Ratings

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
NAME
formula - The formulas used to calculate rating changes

DESCRIPTION
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.

SEE ALSO
ratings

>

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
much.

-Patti
--
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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### Ratings

Constructing a ratings system  (Matti Rinta-Nikkola, Dec 1998)
Converting to points-per-game  (David Montgomery, Aug 1998)
Cube error rates  (Joe Russell+, July 2009)
Different length matches  (Jim Williams+, Oct 1998)
Different length matches  (Tom Keith, May 1998)
ELO system  (seeker, Nov 1995)
Effect of droppers on ratings  (Gary Wong+, Feb 1998)
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)
FIBS vs. GamesGrid ratings  (Raccoon+, Mar 2006)
Fastest way to improve your rating  (Backgammon Man+, May 2004)
Field size and ratings spread  (Daniel Murphy+, June 2000)
Improving the rating system  (Matti Rinta-Nikkola, Nov 2000)
KG rating list  (Daniel Murphy, Feb 2006)
KG rating list  (Tapio Palmroth, Oct 2002)
MSN Zone ratings flaw  (Hank Youngerman, May 2004)
No limit to ratings  (David desJardins+, Dec 1998)
On different sites  (Bob Newell+, Apr 2004)
Opponent's strength  (William Hill+, Apr 1998)
Possible adjustments  (Christopher Yep+, Oct 1998)
Rating versus error rate  (Douglas Zare, July 2006)
Ratings and rankings  (Chuck Bower, Dec 1997)
Ratings and rankings  (Jim Wallace, Nov 1997)
Ratings on Gamesgrid  (Gregg Cattanach, Dec 2001)
Ratings variation  (Kevin Bastian+, Feb 1999)
Ratings variation  (FLMaster39+, Aug 1997)
Ratings variation  (Ed Rybak+, Sept 1994)
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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