Understanding diminishing returns - A closer look ( HOW DOES IT WORK)

[truculent]

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]

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]

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]

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]

@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]

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]

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]

this information listed above is current?

[Airowird]

It is as current as it can be. Whatever that means

[Bigbad]

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]

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]

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]

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?

[Bigbad]

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]

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]

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 = 742.777824/74.06106525
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?

[Bigbad]

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]

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]

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]

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!