you got a piece of gear that has 100 more parry rating. Normally, without DR, 100 parry rating would be an additional 0.5659% parry, but because we are at 75% efficiency, it will be less than 0.5659*0.75 = 0.4244% parry. The actual amount you get will be slightly less because the 75% is taken at the instantaneous point of 2000 parry rating specifically and every infinitesimal step in parry rating nets a lower and lower efficiency. As a matter of fact, if you look at the 2100 point on the chart, that last 100 rating only gave 0.4216%, but the 0.4244% was pretty close.

So the 75% isn't good for hard calculations unless you are moving in really small steps (probably 0.001 percentage points if I had to guess), but it gives you an idea of what kind of impact DR will have on the next bit of parry rating you add. Will it be half as effective, or 75% as effective, roughly? That's what the number seeks to give some insight on.

EDIT: Mind you, I use the term efficiency, but that may not be a 100% good word to use for this. What that 75% is in mathematical terms is simply the instantaneous slope of the DR equation line (or the derivative for those who are familiar with calculus).

Loganisis
05-02-2011, 04:55 PM
Reading it, I think I see why I'm having a hard time. The work is centered on the fractional and I find it easier to look at the whole. How much rating is needed for 1% Well currently it's X, so to get from Y% parry to Z% parry I'll need more than X.

The exact numbers don't matter, since I know how to figure them out know, but looking at the 'cleaner' side, works for me. But I can see how it can open up to a lot of confusion. Since, for example, at 2000 parry ratting, it's basically 200 rating per % of parry after DR, but it will require more than 200 rating to get to the next % of parry because of the increasing DR on the next points.

Probably just going to help me since I never see things the same way as others. Thanks!

jere
05-02-2011, 05:11 PM
It can give you a ballpark.

If Y = 0.75x, then x=Y/0.75

So to get 1% parry after DR, you need slightly over 1.33% parry (before DR).

Multiply that by the conversion rating and you get 1.33333*176.7189 = 235.6 or about 236 rating. It will probably be slightly higher than that given that the 75% is an instantaneous point.

I think I had a "delta" rating equation at one point, I'll see if I can dig that up in my notes.

Airowird
05-03-2011, 04:06 AM
I looked at a delta-formula, but there is no clear cut way to define dx/dx' from the original formula without using advanced math stuff.

However, if you prefer the rating-way, here's my shot at it:
1/x' = 1/C + k/x with x = rating / A (A = 176.7189 for all plate tanks)
You are looking to know what the rating required is (defined as dr, with rating you have as r) at x' + 1%, so:

1/x' = 1/C + Ak/r => x' = (rC) / (r + AkC)
1/(x' + 1%) = 1/C + Ak/(r+dr)
x' + 1% = [C*(r+dr)] / [(r+dr) + AkC]
adding in the earlier found x'
(rC) / (r + AkC) + 1 = [C*(r+dr)] / [(r+dr) + AkC]
(rC)*[(r+dr) + AkC] + [(r+dr) + AkC]*(r + AkC) = [C*(r+dr)]*(r + AkC)
rēC + rC*dr + AkrCē + (rē + 2* AkrC + r*dr + AkC * dr + AēkēCē) = rēC + rC*dr + AkrCē + AkCē*dr
worked out everything & putting all dr on one side:
rēC + AkrCē + (rē + 2* AkrC + AēkēCē) - rēC - AkrCē = [rC + AkCē - rC - (r + AkC)*dr
(rē + 2* AkrC + AēkēCē) = [AkCē - (r + AkC)]*dr
dr = (r + AkC)ē / [AkCē - (r + AkC)]
dr = (r + AkC)ē / [AkC(C-1) - r]
dr = (r + 11088)ē / (716633 - r)

Could use some extra eyes checking the numbers, just in case I made a mistake somewhere :)
I did, but it's fixed now, thanks Booi & jere!

Just double-checked with Maple, Rating need for 1% avoidance =

(R + 11088)ē
-------------
716633 - Rwith R the rating you currently have. (This includes the DR from rating you have yet to gain).
Also, to find the rating for any n% avoidance gain:

(R + 11088)ē
--------------------------
11088(65.63144/N - 1) - R

Here are some numbers for the 1% calculation:
Rating -> rating required for next 1%
1000 -> 204.2
1100 -> 207.6
1200 -> 211.1
1300 -> 214.5
1400 -> 218.0
1500 -> 221.6
1600 -> 225.1
1700 -> 228.7
1800 -> 232.4
1900 -> 236.0
2000 -> 239.7
2100 -> 243.4
2200 -> 247.1
2300 -> 250.9
2400 -> 254.7
2500 -> 258.5
2600 -> 262.4
2700 -> 266.3
2800 -> 270.2
2900 -> 274.1
3000 -> 278.1
At 1481 rating, you are at 80% efficiency or you need to add 25% more rating to make up for DR.
At 1889 rating, you are at 75% efficiency or you need 33.33% more rating.
At 2341 rating, you are at 70% efficiency or you need 42.87% more rating.
At 2669 rating, you are at 66.67% efficiency or you need 50% more rating.

