How to calculate the scholastic rating
A rating is a numerical evaluation of the playing strength of a player. The higher the number, the better the player. World champion Magnus Carlsen has a rating close to 2800. An average 5 year-old is rated at 200, while the average grade 6 player is rated 800. Scholastic ratings are obtained by playing in tournaments rated by the Chess'n Math Association. A youngster's initial rating is based on his/her grade and performance (see the initial rating below).
Once a player has a rating, a mathematical formula is used to determine the new rating after each event. It usually takes about 5 tournaments or twenty-five games for a rating to accurately reflect the playing strength of a player. Any school, group or organization can have a tournament rated (see How to have your tournaments rated?).
Calculating a rating
Here is the formula used for players with ratings: Rn = Ro + (W - L) x 16 + D x 0.04 + bonus points if it is appropriate.
Rn = New Rating; Ro = Old rating; W = Wins; L = Losses; and D = The sum of the differences between your rating and that of your opponents, with the limitation that individual differences cannot exceed 350 (e.g., if your rating is 600 and your opponents is 1000, use 350, not 400).
Rating Example
Jack has a rating of 600 (Ro). He then plays 5 games and wins 3 (W), loses 1 (L) and draws 1. His opponents were rated 575, 600, 625, 650 and 675.
D = -25 + 0 + 25 + 50 + 75
Therefore D is equal to 125. This is then multiplied by .04, which gives us 5.
Now we have all the data: Rn = 600 + (3 - 1) x 16 + 5 or Rn = 600 + 32 + 5 or Rn = 637
Bonus Points
There are two bonus calculations, the one linked to the performance of the player and that associated with the number of games played since the beginning of the school year.
If a player does very well, then he receives bonus points. There is a bonus of 1 point for every point earned over 22 for a 3-game event, 24 for 4 games etc.
Jack played 5 games, so he receives bonus points for every point earned above 26. Since he gained 37 points, he will also collect 11 bonus points (37 - 26). Therefore his new rating (Rn) will be 648.
Also, add 2 points per game played, up to a maximum of 100 points per academic year (September 1 to August 31). Beyond the 50 games played the bonus no longer apply.
Since Jack has less than 50 games played since the beginning of the school year, he will receive 10 extra points (2 points X 5 games played), his new rating (Rn) will be 658 points!
Can you make it simpler to understand?
Sure. Basically, I never wanted to go to the trouble of working all this out with pen and paper (you may ask what I am doing working for Chess'n Math in that case), so I used to calculate my rating after every game in my head - but without the formula!
Basically, in every day language, the formula says: For every game you win against an opponent with the same rating as yourself, you gain 16 points; a loss against the same player would result in a loss of 16 points.The number 16 is the basis for all your calculations when a game is won or lost. If it is a draw, you throw the 16 in the garbage and only take account of the difference in ratings
Okay,so if I'm rated 600 and you are rated 600 - and I win the game (since I'm telling the story - when you tell the story, you can say you won), then I gain 16 points and you lose 16 points. What happens if the game is a draw? Simple, we both stay at 600 since there is no rating difference between us.
For every 25 points higher rated (or lower) your opponent is than you, you get 1 point more (or less) for a win (16 + 1); you lose 1 point less (or more) for a loss (16 - 1)
Okay, so if I'm rated 600 and you are rated 575, then I earn 15 rating points if I beat you and you lose 15 points.
If, in the unlikely case that YOU beat me, then you will gain 17 points and I will lose 17 points. If it is a draw, you gain 1 point and I lose 1 point because there is a 25 point difference which means a 1 point rating change.
If the difference between your rating and that of your opponents is 350 points or more, it is calculated as 350.
So, if I have a rating of 600 and you have a rating of 1000, the difference is calculated at 350 or 14 rating points (14 x 25 = 350). If I win, I gain 30 points - the maximum number of points one can gain in 1 game. If you win, which should be the case since you are already at 1000, you gain only 2 points (16 - 14) and I lose only 2. If it is a draw, I gain 14 points and you lose 14 points
There is a bonus if you gain more than a certain number of points. You get 1 bonus point for every point over 22 in a 3-game event, 24 for 4 games, etc.
Add up the points you earned in each game and figure out if you are eligible for bonus points. When you calculate your rating game by game, you will not be totally accurate but it should be very close. The reason is that if you are rated 600 and I am rated 620, I just count that as a 25 point difference because it is easier.
Have fun with this!
Calculating the initial rating
Here is how the system establish the initial rating of a new player:
- Find the average grade of your section. Ex: if you have 2 players in your section, one in grade 4 and one in grade 6, the average grade of your section will be 5. So here, 5,5 would be 5 not 6 (5,9 would also be 5).
- Find the average performance of your new player. If he did 2.5 out of 5 games: 2.5/5 * 100 = 50%
Here are some values you will need (Official after September 1, 2007):
| Kindergarten | a0=100 | aa0=250 |
| Grade 1 | a1=110 | aa1=300 |
| Grade 2 | a2=130 | aa2=350 |
| Grade 3 | a3=150 | aa3=400 |
| Grade 4 | a4=180 | aa4=450 |
| Grade 5 | a5=220 | aa5=500 |
| Grade 6 | a6=250 | aa6=550 |
| Grade 7 | a7=290 | aa7=600 |
| Grade 8 | a8=330 | aa8=650 |
| Grade 9 | a9=370 | aa9=700 |
| Grade 10 | a10=420 | aa10=750 |
| Grade 11 | a11=420 | aa11=750 |
| Grade 12 | a12=420 | aa12=750 |
Here is the formula:
aa + (performance*a / 100) = Initial rating
So it would be aa for grade 5: 500 + (performance: 50 * a for grade 5: 220 / 100)
Finally: 500+(50*220/100) = 610
Once everybody has an initial rating, you can calculate the scholastic rating (see Calculating a rating above).
Calculate your rating
This calculator does not calculate for or with unrated players.