International Rating System

This is from an article written in the swiss magazine chess express, No. 4/5 1971. this is the prelude to that article :- Proffessor Elo set out his system fully in a memorandom for F.I.D.E.    ok now here we go.....

1.) Every player has a rating number. The Grandmasters' (GM's) numbers run from about 2,500 to 2,700+; international Masters (IM's) from about 2,400 to 2,500. The international rating list starts at 2,250. The numbering system can go as low as anyone likes-2,000 is somewhere around B.C.F 175. The numbers were chosen arbitrarily in original U.S.C.F. system nearly 25yrs ago; the difference between them, and not the absolute level, are what are important.

2.) We all know that the stronger player does not always beat the weaker; he often draws and sometimes loses. With the calculus of probabilities, One can calculate what would be the expected result on the laws of probability in a series of games between 2 players when u have there rating numbers. Elo defines the relationship between the difference between there rating numbers and the expected result by the following table....

Rating difference        %score expected

between the players   higherplayer/Lowerplayer

0-3 points diff              50%-50%                   198-206 points diff        76%-24%      

4-10                            51-49                        207-215                       77-23 

11-17                          52-48                        216-225                       78-22 

18-25                          53-47                        226-235                        79-21

26-32                         54-46                         236-245                        80-20

33-39                         55-45                         246-256                        81-19

40-46                         56-44                         257-267                        82-18

47-53                         57-43                         268-278                        83-17

54-61                         58-42                         279-290                        84-16

62-68                         59-41                         291-302                        85-15

69-76                         60-40                         303-315                        86-14

77-83                         61-39                         316-328                        87-13

84-91                         62-38                         329-344                        88-12

92-98                         63-37                         345-357                        89-11

99-106                       64-36                         358-374                        90-10

107-113                     65-35                         375-391                         91-9

114-121                     66-34                         392-411                         92-8

122-129                     67-33                         412-432                         93-7

130-137                     68-32                         433-456                         94-6

138-145                     69-31                         457-484                         95-5

146-153                     70-30                        485-517                          96-4

154-162                     71-29                        518-559                          97-3

163-170                     72-28                        560-619                          98-2

171-179                     73-27                        620-735                          99-1

180-188                     74-26                       over 735                         100-0

 189-197                     75-25                                                                             

One can read off the expected results from this table. If one player's rating is 100 points above the other,his expected score will be 64% and the weakers 36%; if the difference is 200 points, the expectations are 76% and 24% and so on. If both players have virtually the same rating, the expectation is obviously 50/50. If the players are over 735 points apart,say fischer playing a man 2,000, the latter's chance of avoiding the loss is statisticaly infinitesimal. Note that the expected result depends entirely on the diffence between the ratings. It is exactly the same for people with high rating as for low ratings. There is no advantage whatever playing others with much higher or much lower or the same ratings as themselves the table looks after these differences.

The relationship is exsactly the same between the difference between a players rating and tournament average and his expected score in the tournament. The expected result from 12 games with different people is just the same as 12 games with the same person,providing that the average rating difference is the same.

3.) In continuous system (like International rating list and also Ingo) the unit is the tournament or other event, and each player gets a new rating after the tournament . The Elo system can be worked equally well as a periodic system, like the B.C.F. system which measures performance over a specified period of time, but it is described here in the form used for the international ratings list. One calculates the average rating number of the tournament, and thus the difference between the player and his opponents ; and derives from the table his expected score. The difference between his actual score  his expected score is multiplied(x) by a coefficient k; and his new rating number number is above or below his previous by this amount. The coefficent k is an important element in the system, for it determines how much weight is given in the mans performance in the current tournament compared with all his previous performances as represented by his rating number at the beginning of the current tournament. At the beginning of a mans career when he has had very few rated performances and is improving fast, he is given a hight k, so that each tournament has a big weight - for the first 100 games, k, is put at 45. As his performance stabilises, k is reduced, and for those with F.I.D.E. titles k, is put at 10.

For egsample, suppose that Mr.X  a F.I.D.E. International Master (IM), is at 2,430. He plays in a tournament of 15 rounds , averaging 2,350 the difference is 80 , so he would expect from the table to score 61% of 15 ie, 9.15 points. He scores 7.5 . His rating will be  k(10) x the difference between 9.15 and 7.5   ie; 16.5 points below the old rating of 2,430- rounded, this becomes 2,415. So the mans rating is the number calculated after his last performance, incorporating all his previous play.

So we start with the rating numbers; then take the man's difference from the average of the tournament ; then from the table read off his expected percentage score; so get the difference between his actualy score and his expected score; Multiply(x)  by k; add this (or subtract) to his rating number: and that gives his new rating number for his next tournament, and so on............