Note, however, that while the absolute numbers decrease, the relative damage reduction makes up for most of it.
At the same 2669 rating and completely no other avoidance, the 265 rating required for 1% extra avoidance still grants >0.76% of the damage reduction it would grant non-DR.
With a 4.4% miss chance and ratings equally divided between Dodge and Parry (for a total of 5338 ratings), you get 88.23% of the reduction it would give at 0 ratings... excluding Block.
So the DR formula provides roughly the same damage reduction per rating, regardless of current raiding tier (assuming you divide them among dodge & parry).

Theotherone
05-03-2011, 09:23 AM
This just makes my head hurt.

Airowird
05-03-2011, 10:05 AM
Sorry, was at school and was too busy sleeping through class to actually format it :P

Edit: I'm abusing my newly gained blackboard to find any errors now, will let you know if/when I do :)

Booi
05-03-2011, 01:05 PM
Maybe you can help me out wartotem.

Basically I took d/dr of x'
which gave me avoidance / avoidance rating at a given avoidance rating.
Simply inverting provides me with avoidance rating / avoidance as follows:

1000 -> 200.7906
1100 -> 204.1265
1200 -> 207.4899
1300 -> 210.8807
1400 -> 214.2991
1500 -> 217.7449
1600 -> 221.2182
1700 -> 224.7190
1800 -> 228.2473
1900 -> 231.8030
2000 -> 235.3863
2100 -> 238.9970
2200 -> 242.6352
2300 -> 246.3009
2400 -> 249.9941
2500 -> 253.7147

The issue is my ratings are always low balling yours.
I can tell that mine are incorrect because @0 rating, it suggests that I only need 168.943 rating to get the the first percentage point (not semantically true, but you get the point).

Actually, subbing 1000 as r for you, comes up as: 200.1 not the 204.2 you have listed. Is there something muddled in your loop/spreadsheet?
Yours also behaves oddly on the low end of rating values.

EDIT: actually i can't get your formula to throw out any of the values from your result. Either I'm misunderstanding how you intend for it to be used... hopefully you have a ctrl + v error.

EDIT: The issue seems to stem from the fact that I catch 1.0296% avoidance from the first 176.7189 avoidance rating in my original formula:
x' = r * C / (r + 176.7189 * k * C)

where:
C = 65.631440
k = 0.9560

It's weird that despite diminishing returns, it still yields more avoidance than the avoidance per rating stat - which is defined as: before diminishing returns.

Booi
05-03-2011, 03:31 PM
multiply both sides with 100 (to remove 1% issues):
Is this step correct?

The original formula gives avoidance in whole numbers, not as percentages.

jere
05-03-2011, 03:51 PM
Booi,

Taking the derivative gives you the instantaneous value. Like I was saying earlier, the derivative is taken over infinitesimally small steps (much smaller than 1%).

Inverting those points assumes that the DR rate at X% parry is the same value of DR rate at (X+1)% parry, which really isn't technically the case. The DR rate at X+1 is worse than at X, though only slightly, so you will see that the actual number will end up being lightly higher than what you calculated. I was trying to allude to this in my previous post.

Booi
05-03-2011, 03:54 PM
Booi,

Taking the derivative gives you the instantaneous value. Like I was saying earlier, the derivative is taken over infinitesimally small steps (much smaller than 1%).

Inverting those points assumes that the DR rate at X% parry is the same value of DR rate at (X+1)% parry, which really isn't technically the case. The DR rate at X+1 is worse than at X, though only slightly, so you will see that the actual number will end up being lightly higher than what you calculated. I was trying to allude to this in my previous post.

Right, and I say this explicitly in my post. I guess what you are saying is that Wartotem's method has no such draw backs?

Actually, it looks like I edited out the reference to instantaneous - still it is alluded to with the bracket rubbish about semantics.

EDIT:
so forget my rubbish, i still can't get wartotem's to work out.

jere
05-03-2011, 04:28 PM
Wartotem,

I ran the equations as well using your steps and came up with the same equation. However, as Booi suggested, you don't need to multiply by sides 100%, since multiplying by 1% is the same as multiplying by 1 (DR equation is in terms of percent). What you did was valid, but not really necessary.

I did your steps slightly different. I left X as X rather than making it r/conversion. I did that at the very end when I solved for delta_x. I didn't run all the values you listed, but the ones I tried came up with similar values.

The issue is my ratings are always low balling yours.
I can tell that mine are incorrect because @0 rating, it suggests that I only need 168.943 rating to get the the first percentage point (not semantically true, but you get the point).

Just wanted to make a comment on this. Actually, that doesn't suggest you are incorrect. The DR equation at low input values will actually give you more avoidance than you put in, rather than less. In game, they handle this by capping the DR equation output so it can't give more than is put in.. Essentially they use a piecewise function.

