In response to some inquiries regarding how the ratings are calculated; below is an updated version of an article appearing in the June 1996 Queensland Junior Chess Magazine.

The first thing to note is that the Australian Chess Federation (ACF) ratings are different to the Queensland Junior (QJ) ratings. ACF Ratings are the National ratings that are published three times a year. The QJ ratings are produced by myself four times a year and are just for Queensland Junior players.

1. How is my QJ Rating Calculated ?

It is quite simple to understand the concept of how players with established ratings gain and lose points. It depends on three things...

1. Your score in that tournament

2. Your rating

3. The average of your opponents’ ratings

To put it simply,

- If you get a 50% score (for example 3/6, 4/8...) against people who are rated the same as you (on average); you would neither gain nor lose points

- If you score 50% against people rated higher than you; then you would have played better than expected (from your rating) and would gain points

- On the other hand, if you score 50% against people rated lower than you; then you would lose points

- Consequently if you score 75% against people who are rated the same as you; you would gain points

Obviously there are many different variations of this theme, all of which are governed by the Percentage Expected table below.

R.D + - R.D + - R.D + - R.D + -

0-3 50 50 92-98 63 37 198-206 76 24 345-357 89 11

4-10 51 49 99-106 64 36 207-215 77 23 358-374 90 10

11-17 52 48 107-113 65 35 216-225 78 22 375-391 91 9

18-25 53 47 114-121 66 34 226-235 79 21 392-411 92 8

26-32 54 46 122-129 67 33 236-245 80 20 412-432 93 7

33-39 55 45 130-137 68 32 246-256 81 19 433-456 94 6

40-46 56 44 138-145 69 31 257-267 82 18 457-484 95 5

47-53 57 43 146-153 70 30 268-278 83 17 485-517 96 4

54-61 58 42 154-162 71 29 279-290 84 16 518-559 97 3

62-68 59 41 163-170 72 28 291-302 85 15 560-619 98 2

69-76 60 40 171-179 73 27 303-315 86 14 620-735 99 1

77-83 61 39 180-188 74 26 316-328 87 13 >735 100 0

84-91 62 38 189-197 75 25 329-344 88 12

R.D : Rating Difference (between your rating and the average of your opponents’ ratings)

+ : expected percentage when your rating above average of opponents’

- : expected percentage when your rating below average of opponents’

This table is based on the Elo System and is used for most rating systems around the world. It shows us what percentage (%) you would be expected to score against any group of opponents.

The first column is the difference between your rating and the average of your opponents’. The second column (+) shows us what percentage we would be expected to score if our rating was the amount in the first column above our opponents’ average rating. The third column (-) shows us what percentage we would be expected to score if our rating was the amount in the first column below our opponents’ average rating. For example, take the line that says 107-113; 65; 35. This means that if you played a field whose average rating was 110 above yours (eg. Your rating was 1000 and the average of your opponents’ was 1100), you would be expected to score 35%. If they were 110 points below you then you would be expected to score 65%. This leads to the idea of the "expected score".

If you were expected to score 65% in a 10-round tournament then your expected score (ES) would be 0.65 x 10 = 6.5 ie. 6.5/10. If you scored 6.5 points in this tournament then you would have done what is expected of you and your rating would not change. The more points you score above 6.5 the more your rating increases. The less points you score (below 6.5), the more you lose. But how many points do you gain and lose ?

The amount your rating changes is determined by ...

1. The score you achieved : the achieved score (AS)

2. The score you were expected to get : the expected score (ES) - as above

3. The "K-factor"

So that ...

Rating change = (AS-ES) x K

The K-factor is simply a number that determines the amount of change. The ACF uses a K-factor of 15 for all rateable tournaments (over 60 mins. per side).

The QJ uses different K-factors for different tournaments...

Lightning (5mins per side) = 5; Allegro (15) = 10; Rapid (30) = 15; Active (60) & slower = 20

Let's use the above formula to calculate your rating change from a tournament.

Let's say you scored 8 points in a 10 round rapid tournament in which your expected score was 6.5 (as above). You therefore scored more points than expected and your rating will go up.

