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
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
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