# 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............