Forum Archive : Ratings

Table of win rates

From:   William C. Bitting
Address:   wbitting@crl.com
Date:   16 August 1995
Subject:   Re: Strength of program
Forum:   rec.games.backgammon
Google:   40th53$er7@crl9.crl.com

Clearly the EXPERIENCE NUMBER is key to judging the validity of a rating
number. While all FIBS players start at 1500, because of a multipler to
the rating changes, which starts at 5(!) and declines to 4 at an
experience of 100; 3 at 200, etc., 1500 is not what many FIBSsters will
have as their rating when their experience is 200, not to mention 2000.

Some players decline to near 1300, and lower, quickly. Others like
'loner', 'mloner, 'STLguy', etc., quickly pass 1700 or 1800, not to
mention 1900 and 2000 by the former two!

So, while it is true that a 1700 or 1800 rated player may win 8 of 10
seven point matches against many new FIBS players, that won't be true
when the 1500 rated, 0 experience, player is one of the loner's, etc..
Nor will it be true when the 1500 rated player has a couple of thousand
experience points unless, of course, the player 1700 to 1800 player is
somebody on the way to 1900 or 2000.

The following table is the "batting average" the favorite must achieve to
maintain his rating at various rating differences. For players whose
experience level is over 2000, it may have considerably more validity
than for players whose experiece level is under 400. Players with
experience levels under 500 and ratings of mid 1700, not to mention over
1800, may be still be underrated simply because of not having played
enough matches!

(For the underdog, his average is 1 minus the favorite's.)

rate         points in match
diff   1     3     5     7     9     11
  0  .500  .500  .500  .500  .500  .500
100  .529  .550  .564  .576  .585  .594
200  .557  .598  .626  .648  .666  .682
300  .585  .645  .684  .714  .738  .759
400  .613  .689  .737  .772  .799  .822
500  .640  .730  .784  .821  .849  .871
600  .666  .768  .824  .861  .888  .908
700  .691  .802  .858  .894  .918  .935

If the proposition is that a player is going to win 8 of 10 seven point
matches against EXPERIENCED 1500 rated players, that batting average is
.800. From the above table we might therefore concluded the rating of such
an .800 hitter should be about 450 points over 1500, or 1950! Thus a
player who correctly guages that his batting average is .800 against
experienced 1500 rated players, may just as well judge that he is
underrated until his rating reaches 1950 rather than that the 1500
player is overrated.

If the propostion was winning 10 while loosing 2, then the batting
average is .833, and the batter should be above 2000 on his rating index
given enough experience!

Good Dice!   wcb on FIBS
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