test content
Logo
What is the Arc Client?
Install Arc
Options
Diminishing Returns
tk79
Member Posts: 1,020 Arc User
This is an attempt to align knowledge about the definition of Diminishing Returns within the scope of the STO game.
-- Definition --
In economics, Diminishing Returns (DR) relates to the decrease of the marginal gain per unit added to a production process. However, that definition dwells into factors that are not strictly related to math. For example, adding more workers to a job that doesn't have room for all of them in an office.
In STO, the marginal gain per unit is purely mathematic. You don't have constraints like emotions (stressed out workers working in a small lab) affecting the gain per unit and the final productivity. Therefore, the *entire* economic definition of DR can not be applied to our case, but the purely mathematical part mostly can.
-- Gain per Unit, and Perspective* --
In STO, we have a BASE value that is enhanced by a BONUS PER UNIT. The bonus is constant, for example, a purple Tactical Console that adds 30% to base damage.
Depending on perspective, one might say that Tactical Consoles have or do not have diminishing returns.
Using arbitrary numbers, let's say BASE is 200, the BONUS PER UNIT is 30%, and QUANTITY is 3, incrementally seeing the gains as we add units:
BASE + (BONUS PER UNIT * QUANTITY)
200 + (30% * 1) = 260
200 + (30% * 2) = 320
200 + (30% * 3) = 380
The final number, 380, is a straight 90% (30%*3) increase over the BASE of 200.
Hence, you might say Tactical Consoles do not have Diminishing Returns.
But that's because our perspective is based on the BASE value.
When you shift your perspective into the INCREMENTAL gains, you get about:
200 to 260 = 30% gain
260 to 320 = 23% gain
320 to 380 = 18% gain
Hence, you might say Tactical Consoles have Diminishing Returns.
However, when you try to prove a point (does <something> have DR or not?), you need to shift into a perspective that has more than one possible outcome.
Considering the premise that the BONUS PER UNIT is constant, the "INCREMENTAL gain" perspective only yields ONE possible outcome, which is: there will always be diminishing returns, no matter which values you use, all premises respected.
It's like a "constant function", always returning the same value regardless of input. If you use such approach to find out if something has DR or not, you might as well say that everything in the game has diminishing returns.
Which is not true. STO has many linear gains in different areas.
We shift back into our "gain over BASE" perspective. Then you might say that such perspective also has only one possible outcome, which is "always no DR". While it might be true, there are situations where the final value is affected by an explicit diminishing return mechanic:
-- DR Formulas --
There are a couple Diminishing Returns Formulas in the game.
The most outstanding one is used to calculate the final damage resistance value of your ship and personal armor (from STOwiki):
RES=(3*(0.25-(75/(150+DRM))^2))
RES = final resistance value, in percentage
DRM = damage resistance magnitude
Most equipment and skills add to your DRM. Our goal with resistance is to look at RES, not DRM, so if we consider three damage resistance consoles, each one adding +20 DRM, our progression is as follows:
20*1 DRM = 16.6% RES
20*2 DRM = 28.3% RES
20*3 DRM = 36.7% RES
The nature of the formula will diminish the return against the BASE over each item we add.
That said, looking at BASE values as our perspective can yield different outcomes, giving us a way to say if something has DR or not.
-- Reaching Infinity (aka Clarification by Extreme Examples) --
Let's say we could add an infinite amount of consoles to our ships, for the sake of better explaining DR in action.
Thanks to the Damage Resistance DR formula, there will be a point where adding resistance consoles will yield no benefits against the BASE number. The values in RED show DR at work at its best:
20*1 DRM = 16.6% RES
20*2 DRM = 28.3% RES
20*3 DRM = 36.7% RES
...
20*5 DRM = 48% RES
20*10 DRM = 61.2% RES
20*20 DRM = 69.4% RES
20*50 DRM = 73.7% RES
20*100 DRM = ~75% RES
20*1000 DRM = ~75% RES
20*10000 DRM = ~75% RES
20*<INFINITY> DRM = ~75% RES
Tactical Consoles, on the other hand, considering our previous arbitrary values:
200 + (30% * 1) = 260
200 + (30% * 10) = 800
200 + (30% * 100) = 6,200
200 + (30% * 1000) = 60,200
200 + (30% * 10000) = 600,200
200 + (30% * 100000) = 6,000,200
200 + (30% * <INFINITY>) = <INFINITY>
Because there's no DR formula being applied here, the final value will always increase, linearly, as we add consoles.