If it helps, your numbers do end up the same as mine when I run them using DR efficiency values and inverting them. Those that you listed are correct and should be lower than WarTotems in every case, because his equation uses the exact values at each point and calculates the difference while the other method assumes the same DR efficiency for both points on the line.

Booi
05-03-2011, 04:41 PM
Bouncing through wartotem's method I find:

a = 176.7189
C = 65.631440
k = 0.9560

-(r + akC)^2
d = ----------------
(r + ak(C-C^2)

or

(r + 11088)^2
d = ---------------
(716633 - r)

I could be wrong.
I've been wrong a lot lately.

I might have run my delta backwards, I'll have to check after raid. anyways:
1000 - 204.1822
1100 - 207.6035
1200 - 211.0537
1300 - 214.5327
1400 - 218.0408
1500 - 221.5777
1600 - 225.1437
1700 - 228.7386
1800 - 232.3624
1900 - 236.0153
2000 - 239.6972
2100 - 243.4081
2200 - 247.1481
2300 - 250.9171
2400 - 254.7151
2500 - 258.5422

Airowird
05-03-2011, 10:45 PM
I took the rating needed for the next 1%, rather than the derivate (that would be way easier :P).
Also, yes, the DR formula gives you more avoidance than pre-DR numbers at 0 rating (up to 10% extra or so, I believe)
And the 100% thing was because I didn't want to do it in the fraction later on, was easier to do it there in the format I posted it in.

PS: @Booi: It's [r - ak(C - 100Cē)] to be correct, because (r + ak(C-Cē)) would result in a positive value, making d negative.

Booi
05-04-2011, 12:22 AM
and this formula is what then?

Rē + 221.76R + 12294
----------------------
7166.33 - R

I'll go over my signs tomorrow. I'm sure I just mixed something up somewhere along the line.

Airowird
05-04-2011, 01:40 AM
gah, made a typo myself, it's [r + ak(C - 100Cē)] ofcourse (It's the 100Cē I was pointing out).
It's because the 1/C term in the DR formula is never in %, so using avoidance in percentiles (0-100 range) rather than it's mathematical 'real' value requires you to use a different C (100 times bigger, so the relative values remain the same).

jere
05-04-2011, 04:07 AM
It's because the 1/C term in the DR formula is never in %, so using avoidance in percentiles (0-100 range) rather than it's mathematical 'real' value requires you to use a different C (100 times bigger, so the relative values remain the same).

That statement confuses me. C is already in percentage form ( 65.something ). It's not in decimal form (of course neither is the input percentage). Either way, you don't need to multiply the equation by 100 at all. Multiplying the DR equation by 1% is exactly the same as multiplying by 1 since the inputs are all in percentage from the start, so the 1% just goes away.

Airowird
05-04-2011, 06:53 AM
Well some people use 0.65etc and some use 65.something, hence I was making sure Booi was using the right one.
Regardless, it should be 7166.rounding, and not a number 100 times larger, which would result in totally skewed results.

Booi
05-04-2011, 07:22 AM
I'm not really sure how it "skews" my result - my results are posted and they look identical to yours?

As for the negative, did you catch the negative in the numerator of my equation? My formula is resulting positive values. I double checked (not triple checked) my algebra, and it looks fine on my end. The presentation was just the result of too much control's theory.

Editing my above post to include:
C = 65.631440
k = 0.9560
a = 176.7189

I can rearrange it if it makes you happier. I guess it looks prettier this way, and it maintains the form of the the substituted version.

(r + akC)^2
d = ----------------
(ak(C^2 - C) - r)

where:
C = 65.631440
k = 0.9560
a = 176.7189

which again, yields:

(r + 11088)^2
d = ---------------
(716633 - r)

EDIT:
Wartotem's post for the General Form (http://www.tankspot.com/showthread.php?75432-Understanding-diminishing-returns-A-closer-look-(-HOW-DOES-IT-WORK)&p=505524#post505524)

Airowird
05-05-2011, 07:33 AM
Hmmm ... found my error: A = 17671.89 if you use the mathematical values (namely ~17672 rating = 100% pre-DR avoidance)
And that would end up with the same values you found. Thanks for the PoV, would've kept spreading mistakes without ya :)

Airowird
05-05-2011, 01:00 PM
There, updated my post here (http://www.tankspot.com/showthread.php?75432-Understanding-diminishing-returns-A-closer-look-(-HOW-DOES-IT-WORK)&p=505524#post505524) with about all the math/data on it, as well as a formula for n% avoidance
Should provide you with an easy access to finding out your rating needs for unhittability once you come close :)

Booi
05-05-2011, 09:21 PM
Wartotem, you're actually linking to my thread, not your own. I did edit my last post to link to yours as well, since yours has the generalized version.

And np on the pov, thanks for putting up with my ramblings along the way.

Airowird
05-06-2011, 02:13 AM
Haha, was too fast linking, fixed it now :)
It was as much rambling as I did I guess, remember that "No problem can be solved within the mindset that created it."

truculent
05-24-2011, 01:48 PM
/Cheer!