Ahem. Now, where was I? Heh.

I think we (or at least I) lost interest in trying to figure out what your concept of diminishing returns is. Mind explaining that? Also, why is the word annealing in the topic title?

I'll take a stab at interpretating it.

I think there is misinterpretation of the graphs seeing how none of them label the x or y axis (except 1), which is very important because depending on the equation, one of the axis will show diminishing returns and one will show exponential growth.

Most people graph x along the horizontal axes and y along the vertical axes. In AngleWyrm's graph, he uses x along the vertical axes.

This graph may look like diminishing returns but it is in fact showing exponential growth!

f(x) = x*x Shows exponential growth
f(x) = x^(0.5) Shows diminishing return ( also known as f(x)=sqrt(x) )

Switching the x and y axes changes the direction of the graph but the inputed value is still X!

Quote:

Original post by JasRonq You know, I'm not too good with math, but I punched the calculator a few times and it tells me you might be wrong here. 0.1*0.1=0.01 0.1*0.2=0.02 0.8*0.8=0.64 0.8*0.9=0.72 So if I have a skill dictated by two variables multiplied together. Raising one of two skill, both at 10%, up to 20% gives me a 1% overall increase in the skill. Raising one of two variables, both at 80%, up to 90% gives me an increase in the overall skill by 8%. I could be crazy here, but that sort of seems like increasing returns.

I'm surprised nobody picked up on the obvious calculation error in your example.

In your first example you went from 0.01 to 0.02 skill. that is actually a 100% increase in your skill level. Can you see it, your skill level just doubled.

In your second example you went from 0.64 to 0.72. That is a 12.5% increase in the skill level.

I think that is actually a good demonstration of the "Diminishing returns" as I got it. Usually , the end game 10% skill increase will be much more expensive than early game 10% skill increase. Yet, at the same time it will be much less beneficial. So, the gameplay leveling value decrease coupled with the natural relative value decrease combines into to the value returned/resources invested
ratio that tends to go to zero.

The only mathematical connection to the multiplied variables case is the fact that increasing the lower ranked skill gives you a better returned value for your resources invested, at least as I can tell off the top of head.

It was my understanding that that was a graph of the the function, y=√x

How you would logically and naturally use such a function is beyond me, especially as he has been talking about two variables multiplied together to form a single stat which gives in very naturally to cumulative, multiplicative,and averaging effects, but not square roots.

Still wondering how taking the square root of two variables to form a stat with diminishing returns (if such a thing makes any sense) is 'simulated annealing'.

Quote:

Original post by JasRonq Still wondering how taking the square root of two variables to form a stat with diminishing returns (if such a thing makes any sense) is 'simulated annealing'.

Let's say a player gets Experience Points for killing things. Let's also say that more points means the player gets better at killing things. We can define 'better' as improvement Attack rolls, Stats, and Skills. So we have three dimensions on which to improve a character: Attack rolls, Stats, and Skills. The player then 'spends' XP on any or all of those three, so that the total of AttackRoll x Stats x Skills = XP.

Simulated Annealing is just a fancy way of saying cooling, a process that changes less over time -- another form of diminishing return.

Quote:

Original post by AngleWyrm The player then 'spends' XP on any or all of those three, so that the total of AttackRoll x Stats x Skills = XP.

Say what? List one game which you have ever, ever played which requires you to spend points in this way.

Exactly my point!

...so you're saying that there is a theoretical game mechanic out there which nobody does because it's a bad idea.

Okay. Thank you for your insights.

A flaw in this thread is we're not talking about what the RETURN is.

from Wikipedia: "According to this relationship, in a production system with fixed and variable inputs (say factory size and labor), beyond some point, each additional unit of variable input yields less and less additional output."

Quote:

I'm surprised nobody picked up on the obvious calculation error in your example. In your first example you went from 0.01 to 0.02 skill. that is actually a 100% increase in your skill level. Can you see it, your skill level just doubled. In your second example you went from 0.64 to 0.72. That is a 12.5% increase in the skill level. I think that is actually a good demonstration of the "Diminishing returns" as I got it.

0.8*0.7=0.56
0.8*0.8=0.64
0.8*0.9=0.72
0.8*1.0=0.80

.64-.56=.08
.72-.64=.08
.80-.72=.08

The VALUE is your RETURN, and it ISN'T diminishing, the returns per unit are equal.