Forum Archive : Ratings

FIBS rating formula

From:   Patti Beadles
Address:   pattib@mauve.rahul.net
Date:   18 December 2003
Subject:   Re: rating formula
Forum:   rec.games.backgammon
Google:   brsp6v$7s1$1@blue.rahul.net

Here is what you get when you ask FIBS for it's rating formula:

> help formula
  formula - The formulas used to calculate rating changes

  These are the formulas used to determine the ratings of a player:
  Let's say that two players P1 and P2 were playing a n-point match.
  The ratings of the players are r1 for P1 and r2 for P2 .

  Let D = abs(r1-r2)      (rating difference)
  Let P_upset = 1/(10^(D*sqrt(n)/2000)+1) (probability that underdog wins)
  Let P=1-P_upset if the underdog wins and P=P_upset if the favorite wins.

  For the winner:
    Let K = max ( 1 , -experience/100+5 )
    The rating change is: 4*K*sqrt(n)*P
  For the loser:
    Let K = max ( 1 , -experience/100+5 )
    The rating change is: -4*K*sqrt(n)*P

  The 'experience' of a player is the sum of the lengths of all matches
  a player has finished. Every player starts with a rating of 1500 and
  an experience of 0.



Let's walk through this in English.

D is the difference in the two ratings.  If you're rated 1850 and I'm
rated 1750, then D=100.  Easy enough.

n is the match length.  The real workhorse of the formula is in the
P_upset line; that calculates the probability of the lower-ranked
player winning the match.

P then becomes P_upset if the lower-rated player wins, or 1 - P_upset
if the higher-rated player wins.

K is the factor that scales for people with lower experience.  Once
a player hits 400 experience, K is always 1.

So essentially, the winner get 4 * the square root of the match
length * the probability of his winning, and the loser loses that

Patti Beadles,    Oakland, CA |
            pattib@gammon.com |  Going to war over religion is
       http://www.gammon.com/ |  basically arguing over who has the
Check out www.tribe.net!      |  better imaginary friend.
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Constructing a ratings system  (Matti Rinta-Nikkola, Dec 1998) 
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Emperical analysis  (Gary Wong, Oct 1998) 
Error rates  (David Levy, July 2009) 
Experience required for accurate rating  (Jon Brown+, Nov 2002) 
FIBS rating distribution  (Gary Wong, Nov 2000) 
FIBS rating formula  (Patti Beadles, Dec 2003) 
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Ratings on Gamesgrid  (Gregg Cattanach, Dec 2001) 
Ratings variation  (Kevin Bastian+, Feb 1999) 
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Strange behavior with large rating difference  (Ron Karr, May 1996) 
Table of ratings changes  (Patti Beadles, Aug 1994) 
Table of win rates  (William C. Bitting, Aug 1995) 
Unbounded rating theorem  (David desJardins+, Dec 1998) 
What are rating points?  (Lou Poppler, Apr 1995) 
Why high ratings for one-point matches?  (David Montgomery, Sept 1995) 

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