# 14 FIBS RATINGS (First Internet Backgammon Server)

FIBS Rating Formula [From the FIBS man pages.]

NAME
formula - The formulas used to calculate rating changes

DESCRIPTION
These are the formulas used to determine the ratings of a
player: Let's say that two players P1 and P2 were playing a
n-point match. The ratings of the players are r1 for P1 and r2
for P2 .

+ Let D = abs(r1-r2) (rating difference)
+ Let P_upset = 1/(10^(D*sqrt(n)/2000)+1) (probability that
underdog wins)
+ Let P=1-P_upset if the underdog wins and P=P_upset if the
favorite wins.

+ For the winner:
o Let K = max ( 1 , -experience/100+5 )
o The rating change is: 4*K*sqrt(n)*P
+ For the loser:
o Let K = max ( 1 , -experience/100+5 )
o The rating change is: -4*K*sqrt(n)*P

The 'experience' of a player is the sum of the lengths of all
matches a player has finished. Every player starts with a
rating of 1500 and an experience of 0.

ratings

_________________________________________________________________

From:gmortens@newstand.syr.edu (Gerald E Mortensen)
Subject: fibs ratings formula plots
Date: 23 Dec 1994 22:28:16 GMT

i made these plots from the fibs ratings formula. experience >500. if
you can't read these try setting your font to fixed or courier.

```                      P(win) vs. ratings difference
0.8 ++-----+-------+------+-------+------+------+-------+-----++
+      +       +      +       +      +      +       +  C   +
|                             :                     C      |
0.7 ++                            :                 C      B  ++
|                             :             C       B      |
|                             :                 B          |
|                             :          C  B              |
0.6 ++                            :      C   B          A  A  ++
|                             :      B      A   A          |
|                             :  B   A   A                 |
0.5 ++                        A   A  A                        ++
|                 A   A   B   :                            |
|          A   A      B       :                            |
0.4 ++  A  A          B   C       :           1 pt match  A   ++
|              B  C           :           5 pt match  B    |
|          B                  :           9 pt match  C    |
|      B       C              :                            |
0.3 ++  B      C                  :                           ++
|      C                      :                            |
+   C  +       +      +       +      +      +       +      +
0.2 ++-----+-------+------+-------+------+------+-------+-----++
-400   -300    -200   -100      0     100    200     300    400

ratings change for a win vs. ratings difference
10 ++-----+-------+------+-------+------+------+-------+-----++
+      +       +      +       +      +      +       +      +
9 ++  C                         :                           ++
|      C   C                  :                            |
8 ++             C              :           1 pt match  A   ++
|                             :           5 pt match  B    |
|                 C           :           9 pt match  C    |
7 ++                    C       :                           ++
|   B                     C   :                            |
6 ++     B   B                  C                           ++
|              B  B           :  C                         |
5 ++                    B       :      C                    ++
|                         B   B          C                 |
4 ++                            :  B          C             ++
|                             :      B   B      C          |
|                             :             B   B   C      |
3 ++                            :                     B  B  ++
|   A  A   A   A  A           :                            |
2 ++                    A   A   A  A   A   A  A   A         ++
+      +       +      +       +      +      +       A  A   +
1 ++-----+-------+------+-------+------+------+-------+-----++
-400   -300    -200   -100      0     100    200     300    400
ratings diff (your rating - opponent's)
```

ratings change is the same for both players if both have experience >
than 500 (or have equal experience < 500).

