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I am looking for an experience ladder that 'starts' off relatively quickly like a bit of geometric series, then quickly grows like an exponential curve, and then a slow exponetial curve for later levels, in the range of levels 1-5000.

How would I do this mathematically? I am assuming I might just have three sets of equations, but then what is the correct math for getting the level (based on XP), and vice-versa, XP based on level?

I.e., I am thinking something like:

lvl 1 - 10 exp lvl 2 - 12 exp lvl 3 - 15 exp lvl 4 - 18 exp lvl 5 - 22 exp (not quite fibacconi) lvl 6 - 26 exp lvl 7 - 32 exp ... then maybe around level 150 or so it starts growing quickly, like lvl 150 -1000 exp lvl 151 - 1200 exp ... lvl 3000 - 30000 exp lvl 3100 - 40000 exp lvl 4000 - 75000 exp lvl 5000 - 100000 exp

If it's been done, a link would be great (since I am not exactly sure what I am looking for, not quite sure how to find it). Or if it is easy for you to just write the math, please do that too, thanks for your help!

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If you use an exponential function in the form:

XPTotal = 2 ^ (Level * some_function(Level))

Then you can play around with some_function to get different kinds of growth.

Like this makes it so you double every five levels:

some_function() = 1/5

I think what you could use here is something like this, where X, Y, and Z are constants you mess with:

some_function(Level) = X * cos(Y+Level/Z)

Then probably pass the XPTotal through some creative rounding function that gives you XP values like "225" instead of "223.1567017350735012".

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Build a spline and give it as many control points as you think it'll need, my guess is only three unless you want multiple speed-up and slow-down phases. The Y axis is how much XP you're gaining, so the steeper the slope the longer it takes to move across the X axis. And the X axis will represent your 1..5000 "levels." In this you can quickly change the leveling experience just by tweaking the control points of the spline.

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