-- Conclusion --
I hope this post gives folks a better understanding on how to determine if something has Diminishing Returns or not, and that the arguments presented here are valid and make sense. I kept the examples simple because I think it gives a clearer image of how DR works, and to keep things in scope. DR debate is constant, and my hope is that we reach some sort of common point about how to approach DR in STO.
Feedback and constructive criticism always welcome.
(* Acknowledgement: perspective was a matter brought up by virusdancer in a few topics regarding DR in general, where I tried to explain, not so elaborately/clearly/friendly, the points that I have made with this post. I hope that these points can be better understood now.)
-- Definition --
In economics, Diminishing Returns (DR) relates to the decrease of the marginal gain per unit added to a production process. However, that definition dwells into factors that are not strictly related to math. For example, adding more workers to a job that doesn't have room for all of them in an office.
In STO, the marginal gain per unit is purely mathematic. You don't have constraints like emotions (stressed out workers working in a small lab) affecting the gain per unit and the final productivity. Therefore, the *entire* economic definition of DR can not be applied to our case, but the purely mathematical part mostly can.
-- Gain per Unit, and Perspective* --
In STO, we have a BASE value that is enhanced by a BONUS PER UNIT. The bonus is constant, for example, a purple Tactical Console that adds 30% to base damage.
Depending on perspective, one might say that Tactical Consoles have or do not have diminishing returns.
Using arbitrary numbers, let's say BASE is 200, the BONUS PER UNIT is 30%, and QUANTITY is 3, incrementally seeing the gains as we add units:
BASE + (BONUS PER UNIT * QUANTITY)
200 + (30% * 1) = 260
200 + (30% * 2) = 320
200 + (30% * 3) = 380
The final number, 380, is a straight 90% (30%*3) increase over the BASE of 200.
Hence, you might say Tactical Consoles do not have Diminishing Returns.
But that's because our perspective is based on the BASE value.
When you shift your perspective into the INCREMENTAL gains, you get about:
200 to 260 = 30% gain
260 to 320 = 23% gain
320 to 380 = 18% gain
Hence, you might say Tactical Consoles have Diminishing Returns.
However, when you try to prove a point (does <something> have DR or not?), you need to shift into a perspective that has more than one possible outcome.
Considering the premise that the BONUS PER UNIT is constant, the "INCREMENTAL gain" perspective only yields ONE possible outcome, which is: there will always be diminishing returns, no matter which values you use, all premises respected.
It's like a "constant function", always returning the same value regardless of input. If you use such approach to find out if something has DR or not, you might as well say that everything in the game has diminishing returns.
Which is not true. STO has many linear gains in different areas.
We shift back into our "gain over BASE" perspective. Then you might say that such perspective also has only one possible outcome, which is "always no DR". While it might be true, there are situations where the final value is affected by an explicit diminishing return mechanic:
-- DR Formulas --
There are a couple Diminishing Returns Formulas in the game.
The most outstanding one is used to calculate the final damage resistance value of your ship and personal armor (from STOwiki):
RES=(3*(0.25-(75/(150+DRM))^2))
RES = final resistance value, in percentage
DRM = damage resistance magnitude
Most equipment and skills add to your DRM. Our goal with resistance is to look at RES, not DRM, so if we consider three damage resistance consoles, each one adding +20 DRM, our progression is as follows:
20*1 DRM = 16.6% RES
20*2 DRM = 28.3% RES
20*3 DRM = 36.7% RES
The nature of the formula will diminish the return against the BASE over each item we add.
That said, looking at BASE values as our perspective can yield different outcomes, giving us a way to say if something has DR or not.
-- Reaching Infinity (aka Clarification by Extreme Examples) --
Let's say we could add an infinite amount of consoles to our ships, for the sake of better explaining DR in action.
Thanks to the Damage Resistance DR formula, there will be a point where adding resistance consoles will yield no benefits against the BASE number. The values in RED show DR at work at its best:
20*1 DRM = 16.6% RES
20*2 DRM = 28.3% RES
20*3 DRM = 36.7% RES
...
