Forum Archive : Ratings

Converting to points-per-game

From:   David Montgomery
Address:   monty@cs.umd.edu
Date:   24 August 1998
Subject:   Re: JF-5 as good as JF-7?
Forum:   rec.games.backgammon
Google:   6rr1ao$t5l$1@nnrp1.dejanews.com

Gary Wong  wrote:
> How do we convert between FIBS ratings and expected points per game?
> To the best of my knowledge this is an open question.  However, here's
> a simple model.  Assume 1-point matches are being played on FIBS.
> FIBS expects that between players ranked 94 +/- 34 points apart (as
> Chuck found JF 7 to be above JF 5), the favourite will win 52.7% +/-
> 1.0 of the games.  If we assume this constant factor is also correct
> in money games, and assume a win in a money game is worth 2 points on
> average (see my other article for justification), then this 2.7% +/-
> 1.0 CPW is worth 0.108 +/- 0.04 points per game.

I looked at this a few months ago, but I used a much more complicated
model than Gary's.  Instead of just going with the one point match
win percent, here is what I did:

- set a probability distribution for the points won for each player,
  when they win. (for example:  each player might win 1 point 38%,
  2 points 38%, 4 points 20%, 6 points .5%, 8 points 2.5%,
  and 16 points 1%)
- set a probability for how likely it is one player will beat the other.
- play a "long" match between these two players, assuming that the
  results for each game will follow the money distribution until the
  players get "close" to the end of the match.
- at this point, settle the match using a match equity table.
  (An important refinement: use a skill-adjusted match equity table,
   like those in _Can a Fish Taste Twice as Good_.)
- repeat this many times and determine overall match winning chances
  for the two players

Based on the match winning chances, it is easy to get the rating
difference.  Based on the probabilities you set, you have the money
points per game.

I did this for a lot of different probability distributions and
edges in probability of winning, along with a lot of different
definitions of "long" and "close" above.

The overall results are:
A rating difference of 40-50 points corresponds to about a .10ppg
money edge.

The key assumption is that play is like money until you get "close"
to the end of the match.  This is pretty true most of the time.
When the score gets real lopsided, it's not.  Also, there might be
some changes in the low frequency distributions (8-point and 16-point
wins) even fairly early in a match.  I don't think this swings

*Much* more important are many other factors.  Some money players
don't play matches.  And vice versa.  Certain styles of play are
better suited to money or matches.  And so forth.  So this
result, even if valid, is *only an approximate rule of thumb*.

Data from my own real-life money play conforms to this rule.  I think
I have about a 150 point rating edge over my average local opponent,
based on watch FIBS ratings go up and down, and my long-term money
result is about +.30ppg.

David Montgomery
monty on FIBS
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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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