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Chess Ratings Explained One of the more frequently asked questions I receive concerning chess is "What is a chess rating, and how do you get one?" This file will attempt to answer that question in a clear and concise manner. A chess rating is a guideline for measuring a player's performance in tournaments, and ranking him/her against other players. While most people will tell you it is a measure of a player's knowledge of chess or chess ability, this is not exactly true, as there are people who perform better or worse under tournament conditions, just as there are people who perform poorly on tests even though they know the material. Many other psychological factors come into play in tournaments, such as competitive spirit, that are reflected in tournament results, and therefore also in a person's rating. So chess ratings measure performance, not ability. Having said that, chess ratings are computed on a scale of 0 to 3000, 1500 being the theoretical average, and it is supposed to be just as difficult to get a zero rating as it is to get a 3000 rating. For the mathematically inclined, that means that the _theoretical model_ of the rating scale follows a standard bell distribution curve, with the mean rating being 1500. There are many arbitrary subdivisions of this scale, called classes, that give names to certain ranges of ratings. Here is the rating scale and its subdivision into classes as used by the United States Chess Federation (USCF), with stats from the January 1995 rating list: Class Rating # of active players Percentile range Name in 100 pt. range for 100 pt level /~~~~~ 2900-2999 0 100 | | 2800-2899 0 100 | | 2700-2799 5 100 Senior -| Master | 2600-2699 57 100 | | 2500-2599 58 100 | \_____ 2400-2499 132 100 /~~~~~ 2300-2399 251 99 Master -| \_____ 2200-2299 604 99 /~~~~~ 2100-2199 976 97 Expert -| \_____ 2000-2099 1,287 95 /~~~~~ 1900-1999 1,640 92 Class A -| \_____ 1800-1899 1,939 88 /~~~~~ 1700-1799 2,251 83 Class B -| \_____ 1600-1699 2,463 78 /~~~~~ 1500-1599 2,623 72 Class C -| \_____ 1400-1499 2,560 66 /~~~~~ 1300-1399 2,538 60 Class D -| \_____ 1200-1299 2,688 54 /~~~~~ 1100-1199 2,848 47 Class E -| \_____ 1000-1099 2,874 41 0900-0999 3,107 34 0800-0899 3,101 26 0700-0799 2,751 19 0600-0699 2,232 12 Under 600 2,959 7 Total # of Active Players 41,944 Average rating of players on 1995 annual ratings list: 1271 There are also titles that can be earned, such as National Master, International Master, and Grand Master. These are not based solely on rating, and once earned they cannot be taken away - it is a title for life, no matter what happens to your rating afterward. Also, simply achieving a particular rating does not earn you the title - there are other requirements. A National Master (NM) is recognized by his nation's chess federation as a Master, and _typically_ has a rating of 2200-2399. An International Master (IM) is recognized by FIDE as being a master of world-class caliber, and _typically_ has a rating of 2400-2599. Grand Master (GM) is the highest title that can be earned, and GM's _typically_ sport ratings of 2600+. The ones that are truly amongst the best, the contenders for the World Championship, usually have ratings near or over 2700. Becoming a contender for the World Championship is determined by qualifying first in strong tournaments, then competing in one- on-one knock-out matches against other qualifiers - like a playoffs tree). World Champions usually have a rating in the high 2700's, and only the very best of those ever exceed 2800. There is a common misconception that ratings are absolute, but they are not. Because of the many factors involved, the difference between two players' ratings (for the vast majority under 2100) is not considered statistically significant unless the difference is 50 points or more. Also, ratings have a tendency to undergo both inflation and deflation, like the value of currency. Because of this, significant differences can creep in when looking back over long periods of time, so one has to be careful when, say, comparing masters of the distant past to those of the present, just as one has to be careful when comparing a baseball player with a .325 batting average in 1933 to one with a .325 batting average in 1993. The rating system currently in use both nationally and around the world was invented by a man named Arpad Elo, and is called the Elo rating system. Even the World Chess Federation (Federation Internationale de Eschecs, or FIDE) uses this system to give players international ratings. Ratings in one federation are not necessarily comparable to another. For example, since the pool of players that form the United States Chess Federation (USCF), or _any_ national chess organization, includes many amateurs and is thus weaker than the pool of international players (chess professionals), you may have to subtract between 150 and 200 points from a USCF rating to get a comparable FIDE rating. This will also apply to comparing ratings amongst different national federations. The Russians have the strongest chess-playing population, for example, and the average Russian player will be stronger than the average player from any other country. Continuing the baseball analogy, this would be like trying to compare a .325 hitter from Japan to one in the US. The stats are kept the same, but conditions vary, such as the relative strength of the opposition and the rules the game is played under, so the exact meaning of the stats vary. You get a chess rating by first joining your national chess federation (for those in the US that would be the USCF), and then playing in a rated tournament. The ratings of the opponents you play, combined with your results against those opponents, determines your rating. Your results from your first tournament will give you a provisional rating. After you have played in 20 or more rated games (usually spanning about five tournaments), your rating is considered an