The rating system described here is for over-the-board competitiononly. Those interested in correspondence ratings should requestthe correspondence chess pamphlet describing that system.The basictheory of the USCF's rating system is that the difference betweenthe ratings of players is a guide to predicting the outcome ofa contest between those two players.

The specific formula has been worked out according to statisticaland probability theory. No rating, however, is a precise evaluationof a player's strength. Instead, ratings are averages of performancesand should be viewed as approximations within a range. This rangeis at least plus or minus 56 points (the standard deviation) forratings less than 2100. Provisional ratings, based on fewer than20 games, are much less reliable than established ratings.

A player may approximate his or her new rating by using the appropriateformula. The result will probably not be exact, however, becauseofficial calculations in the USCF office are based on currentratings rather than on last published ones. The extreme fluctuationin a newer player's ratings makes approximation all the more difficult.

2200-23992000-21991800-19991600-17991400-15991200-13991000-1199

Senior Master	above2399
Master
Expert
Class A
Class B
Class C
Class D
Class E
Class F	800-999
Class G	600-799
Class H	400-599
Class I	200-399
Class J	Under200

1. Rated games. All games played in USCF-rated eventsare rated, including games decided by time-forfeit, games decidedwhen a player fails to appear for resumption after an adjournment,and games played by contestants who subsequently withdraw or arenot allowed to continue. Games in which one player makes no moveare not rated. There are two separate rating systems. A player's"Quick" rating is calculated if he or she participatesin events with time controls of G/10-G/29. A player's "regular"rating is computed if he or she enters a tournament with timecontrols of G/30 or slower. Events with time controls of G/9 orfaster are not rated.
2. Time controls. Time controls must be announced in advance.Sudden-death time controls require that all remaining moves, nomatter how many, be completed within a fixed time. Sudden deathis becoming popular because it guarantees games will finish ontime.
3. Order of ratings. Normally, events are rated in chronologicalorder by their ending dates. New ratings produced by each eventare used for the next calculation, and so forth. Published ratingsare those current as of the closing date of a given list.
4. Matches. Individual matches are rated with the followingrestrictions:
   1. Both players involved must be rated, with the difference inratings not to exceed 400 points (the latest published ratingprior to the match will be used for calculating the rating difference).Match reports not conforming to this regulation will be returned.
   2. Match reports must be validated by a certified tournamentdirector, or the players must sign a notarized affidavit.
   3. The maximum rating change allowed as a result of a match is50 points.
   4. No player may go up or down more than 200 rating points withina three-year period solely as a result of Match play.
   5. Match results may not be taken into account when a playeris being considered for an invitational tournament unless thoseresults are subsequently confirmed in tournament play.
   6. Equations I and II (see "5. Equations") are usedto rate matches.

Rp is the performance rating (i.e., the new rating).

Rc the average rating of the player's opponents.

W the number of wins.

L the number of losses (a draw counts as half a win andhalf a loss).

N the number of games.

Initializing a player's Quick rating.

After the player's first G/10-G/29 tournament, the pre-tournamentQuick rating is equal to his or her regular rating (unlike thepre-tournament rating of zero if a player is participating inhis or her first regular rated tournament).

The pre-tournament Quick rating is provisional, and the numberof games depends on the regular rating type. If the regular ratingis established, the Quick rating is provisional based on 10 games.For example, if a player's current (established) regular ratingis 1700, the player's pre-tournament Quick rating is initializedto 1700/10. If the regular rating is provisional based on 10 ormore games, the initial Quick rating is based on 10 games.

If the regular rating is provisional based on fewer than 10 games,the initial Quick rating is based on the same number of games.When a player's Quick rating already exists, the regular ratingis not used in calculating the Quick rating.

For players with established ratings (based on 20 games or more)the equation is:

Rn is the new rating.

Ro the old (pre-event) rating.

K a constant (32 for 0-2099, 24 for 2100-2399, 16 for 2400and above).

W the score in the event.

We the expected score (Win Expectancy), either from thechart or the following formula:

"dr" equals the difference in ratings.