Rating change = (AS-ES) x K

= (8.0-6.5) x 15

= + 22.5

You will therefore gain 22.5 points from this tournament.

This is the way in which people with established ratings gain and lose points from playing in tournaments. The way in which players with no rating (unrated players) earn ratings is based on similar principles.

For those who are still interested, feel free to read on more about the QJ rating system ...

(d) Bonus Points

If you win many more games than expected (ie. The AS minus ES is large) then you receive a reward in the QJRS. This reward is in the form of Bonus Points, and for 6 to 8 round tournaments is determined by the following equation... Bonus Points = (AS - ES - 2.0) x K

Only games over 20 mins per side are eligible for bonus points.

(e) Prevention of ratings deflation

The injection of points into a junior rating system is vital as there are a large number of rapidly improving players participating. Without the prevention of ratings deflation players would simply "swap" ratings points. Players who were improving slowly would actually go down because more quickly improving (and therefore underrated) players would take rating points off them. The QJRS therefore has three mechanisms for prevention of ratings deflation. As well as the Bonus Points system and Rating Ceilings mentioned previously, there is the "3% rule". Simply speaking this states that the "Percentage expected" table presented previously is altered by 3%. Therefore a player playing an average opposition the same rating as him/herself is only expected to score 47% (and not 50%) in order not to lose or gain points. With these three mechanisms in place it has been possible to keep QJ ratings comparable with ACF ratings (which was the original intent of the QJRS). It can be argued by purists that players playing large numbers of games will "get points for playing games" and will actually be overrated. A junior playing over 100 games in a single rating period will "risk" several times the rating points gained in playing such a number of games; and any overall effect is to bring the player closer to his/her performance rating for that period.

3. Why do we have QJ Ratings and what are the problems with them ?

The QJRS began in June 1993 with the rating of the 1993 Queensland Junior Championships. The first official list to be produced was in October 1993 and included a little over 100 players. It was started as a joint CAQ/QJCL project. Its aims were to more accurately reflect the playing strength of juniors while also including many more players from school/club chess that could not be ACF rated. Presently there are over 1000 players on the list. About 70-100 players are removed from each published list due to inactivity (12 months for rated players, 6 months for provisionally rated players). It is common for several players each period (3 months) to play over 100 games. Statistics included in the list are for games played since the last rating lists (in the middle column) as well as top improvers/top in each age group etc... The rating lists starts at 650 and finishes at over 2300! (David Smerdon). The list has up until this year appeared in the Queensland Chess Magazine; but now appears solely on the internet.

No Rating system is perfect. The QJRS has some problems with it; and not just in terms of workload!

(a) Overshooting

It is quite possible for players in both the ACF and QJ rating systems to "overshoot" their true rating. A person who is rated at 1000 and plays in several tournaments in which (s)he performs at 1200 strength can actually accrue enough points by the end of the rating list to rise over 1200. This results because ratings only change every 3 months. If ratings changed automatically after every tournament (or even after any game!) this would not happen. The difficulty is actually in doing this automatically, and no-one has succeeded as yet. In order to prevent against overshooting in the QJRS players improving by over 100 points in a rating list have their performance ratings calculated for each major tournament and do not rise above the average of these.

(b) Percentage expected table

The table shown previously was devised by a certain Mr.Elo some years ago after examining results of countless games/tournaments (mostly involving adults). The question is whether this table is relevant for junior chess players in Queensland. It has been suggested to me in the past (and I agreed at the time) that a 100 point rating difference between juniors seemed to be "more significant" than a 100 point rating difference between adult players on the ACF list. Surprisingly some analysis I did in regard to this did not prove this; although I would need to spend more time on this for a definitive answer. I still have my doubts.

(c) Automaticity of ratings

Despite this being the computer age, until very recently the ratings programmes available have been average to say the least. Luckily the new Swiss Perfect programme as well as Pat Byrom’s programme for SwissSys tournaments both look very promising and will reduce my workload significantly.

I hope this has been enlightening reading. Any questions can be e-mailed to r.i.duncan@uq.net.au or you can contact me via 0419 644 695 (and leave a message).

David McKinnon