The Redux Mythology

[imported_Kranar]

I have decided to read the DF Redux section on the official boards, and was surprised to see that people still think that going from 85 percent redux, to 86 percent redux, isn't a big deal. That it's not worth it to train for redux since you're only gaining 1 percent.

Well... I had to respond, and dispell this myth, and so I shall repost my response over here.

[imported_Kranar]

<< (unless you wanted to get to level 500 for another 2%, waste and boring IMO). >>

I think this thinking results from a false interpretation of what a percentage is.

When you deal with a point based system like AS, or DS then yes, every single point increase is weighted equally. That is, if you go from 1 point to 2 points, your gain is linearly equal to going from 10000 points to 10001 points.

However, when dealing with a percentage, such thinking is seriously flawed and leads to erroneous conclusions. For example, going from 90 percent redux to 91 percent redux is FAR SUPERIOR than going from 1 percent redux to 2 percent redux. Infact, the benefit is approximately equal to going from 1 percent redux to 12 percent redux. You may think it's just 1 percentage point, but that 1 percentage point is incredibly valuable at that point! In the same way... going from 99.8 percent redux to 99.9 percent redux is far more valuable than going from 0 percent redux to 50 percent redux, as far as the end roll is concerned. Even though the difference is only .1 percent, at that point, 0.1 percent difference is more valuable than a 50 percent difference.

And as I'm sure you guys can figure out, if you think long enough about it and so some calculations... going from 99.9999 percent redux, to 99.99991 percent redux, is FAR MORE SUPERIOR than going from 0 percent redux to 99.9999 percent redux, even though the increase is only .00001 percent! Once again, superior as far as the end roll is concerned. And finally, going from 99.999999999999 percent redux to 100 percent redux is INFINITELY superior than any other increase imaginable, even though the difference is less than a trillionth of a percent. Of course the fact that it's infinitely superior also makes it impossible (since it requires an infinite amount of primaries)

So in the future... instead of simply saying: "Ah well... it's just one percentage point... no big deal", you have to consider where that one percentage point lays. Is it a one percent increase from 85 to 86? Or is it a one percent increase from 15 to 16?

You will see, that there is a massive difference between the two. Going from 85% redux to 86% redux nets a much bigger benefit than going from 15% redux to 16% redux.

[imported_Kranar]

And just incase anyone is still confused on what I meant... let's take an example... In this example we're going to calculate the end roll per damage. We shall call this number, redux points.

Let's say I have a weapon that has a damage factor of 1.0 against skin armor.
I then have 1 redux point. For every 1 point above 100 in the end roll, 1 damage is dealt to me. Now let's say I have 50 percent redux, well now I have 2 redux points, for every 2 points above 100 in the end roll, 1 point of damage is dealt to me.

Next... I train in many primary skills and manage to increase my redux to 51 percent; my redux points increases to 2.04. I increase my redux by 1 percent, and my redux points increase by 0.04.

Well... let's see what the redux point increase is when I go from 85 percent redux to 86 percent redux. At 85 percent redux, I have 6.7 points, at 86 percent redux it's 7.1 redux points. An increase of 1 percent nets me an increase of .4 redux points. That's much better than before, where an increase of 1 percent only netted 0.04 redux points.

And now let's look at 95 percent to 96 percent. At 95 percent I have 20 redux points, at 96 percent I have 25 redux points, a difference of 5 redux points. That difference is MUCH better than it was when I went from 50 percent redux to 51 percent redux, even though the percentage increase is only 1 percent.

And finally... just to get my point across... if theoretically someone had 99.9 percent redux, they would have 1000 end roll per damage points. If they increased their redux by just .09 percent, they would have 10000 redux points. So .09 percent of a difference increases their end roll per damage points by 9000!!!!!

Now you see... 1 percent of a difference can be a VERY BIG difference depending on what the interval is... heck... 0.09 percent of a difference can be big!

[longshot]

Well, duh!

[imported_Kranar]

Someone was skeptical, so I decided to post a proof of it:

The proof requires some very elementary calculus. Infact the calculus is so elementary I wish I didn't need to use it to prove this finding, but alas there is no way around it.

We begin by expressing redux as a function f(x). I am using the function posted a long time ago by Ophion rearranged so it can be evaluated easily. I do realize that this function is only an approximation, however, the redux function is a hyperbola, and what I'm about to demonstrate can be applied to any hyperbolic function. So while the actual specifics of what I'm going to display is only an approximation, the conclusion is not.

f(x) = 100 - 35000 / 1.7x
x = number of primary ranks

Since secondary ranks are negligible for the sake of this proof, we have excluded it from the equation.

