 | | From: | Floortje | | Subject: | scoring between 0 and 1 | | Date: | Sun, 23 Jan 2005 23:43:33 +0100 |
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 | Hi, I got a problem wich I have no idea on how to fix.
I have a quiz where someone is supposed to guess a certain numer
(4400). For a correct awnser (difference=0) they get 1 point and the
further away they are they should lose more of that point but never
reach zero. Is there a forumula that will give (0)=1 and |(inf)|=0 ?
Thx in advance ,
Floortje
--
www.cavalierpage.com
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| | From: | Lynn Kurtz | | Subject: | Re: scoring between 0 and 1 | | Date: | Sun, 23 Jan 2005 23:38:16 GMT |
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| On Sun, 23 Jan 2005 23:43:33 +0100, Floortje
wrote:
>Hi, I got a problem wich I have no idea on how to fix.
>
>I have a quiz where someone is supposed to guess a certain numer
>(4400). For a correct awnser (difference=0) they get 1 point and the
>further away they are they should lose more of that point but never
>reach zero. Is there a forumula that will give (0)=1 and |(inf)|=0 ?
>
>Thx in advance ,
>
>Floortje
If their guess might be any real number and the number they are trying
to guess is N, the you might look at score = exp(- k * | x - N |)
where k adjusts the steepness of dropping off to zero. I'm guessing
you might want small k values like .01 or smaller.
If their guess is from [0, infinity) you might try something like:
score = (1/N) x exp(-(1/N) x + 1)
--Lynn
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| | From: | Lynn Kurtz | | Subject: | Re: scoring between 0 and 1 | | Date: | Sun, 23 Jan 2005 23:48:42 GMT |
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| On Sun, 23 Jan 2005 23:38:16 GMT, Lynn Kurtz
wrote:
>
>If their guess might be any real number and the number they are trying
>to guess is N, the you might look at score = exp(- k * | x - N |)
>where k adjusts the steepness of dropping off to zero. I'm guessing
>you might want small k values like .01 or smaller.
>
>If their guess is from [0, infinity) you might try something like:
>
>score = (1/N) x exp(-(1/N) x + 1)
>
>--Lynn
Additionally, if you don't like the exponential shape you might
consider:
score = 1 / ( 1 + k (x - N)^2 ) for small values of k.
--Lynn
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| | From: | Tim Peters | | Subject: | Re: scoring between 0 and 1 | | Date: | Sun, 23 Jan 2005 18:52:08 -0500 |
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| [Floortje]
> Hi, I got a problem wich I have no idea on how to fix.
>
> I have a quiz where someone is supposed to guess a certain numer (4400).
> For a correct awnser (difference=0) they get 1 point and the further away
> they are they should lose more of that point but never reach zero. Is
> there a forumula that will give (0)=1 and |(inf)|=0 ?
There are any number of ways to do this, of course. Here's one nice family
of ways: pick real constants A>1 and B>0, and use the formula:
f(difference) = A^(-B*|difference|)
where "^" denotes exponentiation. Note that the value is:
1
---------------
B*|difference|
A
As difference goes from 0 to +inf, B*|difference| goes from 0 to +inf too
(since B>0), so the power goes from 1 to +inf (since A>1), so the reciprocal
goes from 1 to 0.
Note that all functions in this family have the property that the score is
cut in half whenever the difference increases by log_base_A(2)/B. For
example, pick A=2 and B=1. Then log_base_2(2)/1 = 1, and so the score gets
cut in half each time the difference increases by 1:
2^(0) = 1
2^(-1) = 1/2
2^(-2) = 1/4
2^(-3) = 1/8
etc. You can pick A and B to make log_base_A(2)/B as little or big as you
like.
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| | From: | Bart Goddard | | Subject: | Re: scoring between 0 and 1 | | Date: | 23 Jan 2005 23:08:33 GMT |
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| Floortje wrote:
> Hi, I got a problem wich I have no idea on how to fix.
>
> I have a quiz where someone is supposed to guess a certain numer
> (4400). For a correct awnser (difference=0) they get 1 point and the
> further away they are they should lose more of that point but never
> reach zero. Is there a forumula that will give (0)=1 and |(inf)|=0 ?
How about 4400/(1+(4400-x)^2)
If that goes to zero too fast you can divide the difference
by a constant:
4400/(1+((4400-x)/20)^2
for example. Replace the 20 by whatever you like.
Bart
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| | From: | Richard Henry | | Subject: | Re: scoring between 0 and 1 | | Date: | Sun, 23 Jan 2005 15:10:36 -0800 |
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| 1/|(1-x)|
"Floortje" wrote
in message news:mn.bd8f7d517d9980d8.23446@hetminnetjehoort.erbij...
> Hi, I got a problem wich I have no idea on how to fix.
>
> I have a quiz where someone is supposed to guess a certain numer
> (4400). For a correct awnser (difference=0) they get 1 point and the
> further away they are they should lose more of that point but never
> reach zero. Is there a forumula that will give (0)=1 and |(inf)|=0 ?
>
> Thx in advance ,
>
> Floortje
>
> --
> www.cavalierpage.com
>
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