jay (wilfo)
_________________________________________________________________

FIBS - Rating Changes 2/16/95

```                change in rating when favorite wins
rate                    points in match
diff    1       2       3       5       7       9       11
------------------------------------------------------------
0       2.00    2.83    3.46    4.47    5.29    6.00    6.63
40      1.95    2.74    3.33    4.24    4.97    5.59    6.13
80      1.91    2.64    3.19    4.01    4.65    5.18    5.63
120     1.86    2.55    3.05    3.79    4.34    4.77    5.14
160     1.82    2.46    2.92    3.56    4.03    4.38    4.67
200     1.77    2.37    2.78    3.35    3.73    4.01    4.22
240     1.73    2.28    2.65    3.13    3.44    3.65    3.79
280     1.68    2.19    2.52    2.93    3.16    3.31    3.39
320     1.64    2.11    2.39    2.73    2.90    2.99    3.02
360     1.59    2.02    2.27    2.54    2.65    2.69    2.68
400     1.55    1.94    2.15    2.35    2.42    2.41    2.37
440     1.50    1.86    2.03    2.18    2.20    2.15    2.08
480     1.46    1.78    1.92    2.01    1.99    1.92    1.83

change in rating when underdog wins
rate                     points in match
diff    1       2       3      5        7       9       11
------------------------------------------------------------
0       2.00    2.83    3.46    4.47    5.29    6.00    6.63
40      2.05    2.92    3.60    4.70    5.61    6.41    7.14
80      2.09    3.01    3.74    4.93    5.93    6.82    7.64
120     2.14    3.10    3.88    5.16    6.25    7.23    8.13
160     2.18    3.19    4.01    5.38    6.56    7.62    8.60
200     2.23    3.28    4.15    5.60    6.86    7.99    9.05
240     2.27    3.37    4.28    5.81    7.14    8.35    9.48
280     2.32    3.46    4.41    6.02    7.42    8.69    9.88
320     2.36    3.55    4.53    6.22    7.68    9.01    10.2
360     2.41    3.63    4.66    6.41    7.93    9.31    10.6
400     2.45    3.72    4.78    6.59    8.17    9.59    10.9
440     2.50    3.80    4.89    6.76    8.39    9.85    11.2
480     2.54    3.88    5.01    6.93    8.59    10.1    11.4

ratio  -  points lost to points won by favorite
rate                     points in match
diff    1       2       3       5       7       9       11
------------------------------------------------------------
0       1.00    1.00    1.00    1.00    1.00    1.00    1.00
40      1.05    1.07    1.08    1.11    1.13    1.15    1.17
80      1.10    1.14    1.17    1.23    1.28    1.32    1.36
120     1.15    1.22    1.27    1.36    1.44    1.51    1.58
160     1.20    1.30    1.38    1.51    1.63    1.74    1.84
200     1.26    1.38    1.49    1.67    1.84    2.00    2.15
240     1.32    1.48    1.61    1.85    2.08    2.29    2.50
280     1.38    1.58    1.75    2.06    2.35    2.63    2.91
320     1.45    1.68    1.89    2.28    2.65    3.02    3.39
360     1.51    1.80    2.05    2.53    2.99    3.47    3.95
400     1.58    1.92    2.22    2.80    3.38    3.98    4.61
440     1.66    2.05    2.40    3.10    3.82    4.57    5.37
480     1.74    2.18    2.60    3.44    4.31    5.25    6.25
```

Batting Average for favorite to maintain rating
points in match

```   diff   1    2    3    5    7    9   11
--------------------------------------
0  .500 .500 .500 .500 .500 .500 .500
40 .512 .516 .520 .526 .530 .534 .538
80 .523 .533 .540 .551 .561 .569 .576
120 .534 .549 .560 .577 .590 .602 .613
160 .546 .565 .579 .602 .619 .635 .648
200 .557 .581 .598 .626 .648 .666 .682
240 .569 .596 .617 .650 .675 .696 .714
280 .580 .612 .636 .673 .701 .725 .744
320 .591 .627 .654 .695 .726 .751 .772
360 .602 .642 .672 .716 .750 .776 .798
400 .613 .657 .689 .737 .772 .799 .822
440 .624 .672 .706 .756 .793 .820 .843
480 .635 .686 .723 .775 .812 .840 .862
```

FIBS ratings tables submitted by William C. Bitting
btbr68a@prodigy.com
wbitting@crl.com

_________________________________________________________________

FIBS ratings reports are posted regularly to Rec.games.backgammon.
Back issues are available from:
http://www.cs.ualberta.ca/~banks/fibs/test.html

Continue to: