Forum Archive : Ratings

Different length matches

From:   Jim Williams
Address:   jimw@giga-net.com
Date:   21 October 1998
Subject:   Re: FIBS formula question/comment
Forum:   rec.games.backgammon
Google:   362E02C4.38D4@giga-net.com

This touches on a question I have been evaluating.  I am suspicious of
the fibs rating forumla in the way it accounts for match length.  I have
collected a lot of match results and checked empirically whether the
winning probability as predicted by the FIBS rating formula actually
matches the observed winning probability for a given match between
players of known ratings.  I sampled the players ratings before recording
any matches so that the random errors in the ratings would be uncorrelated
with with the outcome of the observed games.  Only matches where both
players had at least 1000 experience points were included.  Currently
the number of recorded results is as follows:

        1 point matches         19926
        3 point matches         12036
        5 point matches         8621

1, 3, and 5 account for 90% of all matches.

I then took the fibs ratings formula for win probability:

        P = 1/(1 + 10^(D*sqrt(N)/2000))

Rather than using the match length for N, I used an effective
match length where the effective match length was chosen so
that the formula gave the best fit with the observed data.

The results were what I expected only more extreme.  The effective
match lengths which gave the best fit were as follows:

        match length            effective match length
                1                       1.6
                3                       1.6
                5                       2.1

Due to the limited number of matches recorded, the standard error
on these effective match lengths is about 0.25 .  If anyone notices
zbest lurking on fibs, he is collecting more data to try to get
a more accurate fix on these numbers.

These numbers suggest that a 3 point match has exactly the same
skill component as a 1 point match, and a 5 point match only
slightly more.

I am at a loss to explain these numbers, but the implication is
that if you want to increase you rating, play 1 point matches
agains the weakest opponents you can find, and play long matches
against the strongest opponents you can find.  It also suggests
that if we want to make backgammon more a game of skill and less
a game of luck, we should eliminate the doubling cube.

Tom Keith  writes:

Douglas Zare and Adam Stocks comment on this posting in their article
"Ratings: A Mathematical Study"
Did you find the information in this article useful?          

Do you have any comments you'd like to add?     



Constructing a ratings system  (Matti Rinta-Nikkola, Dec 1998) 
Converting to points-per-game  (David Montgomery, Aug 1998)  [Recommended reading]
Cube error rates  (Joe Russell+, July 2009)  [Long message]
Different length matches  (Jim Williams+, Oct 1998) 
Different length matches  (Tom Keith, May 1998)  [Recommended reading]
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)  [GammOnLine forum]
Fastest way to improve your rating  (Backgammon Man+, May 2004) 
Field size and ratings spread  (Daniel Murphy+, June 2000)  [Long message]
Improving the rating system  (Matti Rinta-Nikkola, Nov 2000)  [Long message]
KG rating list  (Daniel Murphy, Feb 2006)  [GammOnLine forum]
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)  [GammOnLine forum]
Ratings and rankings  (Chuck Bower, Dec 1997)  [Long message]
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) 

[GammOnLine forum]  From GammOnLine       [Long message]  Long message       [Recommended reading]  Recommended reading       [Recent addition]  Recent addition

  Book Suggestions
Computer Dice
Cube Handling
Cube Handling in Races
Extreme Gammon
Fun and frustration
GNU Backgammon
Luck versus Skill
Magazines & E-zines
Match Archives
Match Equities
Match Play
Match Play at 2-away/2-away
Opening Rolls
Pip Counting
Play Sites
Probability and Statistics
Source Code
Strategy--Bearing Off
Strategy--Checker play


Return to:  Backgammon Galore : Forum Archive Main Page