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Old 10-07-2007, 05:11 AM   #1
chaosprime
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Lightbulb Diminishing returns formula

I have just put up a page publishing the best of the diminishing returns formulae I've hacked around with over the years: Lost Souls MUD Diminishing Returns Formula. Since it took a fair amount of effort and trying different things that didn't work nearly as well, I thought others might find it useful. Includes explanation, interactive calculators so you can see how it actually performs, and code snippets in six languages.
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Old 10-07-2007, 11:41 AM   #2
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Re: Diminishing returns formula

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Originally Posted by chaosprime View Post
I have just put up a page publishing the best of the diminishing returns formulae I've hacked around with over the years: Lost Souls MUD Diminishing Returns Formula. Since it took a fair amount of effort and trying different things that didn't work nearly as well, I thought others might find it useful. Includes explanation, interactive calculators so you can see how it actually performs, and code snippets in six languages.
Diminishing returns of what? Gold, XP, Poppy seed muffins?
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Old 10-07-2007, 11:53 AM   #3
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Red face Re: Diminishing returns formula

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Diminishing returns of what? Gold, XP, Poppy seed muffins?
Uh... yes. Like most mathematical formulae, it's insensitive to its units.

I use it often for things like deriving effectiveness ratings from things that are potentially unbounded, like (in my little world) attribute and skill levels, or item value.

It could be used to calculate diminishing returns on the gold randomly bestowed on someone for sacrificing to Eris (across input values of sacrifice value), or the XP obtained from repeatedly killing the same thing (across input values of unmodified XP value), or the poppy seed muffins created by the Conjure Poppy Seed Muffins spell (across input values of caster charisma, conjuring, and cooking).
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Old 10-07-2007, 02:29 PM   #4
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Re: Diminishing returns formula

In that case, interesting work.

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Uh... yes. Like most mathematical formulae, it's insensitive to its units.

I use it often for things like deriving effectiveness ratings from things that are potentially unbounded, like (in my little world) attribute and skill levels, or item value.

It could be used to calculate diminishing returns on the gold randomly bestowed on someone for sacrificing to Eris (across input values of sacrifice value), or the XP obtained from repeatedly killing the same thing (across input values of unmodified XP value), or the poppy seed muffins created by the Conjure Poppy Seed Muffins spell (across input values of caster charisma, conjuring, and cooking).
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Old 10-07-2007, 02:53 PM   #5
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Smile Re: Diminishing returns formula

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In that case, interesting work.
Why, thank you.
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Old 10-08-2007, 12:37 AM   #6
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Re: Diminishing returns formula

Hey! Just took a quick glance. Thanks for the contribution. I'm gonna take the time to really look it over in the next few days.
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Old 10-08-2007, 09:34 AM   #7
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Re: Diminishing returns formula

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Hey! Just took a quick glance. Thanks for the contribution. I'm gonna take the time to really look it over in the next few days.
Looking forward to hearing what you think.
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Old 10-08-2007, 03:36 PM   #8
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Re: Diminishing returns formula

There are, of course, many ways to implement diminishing returns. This one is fairly "mild" compared to some. For example, Eve Online has each skill level cost 2^2.5 more than the previous (which is a factor of roughly 5.65). So, for your 20 pt example, the progression would go: 20, 113, 640, 3620, 20480 (skills only have 5 levels).
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Old 10-08-2007, 06:20 PM   #9
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Post Re: Diminishing returns formula

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There are, of course, many ways to implement diminishing returns. This one is fairly "mild" compared to some.
Sure, no question. That's the main reason I put this one together: because the more typical, simpler logarithmic formulae were way too harsh.

Whether this formula is going to be what you want depends on context -- I use several others in different situations, just this is the one that turned out to be useful far more often than the rest -- and design style. I prefer to have development scales relatively open-ended, but with braking factors like this formula in them to reduce the amount of insanity you easily wind up with. If one is comfortable with things like that example from EVE, of just saying "there are five skill levels, that's it", this sort of thing is probably less crucial, I imagine.
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