What is the Equation for Calculating Probability in a Specific Range?

[dave2118]

Hello

I'm trying to remember back to my high school / college days and have no idea where to start.

Basically, I'm trying to find probability in numbers for a specific range. I'd like to figure out an equation so I can plug it into software. Here are my sample values below:

0,36
100,55
200,66
300,80
400,97
700,99
800,99.3

So this line will basically never hit 1. I can't for the life of me figure out what to search for on google for this, I remember doing something easy back in school, but it's been a good 20 years, and actually need to use it.

Any direction would be great.

Dave

 

[gb7nash]

What's the exact problem? I can't really tell what your question is. What does it mean to "find probability in numbers for a specific range"? What are those sample values you listed? What exactly are you trying to find the probability of? etc..

 

[dave2118]

There's a system called the Elo Rating System (http://en.wikipedia.org/wiki/Elo_rating_system). I'm trying to figure out the probability of Player A vs Player B. I played around in excel using Ln which is sort of what I'm looking for based off of a table similar to http://www.ascotti.org/programming/chess/elo.htm

I was hoping to simplify it the best I could.

 

[spamiam]

If you really want there to be a horizontal asymptote at y=1, log won't do the trick since it's unbounded. Maybe something more along the lines of
$$f(x) = \frac{x+1}{x+2} = 1 - \frac{1}{x+2}$$
would work, since it does have a horizontal asymptote.