20*5 DRM = 48% RES
20*10 DRM = 61.2% RES
20*20 DRM = 69.4% RES
20*50 DRM = 73.7% RES
20*100 DRM = ~75% RES
20*1000 DRM = ~75% RES
20*10000 DRM = ~75% RES
20*<INFINITY> DRM = ~75% RES
Tactical Consoles, on the other hand, considering our previous arbitrary values:
200 + (30% * 1) = 260
200 + (30% * 10) = 800
200 + (30% * 100) = 6,200
200 + (30% * 1000) = 60,200
200 + (30% * 10000) = 600,200
200 + (30% * 100000) = 6,000,200
200 + (30% * <INFINITY>) = <INFINITY>
Because there's no DR formula being applied here, the final value will always increase, linearly, as we add consoles.
-- Conclusion --
I hope this post gives folks a better understanding on how to determine if something has Diminishing Returns or not, and that the arguments presented here are valid and make sense. I kept the examples simple because I think it gives a clearer image of how DR works, and to keep things in scope. DR debate is constant, and my hope is that we reach some sort of common point about how to approach DR in STO.
Feedback and constructive criticism always welcome.
(* Acknowledgement: perspective was a matter brought up by virusdancer in a few topics regarding DR in general, where I tried to explain, not so elaborately/clearly/friendly, the points that I have made with this post. I hope that these points can be better understood now.)
Post edited by Unknown User on
0
Comments
I'm not sure "incremental gains" is the best term for this; after all, marginal returns are also incremental. I've used the term "percentage returns" in the past, but I'm not sure that is the best term either.
While a linear function always exhibits diminishing percentage returns, an exponential function does not. I'm not sure what in STO exhibits exponential behavior though---possibly the effective HP gained from shield resistance stacking.
I understand that the definition of "diminishing returns" in economics is based on marginal returns. The problem is that the MMO community has adopted the term without giving it a formal definition. Most players use the term "diminishing returns" in a vernacular sense; that is, they use it in the same imprecise way that most people use words when they are not having a technical conversation. They probably don't have a precise mathematical idea about what they mean when they say it. Also, there are always new players who haven't seen the previous threads on the topic.
I'm not sure what you mean by "deterministic". I am familiar with the following uses of "deterministic".
deterministic vs. non-deterministic: for example, deterministic Turing machine vs. non-deterministic Turing machine
deterministic vs. probabilistic: for example, deterministic algorithm vs. randomized algorithm, or classical mechanics vs. quantum mechanics
If you actually graph out the effects of all these things, you will see a linear gain on everything. Damage increase from consoles and skills, strength bonuses to abilities via consoles and skills (more specifically science based), hull and shield bonuses via equipment and skills, all that fun jazz. All linear bonuses. No change to how much they give in bonuses, regardless of how much you add.
But as soon as you even BREATHE damage resistance, you immediately see a logarithmic curve. For those not so savvy in math, it means early on, it gives large bonuses, but as you add more, it gives exponentially less (hence why log curves are called inverse exponential curves).
So does that mean diminishing returns? Just something to think about.
Honestly, I think it's better to just let people know exactly what things do, instead of trying to call them diminishing returns, not diminishing returns, blah blah blah etc. Simply because arguments about whether or not they are or aren't something can go on for weeks and pages and posts etc. (and have been proven to do so on many occasions on these forums)
The damage resistance curve is not logarithmic; it is an increasing concave function that asymptotically approaches an upper bound. A logarithmic function has no upper bound.
I have tried this approach before. While I still think it is the best approach, it doesn't necessarily extinguish the arguments over diminishing returns. Someone else will always start the argument, even if you don't. The problem is that most people have heard of diminishing returns (whether from other games or from other people in this game), but they haven't actually thought about what they mean mathematically when they say it.
I was trying to keep it simple and relatively easy to understand.
Welcome to the internet lol...
i actually think this should be a sticky post. very well explained, especially the part of the perspective and how many people wrongly look at the INCREMENTAL gains and claim that tac consoles have diminishing returns...which is utterly wrong.
The term "logarithmic" has a formal mathematical definition though, and its use is not limited to mathematics. It is used in the same sense across many scientific and engineering disciplines, so I feel that this is one definition worth fighting for. On the other hand, "diminishing returns" seems to be an economics term adopted by the MMO community. I am not aware of its use in mathematics or other sciences.
