                             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 statistical 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 average 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 one 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 (this 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 around 100 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 oppenents, 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 + or - 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.  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 before 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
       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:
 
GUIDELNS.TXT - Guidelines to playing better chess for beginners & amateurs.
 
NOTATION.TXT - A tutorial on the three common forms of chess notation -
               algebraic, coordinate, and descriptive.
 
ENPASANT.TXT - An explanation of the chess move known as "en passant".
 