Now we look at our second function, the damage per end roll function, which we will call g(x).

g(x) = 100 / [100 - f(x)]

g(x) is set up under the assumption that the damage factor for a weapon is 1.0. This can easily be changed and the result remains the same. Basically, you just replace f(x) with your redux percentage, and g(x) spits out the end roll per damage.

Now... we substitute f(x) into g(x) so that g(x) is in terms of primary ranks. The result is a function that spits out someones damage per end roll based on how many primary ranks they have. After simplifying and factoring, we end up with this:

g(x) = 17x / 3500

And voila... how simple a formula that is. You just substitute x with how many primary ranks you have, and g(x) will tell you your end roll per damage. Now we know that redux only kicks in after you have a certain amount of primary ranks. That amount of primary ranks happens to be 206. So g(x) only works once you have atleast 206 primary ranks.

Now the derivative part...

g'(x) = 17 / 3500

g'(x) is the derivative, a linear function, and a very simply linear function at that. And from the above, one can easily find the second derivative:

g''(x) = 0

Zero... If g''(x) were less than 0, then there would have been a diminshing returns effect, if it was greater than 0, then the more primary ranks you put in, the more you would get out. But since it's exactly 0, every single primary rank you put in, gives you exactly the same benefit.

Just like every rank of physical training gives you a constant amount of health points, every primary rank gives you a constant redux bonus.

Therefore in my humble opinion, one has a better understanding of their redux bonus, by evaluating the end roll per damage, instead of evaluating the percentage.

The final function I present is R(x), a redux formula that anyone can use, that looks at end roll per damage, and not at the percentage.

R(x) = DF * (17x + 6y) / 3500
x = number of primary ranks
y = number of secondary ranks

That formula, as you can no doubt tell, illustrates that redux is not subject to diminishing returns.

With Gemstone IV coming along, I'm sure the weighting of primaries (1.7) and secondaries (0.6) will be changed, as well as the 350 factor. However, all these changes can easily be incorporated and so unless redux uses an entirely different type of function (a function other than a hyperbola), then what I stated will still be true.

[Edaarin]

Down with redux.

[Bobmuhthol]

Math rox0rz your world. You got pwned my math.

[Suppa Hobbit Mage]

So the argument wasn't going your way on the official boards so you decide to spam these boards with the EXACT same messages?

[imported_Kranar]

<< So the argument wasn't going your way on the official boards so you decide to spam these boards with the EXACT same messages? >>

Do you have any idea what you're even talking about because the above has got to be one of the dumbest responses I've read to date. Not only is it a baseless assumption... but it has nothing to do with anything and shows your clear ignorance of the contents posted. The only explanation I can think of is that you were too stupid to read any of it and so decided to post some garbage in frustration.

At any rate... if you want the responses here they are:

I made the first two posts (before the proof) then Psycat responded with the following:
------------------------------------------------

I think people would be more interested to know the practical side of it. Redux, like so many other systems in GS3, falls prey to diminishing returns. Sure, each percentage point is worth more the higher you go, but it becomes increasingly difficult to make significant gains. Eventually, the difference between one warrior and the next is effectively nothing - no matter how hard you train for redux.

Psycat

-----------------------------------------------------

Then I posted the proof, then the following response was made by Edshras33:

Heh, you should know better than to post math in a folder for warriors

- a wandering rogue who forgot all the calculus he learned in high school after 3 months.
---------------------------------------------

Then I responded:

<< Heh, you should know better than to post math in a folder for warriors >>

Hah! Yeah, but reading the math is entirely unnessecary. I just put it in there for those who remain skeptical and needed a proof.
-------------------------------------------------

Then Furryfoot:



Reply

Ah, if only we had the full differential equation, now THAT would be some fun math ;)

--Furrowfoot

"For what is a man, what has he got?
If not himself, then he has naught.
To say the things he truly feels;
And not the words of one who kneels.
The record shows I took the blows -
And did it my way!"

------------------------------------------------

Then Psycat:

I think you're on to something. However, I'm noticing a problem. Now maybe this is because math isn't one of my strong points, but when I look up my own redux according to your function I get 78.37%. Probably a little on the high side, but I haven't checked in awhile. The problem is, when I check a warrior of the same level with 12 primary ranks per level to my 8.5, I get 84.68%. At 160, that would be about 90% at 12 primary ranks per level. I'm pretty sure these calculations are way off the mark.

What do you make of it? Could there be a diminishing return effect for primary ranks per level in excess of 8? Or am I just botching the formula?

Psycat

----------------------------------------------------

Now if you can show me where the argument isn't going my way... or where the argument is supposed to go... feel free.

Otherwise the only one spamming worthless posts here is you.

[Edited on 7-31-2003 by Kranar]