Diminishing returns are pretty common in life...one just needs to look around to see the countless areas where simply adding the same thing again or more of the same thing does not result in the returns one previously expected. It's basically life...
0 tac consoles : 1034 - 413.6
1 tac console : 1126.5 - 450.6 - 8.9% - 8.9%
2 tac console : 1219 - 467.6 - 17.8% - 8.2%
3 tac console : 1311.4 - 524.6 - 26.8% - 7.6%
4 tac console : 1403.8 - 561.5 - 35.7% -7.0%
5 tac console : 1496.3 - 598.5 - 44.7% - 6.6%
Where is: damage - base damage - overall increase in damage - increase of damage per console based on last number.
This looks like strait forward increase in DPS by 8.9% per console based on damage without consoles.
Diminishing results might seems to you if you are expecting to gain same DPS increase based on your current DPS in tooltip
While diminishing returns are common in life, I'm not sure that the term "diminishing returns" is so common. You might see a newspaper use "diminishing returns", but it is usually in an economics context. Even then, I'm not sure that the author has a mathematical meaning in mind when he writes "diminishing returns". A journalist writing an article about manufacturing might use the term, because he heard an economist he interviewed use it, and he vaguely remembers hearing about that in his introductory economics class in college.
Terms not tossed around - it's not part of the common vernacular in that sense - but we see it in everything from trying to get to work faster, buying presents for a loved one, and our work product whether in school or on the job...it's pretty much everywhere.
edit: It's kind of funny thinking about the various things in science and math where it's demonstrated, but it's almost never referred to as such outside of economics.
I've changed my mind after searching news.google.com for "diminishing returns". There is some evidence that "diminishing returns" has passed into the vernacular. Here are some of the search results.
http://finance.townhall.com/columnists/politicalcalculations/2014/04/07/diminishing-returns-to-higher-education-n1819564
http://www.forbes.com/sites/greatspeculations/2014/04/02/law-of-diminishing-returns-hits-social-media-companies/
http://blog.al.com/wire/2014/04/tornado_watches_not_effective.html
http://www.huffingtonpost.com/mary-manning-cleveland/congressman-bill-foster_b_5101736.html?utm_hp_ref=business&ir=Business
http://www.bellinghamherald.com/2014/04/08/3576583/sam-mellinger-time-to-stop-dawdling.html
http://www.eenews.net/stories/1059997508
http://www.lsureveille.com/entertainment/film/the-great-decline-of-quentin-tarantino/article_ff0a2e4c-beaa-11e3-adc2-0017a43b2370.html
http://bleacherreport.com/articles/2018516-star-players-vs-star-coach-which-is-more-important-for-success
I would divide the usage of "diminishing returns" from the articles above into roughly three categories:
1. The author uses "diminishing returns" in the same way an economist would.
2. While the statement contains economic content, it is not entirely clear what the author means by "diminishing returns".
3. The author has no idea what "diminishing returns" means and is using the term because he thinks it sounds good.
The above categories are not meant to be exact, as the usage of "diminishing returns" seems to lie on a continuum. For an example of the last category, see the following excerpt from the article on Quentin Tarantino:
Buy 1 rose. Buy 2 roses. Buy 3 roses. As you're buying roses, eventually the additional roses won't result in any greater level of appreciation for the gift.
vs.
Buy a dozen roses. Next year the same. Next year the same. Eventually there will be a diminished return on the same gift. One could say that it is a matter of perspective, that as a whole there is diminishing returns with them taken as a whole - where the period is spread out over years...or it could just be viewed as less of a return (thus a diminished return) in each case.
Where one can run into taking things for granted or an increase of expectations...along the lines of somebody could get a 5/5 on their performance reviews year after year, and suddenly find themselves with a 4/5 instead - when they've done the same excellent job they have in the past. The expectations have increased...so there's a diminished return on the effort.
Course, there's also the recent "craze" (for something that's been around as long as I can remember - and - the reason why folks have done what they've done forever) about muscle memory and diminishing returns...thus changing up the exercise that one is doing. Yeah, ye olde life circuits and even before then - weren't just about working different sets of muscles in different ways, it was because it was all but pointless to continue working certain muscles beyond a point.
But in the end, I do feel it comes down to that differentiation of what a diminished return might be and what diminishing returns entails. Something can have a diminished return without having diminishing returns...or is it just a matter of perspective? The point in time or the frame of time that one is viewing it in?
In the end, meh - it's hard to refer to diminishing returns in most cases outside of trying to verify that's what the other guy is looking at, so you can make sure that they're looking at the base math correctly...
Tom: There's diminishing returns with Tac consoles!
Jerry: Where are you seeing that?
Tom: My final amount grows by a smaller amount with each one added.
Jerry: Yep, that's going to happen with anything. Is each one adding the same actual amount though? Is it giving you +X damage?
Tom: Er, well yeah. What do you mean that's going to happen with everything?
Jerry: Got a handful of pennies? Take one and add a second, eh? That second penny increased the number of pennies you have by 100%, right?
Tom: Yeah.
Jerry: Add a third penny. You've got three pennies now, but that third penny only added 50%.
Tom: Exactly!
Jerry: But it was still a whole penny you added, right?
Tom: Er...yeah.
Jerry: Then you're all good...have a nice day.
I did some research and I realized I used the wrong term. I was looking at "deterministic algorithms" that I thought produced the same output regardless of input, but I got the input part mixed up. Thanks for pointing it out.
The term I was looking for was "constant function".
STO Screenshot Archive
Yes, that is correct. While I understand what you mean, a new player asking "Do tac consoles have diminishing returns?" might not. Many people asking that question have heard of diminishing returns, but they haven't necessarily thought about what "diminishing returns" means in a precise mathematical way.
It's really important to be clear or certain what is measured and compared when you try to take meaning from statistics. Which is often not done, sometimes intentionally, sometimes unintentionally.
Without directly looking at diminishing returns. Let's say we talk about damage reduction in percentage of damage taken away.
The move from 50 % to 75 % might sound just as powerful as the move from 25 to 50, or from 0 to 25. obecause it's 25 points difference. But it's not that simple.
1
If something has 25 % DR, you need to deal 113 damage instead of 100 damage for the same efect. (33 damage difference)
If something has 50 % DR, you need to deal 200 damage instead of 100 damage for the same effect. (77 damage difference to 25 DR and 100 damage difference to 0 %)
If something has 75 % DR, you need to deal 400 damage instead of 100 damage for the same efect.(200 damage difference to 75 % or 300 damage difference to 0 %)
Now, if you consider the above and the designers make some kind of complicated formula for diminishing returns that mean that if you spend the points to get 50 resistance, you need to spend 2 times as much to get to to 75 instead, some player might say "nah, 75 is much too expensive with all those diminishing returns", but in truth, the effect seems quite reasonable - you last twice as long as with the DR bonuses for the 50 %, so of course you should pay twice as much.
Extending off of this, which to me is the best choice, instead of explaining the long and convoluted discussion on diminishing returns, if a player asks if it has diminishing returns, why not just tell them exactly what it does?
If someone asks if tac consoles have diminishing returns, just tell them that it only boosts base damage. If someone asks if engi consoles have diminishing returns, just tell them it boosts resistance, but each consecutive console gives less of a bonus. If they say "But that's diminishing returns!", direct them to one of those obscenely long threads of 10 players arguing about it over 8 pages and 75 posts.
Simple enough no?
Like if a tac console when examining that actually stated: Adds +x to beam array, +x to dual cannon, etc etc.
And if you did it on your beam array equipped it would list..
Base Damage Value: 100
Tactical Console: +x
Tactical Console: +x
Weapon Skill: +x
etc etc etc
Would clear up so much confusion I would thinks. Telling someone +X% without bother to say what it is a percent of is basically pointless. And at times even worse, misleading.
Yeah true. Or it would be better if the tooltip actually explained that tac consoles only add to base damage, engi consoles added less each time with a cap at 75%, science consoles... etc.
But... that would involve too much work on Cryptic's part methinks.
While I'm sure that there are people who specialize in distorting the facts to fit their own preferred interpretation of the data, my view is that the data doesn't lie---only people do. I'm not sure what your point has to do with the present discussion though.
When the average person equips something that states: "+20% Damage" and their damage does not increase by 20% they tend to get confused. Absolutely nothing in STO properly explains how it works in detail mathematically. Nothing. Unless you resort to your own testing or research outside of the game you will not be able to find the answer. Furthermore finding an actually official 'Cryptic Endorsed' explanation for most mechanics is impossible and you must rely upon what others tell you. That lack of a central authority on how the game does its math leads to confusion among it's community.
So we test, we experiment, and we attempt to explain the best we can so others can understand. But we are all human, and we are all players who can only see the reaction of the game systems. We are not privy to the actual 'under the hood' formulas and that leads to errors and confusion. Especially considering that we can only determine results and can only speculate on how those results are created and if they are working as intended or not.
Heh, almost none of it actually does what it says it does. :P
That's basically the problem.
The +30% Tac Console is not adding 30% damage like it says.
The +20% Field Gen is not adding 20% shield cap like it says.
Even the +X Power Eng Consoles don't add +X Power...because of efficiency, etc, etc.
So there will be the folks that read the tooltips - see they're supposed to be getting something - they don't get it...and endless discussion follows.
Improved tooltips wouldn't end all the discussion, because there would still need to be the explanation of what it means.
Tom: So this adds +30% base damage? What's that mean.
Jerry: Rambles on for a bit.
Tom: So this doesn't actually add +20% shield cap? What does it add?
Jerry: Rambles on for a bit.
Tom: Something...
Jerry: Rambles...
Etc, etc, etc.
And even then, you're still mainly working with things where there's some info coming back...other things? Well, it's from folks testing - so either the folks have gone through the manual testing themselves or they saw one of the threads in the forums on it.
Things like shield damage reduction, shield regeneration, or the Dyson Rep stuff with hull damage resistance where you get to dance with both DRR->DR conversion as well as the shield damage reduction formula...
And even when you get folks going through stuff like that, you come back to the simple stuff of damage and you're looking at +10% X is not the same as +10% Y - because one is a boost to damage strength and the other is a bonus boost...which isn't even taking into consideration where the weapon ability bonuses/critical severity come into play before running into bleedthrough/penetration - shield damage reduction - hull damage resistance.
You get somebody new looking at it - even if they've played other MMOs; there's still a damn good chance they're going to go WTF? over it...lol...meh...lol.
edit: Still, part of it is just going to come down to some folks not paying attention. Like the "skills have diminishing returns" - because folks never looked at 1-3 providing +18, 4-6 providing +10, and 7-9 providing +5 skill. It's right there, Cryptic actually provided that info...click a skill in the skill window, that other window pops up - it's right there. But folks don't read...and there's not much you can do about that outside of trying not to be too cruel when pointing out they need to L2R.
Normally in gaming when we say diminishing returns it means that as you increase x the value of y becomes less. With tac consoles the value of y is CONSTANT. If tac consoles had diminishing returns the value of y would be less. Sure the value of z will not be what some would expect. But that's only because it only increases base damage. If it increased our overall damage then we'd never be discussing DR for tac consoles. But there is NO DR for tac consoles period. Anyone that says otherwise is in error.
As regards hull resistance we know there is a DR for that. Heck we even have the math for it. Well the old math via the old wiki that is. If we include rep passives it should instead be as follows.
DR=[(3*(0.25-((75/(150+R+AHH))^2)))]+[(3*(.25-((75/(150+AHR+CCR))^2)))*(1-(3*(0.25-((75/(150+R+AHH))^2))))]
Where DR=Diminished Resistance. Resistance % as shown under ship/defense
R=Resistance, such as accolades, consoles, skills, etc. as in normal resist be it as a percentage or just a number
AHH=Active Hull Hardening (Currently this is giving the wrong value on Holodeck and is ((1-hull%)*50) This is to be fixed for S9 and will be ((1-hull%)*75) )
AHR=Advanced Hull Reinforcement
CCR=Crucial Component Redistribution (for S9 and is assumed until testing proves otherwise)
I seriously need to update that old wiki. :rolleyes:
There are several factors that the wiki formula doesn't take into account. There are special exceptions like the Ablative Generator, which gives about 90% damage resistance. I think the most important factor left out is damage resistance debuffs, but I'm not entirely sure how that works. I've tried to make sense of virusdancer's numbers in this post. The results are very odd if you start with positive damage resistance and then apply damage resistance debuffs. I wouldn't be surprised if Cryptic has some bugs in the calculation.
