Ratings

Forum Archive : Ratings

 Strange behavior with large rating difference

 From: Ron Karr Address: karr@best.com Date: 26 May 1996 Subject: Re: rating calculation Forum: rec.games.backgammon Google: 4oa652\$jk9@nntp1.best.com

```Sheldon Richter wrote:
> I really do not understand the ratings calculations.
> I thought that the ratings would change more for
> longer matches, and less for shorter matches.
> Can anyone please explain the logic of the following:
>
> rating calculation:
> rating difference D=1190.934235
> match length      N=64
> Experience: magic_one 6961 - wes 7871
> Probability that underdog wins: Pu=1/(10^(D*sqrt(N)/2000)+1)=0.000017
> P=0.000017 is 1-Pu if underdog wins and Pu if favorite wins
> K=max(1 , -Experience/100+5) for magic_one: 1.000000
> change for magic_one: 4*K*sqrt(N)*P=0.000551
> K=max(1 , -Experience/100+5) for wes: 1.000000
> change for wes: -4*K*sqrt(N)*P=-0.000551
>
> rating calculation:
> rating difference D=1187.363751
> match length      N=3
> Experience: magic_one 6967 - wes 7874
> Probability that underdog wins: Pu=1/(10^(D*sqrt(N)/2000)+1)=0.085668
> P=0.085668 is 1-Pu if underdog wins and Pu if favorite wins
> K=max(1 , -Experience/100+5) for magic_one: 1.000000
> change for magic_one: 4*K*sqrt(N)*P=0.593523
> K=max(1 , -Experience/100+5) for wes: 1.000000
> change for wes: -4*K*sqrt(N)*P=-0.593523

The theory is:  in a longer match, the lower-ranked player is less likely
to win than in a shorter match.  The points awarded to the favorite, if
he wins, are proportional to this probability.  It's also proportional to
the square root of the match length.  In most cases, the favorite will
get more points for winning longer matches; it's just that the amount
increases less than linearly as the match length increases.

This is a very odd case, where the ratings difference is unusually huge
(and wes is known as a player who deliberately throws matches).  So in a
64-point match, the odds of the "underdog" winning are calculated as
infinitesimal, so the favorite will not get very many points for winning
the match.  (If wes had won, he would have gotten a ton of points.) In
the 3 point match, the favorite "only" has an 85% chance of winning, so
even though the match is shorter, he gets more points for winning.

Technically, this could be considered a "flaw" in the ratings formula,
but in reality I wouldn't even try to have the formula be accurate in the
ridiculous case of an 1190-point ratings difference between players.
It's more important to be accurate in the normal cases of a few hundred
points difference.

Ron
```

### Ratings

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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)