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November 28th, 2009, 11:38 PM   #1
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Help to create ranking formula!

I am a computer scientist and I want to create a ranking formula for an application, so I thought to post in a math forum instead of developers forums coz you are the gurus in topics like this!

Basically I want to create a ranking formula where the rank number (result) will be between 0-1 inclusive.

And the problem is:
I have two variables, x and y, where x&y can take values between 1-9, inclusive. And I want a formula where I can manipulate these variables and get a result (e.g 0.765 or 0.453). The highest the better, so if both x and y take the max value (=9) then the number should be really close to 1 (e.g 0.928 or something or if not so close, to be the closet to 1 if x and y take the max value)

I thought of this:

1-1/((x*y)^2)

but when
x= 9
y=9
result = 0.9998475...

and when
x=5
y=5
result= 0.9984

also when
x= 1
y= 1
result= 0

so I don't think this is efficient and I am sure there must be a better formula than this.

Any help or hints on how to design my formula ?
demec is offline  
 
November 29th, 2009, 09:29 AM   #2
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Re: Help to create ranking formula!

You want a number that is highest when x and y are equal and lowest when min(x,y) is substantially different from max(x,y), right?

Try something like 1-(x-y)^2/(x+y)^2, I guess.
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November 29th, 2009, 11:59 AM   #3
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Re: Help to create ranking formula!

well, you give very minimal info so my minimal sol'n would be to just sum x&y, and offset/scale to put into desired ranging. So, if x,y range is 1-9, the range of the sum is 2-18. We offset by 2 and divide by 16 to give result=(x+y-2)/16. It will then range 0-1, and peak when x&y both peak. A previous post thought maybe the result peaks when x=y but I did not interpret it this way. If so, post back and we can give it another go.
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