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Technical
Winning Percentages Associated with Grade Differences

by Louis Nel

For idealized players who always play according to their Grade, a difference in Grades is associated with a winning probability. Indeed, the Index Adjustment Table in the document [World Ranking system explained] implies that in a game between two such players there is a certain probability that the weaker player wins and a corresponding probability that the stronger player wins.

To illustrate, suppose that the weaker player's Grade is 90 less than that of the stronger player. Since 90 lies in the range 80 .. 97, the Index Adjustment Table shows that the stronger player will gain 20 Index points by winning. Similarly, since -90 lies in the range -97 .. -80, the weaker player will gain 30 points by winning. A steady state will be maintained if the weaker player wins 20 games for every 30 games lost against the stronger player i.e. wins 20 out of 50 games or, equivalently expressed, has a 40% winning percentage. Accordingly, the stronger player then has a 60% winning percentage. Notice that both of these percentages are determined by the equation

  • Absolute Grade Difference = Larger Grade - Smaller Grade,

which was 90 in the above example.

The table to follow gives the corresponding winning percentages for various ranges of Absolute Grade Differences.

          WINNING PERCENTAGE TABLE
X = Absolute Grade Difference
%WP(X) = Winning % of Higher Graded player

100-%WP(X) = Winning % of Lower Graded player


  X        %WP(X)   100-%WP(X)

  10       51.2       48.8
  20       52.3       47.7
  30       53.4       46.6
  40       54.6       45.4
  50       55.7       44.3
  60       56.9       43.1
  70       58.0       42.0
  80       59.1       40.9
  90       60.2       39.8
 100       61.3       38.7
 110       62.4       37.6
 120       63.5       36.5
 130       64.5       35.5
 140       65.6       34.4
 150       66.6       33.4
 160       67.6       32.4
 170       68.6       31.4
 180       69.6       30.4
 190       70.6       29.4
 200       71.5       28.5
 210       72.5       27.5
 220       73.4       26.6
 230       74.3       25.7
 240       75.1       24.9
 250       76.0       24.0
 260       76.8       23.2
 270       77.6       22.4
 280       78.4       21.6
 290       79.2       20.8
 300       79.9       20.1
 310       80.7       19.3
 320       81.4       18.6
 330       82.0       18.0
 340       82.7       17.3
 350       83.4       16.6
 360       84.0       16.0
 370       84.6       15.4
 380       85.2       14.8
 390       85.8       14.2
 400       86.3       13.7
 410       86.9       13.1
 420       87.4       12.6
 430       87.9       12.1
 440       88.4       11.6
 450       88.8       11.2
 460       89.3       10.7
 470       89.7       10.3
 480       90.1        9.9
 490       90.5        9.5
 500       90.9        9.1
 510       91.3        8.7
 520       91.6        8.4
 530       92.0        8.0
 540       92.3        7.7
 550       92.6        7.4
 560       92.9        7.1
 570       93.2        6.8
 580       93.5        6.5
 590       93.8        6.2
 600       94.1        5.9
 610       94.3        5.7
 620       94.6        5.4
 630       94.8        5.2
 640       95.0        5.0
 650       95.2        4.8
 660       95.4        4.6
 670       95.6        4.4
 680       95.8        4.2
 690       96.0        4.0
 700       96.2        3.8
 710       96.3        3.7
 720       96.5        3.5
 730       96.6        3.4
 740       96.8        3.2
 750       96.9        3.1
 760       97.1        2.9
 770       97.2        2.8
 780       97.3        2.7
 790       97.4        2.6
 800       97.5        2.5
 810       97.7        2.3
 820       97.8        2.2
 830       97.9        2.1
 840       98.0        2.0
 850       98.0        2.0
 860       98.1        1.9
 870       98.2        1.8
 880       98.3        1.7
 890       98.4        1.6
 900       98.4        1.6
 910       98.5        1.5
 920       98.6        1.4
 930       98.6        1.4
 940       98.7        1.3
 950       98.8        1.2
 960       98.8        1.2
 970       98.9        1.1
 980       98.9        1.1
 990       99.0        1.0
1000       99.0        1.0
Author: Louis Nel
All rights reserved © 2005


Updated 28.i.16
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