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## Re: [Bug-gnubg] match winning chances

 From: Michael Petch Subject: Re: [Bug-gnubg] match winning chances Date: Mon, 12 May 2008 10:33:43 -0600 User-agent: Microsoft-Entourage/11.4.0.080122

The calculation that Gnubg uses is based upon Kees van den Doel:

http://www.cs.ubc.ca/~kvdoel/tmp/ratings/

The calculation and the variables you plug in are summarized at the top. How the calculation is arrived at it discussed in the 90% of the article after that.

Once you get a Ratings difference from that equation you then use the Fibs formula to convert the ratings difference into MWC. The part of the fibs formula you want is here:
Take the ratings difference computed in the part above and use it as the value for variable “D” in the formula below. The match length is variable “n”

First we compute U (Chances of Underdog to win) as U = 1/(10^(D*SQRT(n)/2000)+1)
To compute the chances of the favorite winning its simple computed as   1-U

So if you were playing a 15 point match (n) and the rating difference computed by Kee’s forumla at the link provided was 47.13 (for example), you would get soemthing like:

D = 47.13 (Rating difference)
n = 15 (Match length)

U = 1 / (10^(47.13*sqrt(15)/2000)+1)
U = .447655

Chance of underdog Winning - U * 100 = 44.77%
Chance of Favorite winning - (1-U) * 100 = 55.23%

I haven’t done any investigation, but I’m not sure if the information needed to do the ratings difference calculation (Part 1 above) is available through standard player records, but I am pretty sure if you use the relational database to store the records that all the info you need is there.

Let me know if this helps at all.

Mike

On 5/12/08 10:11 AM, "Thomas Koch" <address@hidden> wrote:

Is there a possibility to derive (e.g. calculate) my match winning chances against a certain person from the gnubg error rate shown in the player records? Let's say my error rate in the player record is 0.0200 and my opponents error rate is 0.0300. How can I calculate my match winning chances for a 5pt, 11pt, 25pt- match etc.? I would like to get something like the "luck adjusted result" from the match statistics which tells me that I am e.g. 60% favorite to win a 5pter against this opponent. What is the formula?