I'm not giving specifics. But since people seem to want to get some idea of what's going into the formula, I might as well give the generalities.
THIS IS FOR INFORMATION PURPOSES ONLY. I will not be debating this, and both Melkir and I agree that this information will not stand a chance of changing until after the beta period. If this turns into a raging thread like Melkir's +award, I'm locking the darn thing.
// BEGIN FAQ
1. What is the formula?
The formula is a scalable 4-point bezier curve that uses percentage of karma cap to determine a player's place on the 0 to 1 range scale for the formula.
2. Huh?
Bezier curves are a fancy type of mathematical curve that allow for precise curve control. Think of it as a continuous curve that you can make do almost anything, including loop back on itself. It's possible to add even more control points to reshape the curve even further.
3. Still doesn't explain what happen.
Okay. A value on a bezier curve is generated by a Z value between 0 and 1, or 0% and 100%. If the cap is 40 karma and your character has 10 karma, your z value will be 0.25. This generates the Y value on the graph that applies against your karma.
4. Okay. We have a Y value. Now what?
Well, the Y value is a multipler - a percentage multiplier. It determines what percentage of 1 karma you're awarded. It can range from 0% to Infinity%.
5. So what's the precise formula you're using?
Not telling.
6. A hint?
Okay. As an approximate, until you reached 25% of the cap, your karma award was around 1.3 karma per +award. It then continually declined as you reached the cap.
7. Hold on - does that mean I might end up getting only 0 karma?!?!?!?!
Mmm... you almost caught me. As long as the last end point doesn't have a Y value of 0, you will never receive 0 karma for an award.
8. But... hold on, that means I can exceed the cap!
Theoretically, yes. But that's all I'm saying.
9. I wanna know the exact formula!
No. We're holding the formula back because we want to be able to tweak the numbers.
10. And what testing did you do?
Me? I ran a few numbers to see if it looked reasonable. Melkir took the application I wrote and tinkered until he found values that seemed fair and equitable to him. The testing on both our parts was done using an assumption of how many +awards an average player could expect over the beta period.
11. Okay... but this means that if I play regularly, some little snot can come out of chargen and....
No, not really. Those who play regularly and receive more +awards will tend to stay ahead. Remember - diminishing returns; even though they might initially be getting 1.3 karma when you're only getting 0.5 per award, their initial huge jumps in growth are going to slow down all too soon. What this does is help the occasional player and the new player remain competitive in terms of sheet improvements.
Plus, this is a bezier curve, not a straight formula. There can be flat places here, and if the curve essentially flattens at z=0.7, then that last 30% of cap you're going to remain ahead.
12. Why aren't you using a straight declining formula? Why aren't you using differential calculus? Why..?!?!?!?!
Because I like bezier curves. They give a higher degree of control than a straight mathematical formula, and they can be tweaked without severe difficulty. And because I'm the one coding the thing!
13. I just don't agree with this diminishing thing!
I have concerns with it as well. However, I think it's an idea worth pursuing for Beta to see what happens. And I completely stand behind Melkir in that it _will_ be happening for beta.
// END OF FAQ.
NS:SE
