I need a math genius!

No, not really a genius. I'm so bad at maths anyone could probably help me out.

There is some kind of diminishing return pattern I want to use for my game, but I can't figure out the formula for it. Without a formula I'd have to use a long array of values for my variables to match up with. I can do that instead, but I'm curious if there is a formula exist for this kind of pattern.

It goes something like this: 100% -> 50% -> 33% -> 25%-> 18%-> 14%, and so on. The pattern pictures some kind of a declining curve graph in my mind, but I just can't remember any terminology related to that sort of mathematics to google it in the first place.

I'd say try out y = (1/x+1) * 100. With an input of 0 'steps' you will get an output of 100, with input of 1 you will get 50, 2 gives you 33, 3 gives you 25, just as you asked.

See the graph here.

One way to go about it is to look up graphs of various formulas and see which most closely matches the shape of a plot of your numbers. Then you could then use some sort of regression to find a formula for it.

In this case a little bit of intuition helped me find the formula. The more you do the easier it gets.

formula:

(1-n/(n+1))*100

where n is the nth number (0 for the first)

Edit: ninja'd with a simplified formula.

Thank you guys. Never have thought I'd be interested in maths one day.