established rating, and can then reasonably be compared with other established ratings. For those who are mathematically inclined and interested, the formula for a provisional chess rating is: 400 (W-L) Rp = Rc + --------- N where: Rp = the player's provisional or performance rating Rc = the average rating of the player's opponents W = the number of wins L = the number of losses N = the total number of games played (N <= 20 for a provisional rating) A draw counts as half a win and half a loss. When a provisional rating is calculated, all the players rated games to date (up to the first 20 played) are used. The same formula is also used to calculate someone's performance rating for a particular event or tournament, to gauge how strong a player played in any one event. When this is done, only the games for that event are used in the calculations. Notice that for one game, your performance rating is your opponent's rating plus or minus 400 points, depending on whether you won or lost. If you drew, your performance rating is your opponent's rating. These performance ratings are then averaged to determine your provisional rating. For an example, suppose you play five games in your first rated event. Your results for this tournament are: Opponent's Rating Result Performance rating ~~~~~~~~~~~~~~~~~ ~~~~~~ ~~~~~~~~~~~~~~~~~~ Round 1: 1350 Won 1750 Round 2: 1700 Lost 1300 Round 3: 1400 Lost 1000 Round 4: 1600 Drew 1600 Round 5: 1450 Lost 1050 ---- Total 6700 6700/5 = 1340 Or using the equation: 400 (1.5-3.5) Rp = 1500 + ------------- = 1500 + -160 = 1340 5 This would be your provisional rating (and also your performance rating for this event - they are always the same for your first tournament). Now suppose you play three games in your second rated tournament, as follows: Opponent's Rating Result Performance rating ~~~~~~~~~~~~~~~~~ ~~~~~~ ~~~~~~~~~~~~~~~~~~ Round 1: 1400 Won 1800 Round 2: 1580 Lost 1180 Round 3: 1200 Drew 1200 ---- Total 4180 Again, there are two ways to calculate this. First, take your old rating and multiply it by 5 to give it a proper weighting for the five games you played previously. Then add in the new performances. (1340 x 5) + 4180 Rp = ----------------- = 10880/8 = 1360 8 Or using the formula, remembering Rc is the average of all 8 opponents' ratings, and wins and losses are the total wins and losses of both events, we have: 400 (3-5) Rp = 1460 + --------- = 1460 + -100 = 1360 8 The formula for an established rating is a bit more complex. It is: Rn = Ro + K(W-We) where: Rn = the player's new established rating Ro = the player's old established rating K = a constant (32 for players rated 0-2099, 24 for 2100-2399, and 16 for 2400-3000) W = the number of wins the player had in the event We = the number of wins the player was expected to have (win expectancy), which is calculated by the following formula: 1 We = -------------- dR/400 10 + 1 where dR (delta R) = the difference in ratings between the player and his opponent (the player's rating minus the opponent's rating). Suppose you've got an established rating of 1500, and you play in six-round event, with the following results: Opponent's Rating Result Difference in rating Win Expectancy ~~~~~~~~~~~~~~~~~ ~~~~~~ ~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~ Round 1 1700 Drew -200 .240 Round 2 1600 Won -100 .360 Round 3 1850 Lost -350 .118 Round 4 1900 Drew -400 .091 Round 5 1800 Lost -300 .151 Round 6 1550 Won -50 .429 ----- Total We 1.389 Your score in the event is .5 + 1 + 0 + .5 + 0 + 1 = 3, so W = 3 Plugging these values into the equation, we have: Rn = 1500 + 32(3-1.389) = 1500 + 51.552 = 1552 Some other rules apply to ratings: Ratings floors: Once a player has an established rating, a floor 100 points below his highest rating prevents his rating from falling any lower than this. In our example, if the player's highest rating were 1552, then his floor would be 1452, and his rating could not fall below this. Unrated players' ratings are calculated first. Once an established rating goes over 1000, it does not go below that number. A player may become a Master only by achieving that rating in tournament competition against Masters or Experts. Similarly, a player may become a Senior Master only by achieving that rating in tournament competition against Masters and Senior Masters. Also, there are currently 3 types of ratings in the USCF. There is the regular "over-the-board" or OTB rating, for games played at a time control of no less than 30 minutes per player. This is the most common type of rating, and usually the one referred to when a player asks another what his rating is. There is the Quick Chess rating, for games played at time controls of less than 30 minutes per player. There is also a Correspondence Chess rating, for games played under Correspondence Chess rules. This is because each type of chess measures different skills or the same skills in different proportions, and some players are good at one type of chess and not at others. Each type of rating uses the same formulae and the same classifications, the only difference being the rules each type of game is played under. To join the USCF or to receive further information related to chess, write to: US Chess Federation 186 Route 9W New Windsor, NY 12553 or call them at: 1-800-388-KING (1-800-388-5464) or fax them at: 1-914-561-CHES (1-914-561-2437) Please make this file freely available. If you find this file useful, please let me know by sending me (Joe Brooks) mail either through the FidoNet CHESS echo, or at one of the following addresses: FIDONet net-mail address - 1:2609/202 Internet e-mail address - joe.brooks@newhor.uu.holonet.net. Other freely available chess tutorial files by me to look for are: GUIDELN2.TXT - Guidelines to playing better chess for beginners & amateurs. NOTATN2.TXT - A tutorial on the three common forms of chess notation - algebraic, coordinate, and descriptive. ENPASNT2.TXT - An explanation of the chess move known as "en passant".