The Intreped's Ablative Generator +900 resist armor goes into my equation at the same spot Advanced Hull Reinforcement goes. Although it's an assumption as i've not tested it personally. You can get up to 93.4% resistance as shown under ship/defense. Assuming you were already at 75% resistance. Which quite frankly is very improbable. This agrees with the dev responses where they said you could get approx 90% resistance. I don't believe they were being precise and just shooting a semi close number. So i'm fairly sure i'm correct. So it looks like this.
DR=[(3*(0.25-((75/(150+R+AHH))^2)))]+[(3*(.25-((75/(150+AHR+CCR+AG))^2)))*(1-(3*(0.25-((75/(150+R+AHH))^2))))]
Where DR=Diminished Resistance. Resistance % as shown under ship/defense
R=Resistance, such as accolades, consoles, skills, etc. as in normal resist be it as a percentage or just a number
AHH=Active Hull Hardening (Currently this is giving the wrong value on Holodeck and is ((1-hull%)*50) This is to be fixed for S9 and will be ((1-hull%)*75) )
AHR=Advanced Hull Reinforcement
CCR=Crucial Component Redistribution (for S9 and is assumed until testing proves otherwise)
AG=Ablative Generator
As regards negative resist. I understand it's supposed to be 1 for 1 until you are actually at 0 resist. From there i'm still unsure how it works. You would think that you'd enter in my formula where it says (R) the negative value. So it would be (+R-R) where -R=the negative resist amount. However the devs posted math does not show it this way. They instead add everything up. Once that's done then they do negative resist. Assuming they're even using the old math in which based on my formula clearly shows they are not. Until we can get an updated formula from them it means we have to come up with formulas ourselves, like i did for the positive values. I guess i could make another spreadsheet and use the math posted by the devs. But i don't think it'll match what we see in game. But who knows. It's not really something i'm focusing on. I'm more concerned with how much resist we can get for our ships via consoles and passives. So i may never get around to it.
Looking at the post you linked i can only say that there is no rounding issues. If it does not match then look elsewhere. I assumed a while back that rounding was causing a problem. But after testing and trying several different formulas my formula matches exactly given any positive resist amount. I don't round up or down. I only round mine at the end to have it show 1 decimal point as ship/defense does.
I don't have the Ablative Generator, so it's not something I can test. My guess is that the damage resistance from the Ablative Generator stacks with your other damage resistances using adjudicatorhawk's rule, or equivalently, the shield resistance stacking formula. What I'm not sure about is if the 900 damage resistance rating is first converted to a damage resistance using a diminishing returns formula. The wiki formula is actually a simplification of Geko's formula assuming that the maximum damage resistance is 75%. If you assume a maximum damage resistance of 90% and put 900 damage resistance rating into that formula, you still get something close to 90%. So it's hard to know exactly what's going on without testing it.
I agree that the discrepancies that virusdancer saw are not due to rounding. Either there's some part of the calculation that we don't understand, or Cryptic actually has bugs in the calculation.
And to answer your question in regards to being unsure if the Ablative Generator uses DR. Yes it should. But it also uses the shield resist formula. You can break down my formula as such. The formula is in 3 parts. Part 2 is where AHR, CCR and AG are entered into the formula. As you can see these 3 combine yet are not a part of part 1 of the formula. Part 1 is capped at 75%. Part 2 is also capped at 75%. Part 3 combines with part 2. They are then added together. Part 3 is more or less the shield resist formula. Basically if part 1 is 75% then only 25% of part 2 is added to part 1.
Part 1=simplified original formula. Well except the ((1-hull%)*50) for AHH was added.
DR=[(3*(0.25-((75/(150+R+AHH))^2)))]+
Part 2=The exact same formula except different things go here which i'll call the exceptions
[(3*(.25-((75/(150+AHR+CCR+AG))^2)))*
Part 3=shield resist formula Basically this is part (1-part 1) or 1-60%=40% for example
(1-(3*(0.25-((75/(150+R+AHH))^2))))]
We know that R is eng resist consoles, brace for impact, subspace field mod, engineering fleet, accolades. Basically most all resistance goes here. The exceptions are in part 2 and there may be other exceptions that i haven't included. In fact i'm fairly sure there are other exceptions.
So the only question left is what other exceptions are there to include in part 2.