Diminishing returns formula

rpg_functions.java

public static double diminishing_returns(double val, double scale) {
    if(val < 0)
        return -diminishing_returns(-val, scale);
    double mult = val / scale;
    double trinum = (Math.sqrt(8.0 * mult + 1.0) - 1.0) / 2.0;
    return trinum * scale;
}

Taken from here. Can be greatly useful.

For example, suppose you define a Skill, Climbing, that makes you decently good very fast but it takes a huge amount of effort to really master. Suppose each skill has levels from 0 to 500, and to go up one level it requires a certain "effort" (experience, money, whatever). Now, if "decently good" means skill level 100 and "mastering" means skill level 500, we could use a scale of 20 to get the following progression:

Effort	Level
20	30.622
50	61.803
100	100
200	156.155
300	200
500	270.156

So, before skill level 100, small efforts yield big level increases. So we get to "decently good" quite fast.

After skill level 100, increasingly more effort is required to go up one level. To get to a level less than 3 times higher than "decently good", we need 5 time the effort it took us to get there.