Forum Archive : Ratings

Ratings variation

From:   FLMaster39
Address:   flmaster39@aol.com
Date:   13 August 1997
Subject:   FIBS Rating Variation #1
Forum:   rec.games.backgammon
Google:   19970813181301.OAA06240@ladder01.news.aol.com

The idle brain being the devil's tool, I decided to explore the amount of
random varatiation in FIBS ratings.

I built a model with the following parameters:

1. An individual has a given "true" rating.
2. The FIBS rating formula accurately describes this player's likelihood
of winning a match vs. other players, based on their ratings.
3. Player plays only 5-point matches, against opponents who randomly have
ratings of 1500, 1600, 1700, 1800, or 1900.
4. Ratings were set assuming experience >400.

I'm running a number of tests on it.  The one I've done so far concerns a
player with a "true" rating of 1800, who starts at 1800.  The question is,
if (s)he plays, how high or low will the rating go.

I found that, based on the following number of matches, the AVERAGE
maximum and minimum ratings achieved were:

1000       1881 / 1719
2500       1902 / 1698
5000       1916 / 1682
10000      1929 / 1668

This suggests that for players who play a lot, rating variations of 200
from high to low are not surprising, or alternatively, variations of 100
to 125 from their "true" rating.

In all cases, I am simulating at least 10,000 player histories, sometimes
more.  In other words, I am simulating tens of millions, up to billions,
of matches.  The standard error of my results is likely to be quite small.

I'm going to use the model to run some other tests, and I'll bore the
newsgroup with the results.

- Hank (Hank_VaUSA)

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) 

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