For 1/2-K events, the constant, K, is different; i.e.,16 for 0-2099, 12 for 2100-2399, and 8 for 2400 and up. Informationon Quick rating system's "K" factor is availableon request from the USCF office.

If a player's post-tournament rating crosses the "K"factor boundary (e.g., pre-tournament rating was 2093 and post-tournamentrating was 2105 or vice versa), one of the following equationsis used to adjust the post-tournament rating:

Where Rn is post-tournament rating and Ra is "crossingK factor" adjustment. Ra becomes the new post-tournamentrating.

6. Rating floor: An established player has a rating floor.In most cases, floors are calculated by subtracting 200 pointsfrom the individual's highest rating achieved and setting thelast two digits to zero. If a player's highest rating achievedis less than 1600, the individual's floor is 100. This proceduredoes not apply if an individual wins a large cash prize in a tournament(See explanation in the following paragraph.) No floors above2400 or below 100 are permitted.

Rating floors examples:

1. If Jack's highest rating achieved is 1830, his floor is 1600.
2. If Joe's highest rating achieved is 1599, his floor is 100.

A person's rating floor can also change if he or she wins a largecash prize. The rules governing USCF rating floors for large prizewinners are as follows: Under-2200 or below, $1,000; Under-2300,$1,500; Under-2400, $2,000.

Please note: a player can have a 2300 or 2400 rating floorONLY by winning a large cash prize (under-2300 prizeof at least $1,500 or under-2400 prize of at least $2,000). Theminimum post-tournament rating of players winning the above prizesshall be the lowest rating which would not be eligible for thesection or class prize the player won.

Example: If Sharon won an Under-1900 prize of $1,010 andher pre-tournament rating was 1853, her post-tournament ratingand floor would be at least 1900. Thus, Sharon would be ineligibleto win an Under-1900 prize in future events. If Jack won an Under-1500prize of $1,200, his floor would be set to 1500.

7. When an event is rated, the ratings of previously unratedplayers are calculated first, followed by provisionally-ratedplayers, and finally those with established ratings.

8. The USCF Executive Director may review the rating ofany USCF member and make the appropriate adjustments, includingbut not limited to imposition of a rating "ceiling"(a level above which a player's rating may not rise).

9. The rating system also calculates players' lifetimetitles. One can earn permanent titles by achieving good performancesor norms in events of at least four rounds. Technical informationon lifetime titles is available on request from the USCF office.

Examples of Rating Calculations

1. Previously Unrated and Provisionally Rated Players

A player is given a performance rating for each game in his firstevent. His performance rating for a win is his opponent's ratingplus 400; for a draw it is his opponent's rating; for a loss itis his opponent's rating minus 400. These performance ratingsare then averaged to determine the player's provisional rating.

Example 1: You play five games in your first rated event,defeating a player rated 1350, losing to players rated 1700 and1400, drawing with one rated 1600, and losing to one rated 1450.Your performance ratings are 1750, 1300, 1000, 1600, and 1050.Dividing the sum of these (6700) by the number of games (5) gives1340, your initial provisional rating. The equation will yieldthe same result:

Example 2: You play three games in your next rated event.You beat a player rated 1400, lose to one rated 1580, and drawwith one rated 1200. Again, there are two easy ways to calculate:

1. Your old rating times five (for proper weighting) plus theseperformances divided by eight, which is the total number of games:

2. Or you may use the following equation, (rememberingto use the average of all opponents' ratings for Rc):

II. Players with Established Ratings

A player's rating becomes established when he has played 20 ratedgames, including those in the event being rated.

1. Subtract each opponent's rating from your rating, noting whetheryou are rated higher or lower than each opponent.
2. Find the We for each opponent from the chart, beingsure to use the correct column. (If you are higher rated, yourWe will be greater than .500.)
3. Sum the We values.
4. Find W by summing the game points earned in the event,ignoring byes, forfeits, and other unratable games.
5. Subtract We from W.
6. Multiply this difference by 32 (by 24 if you are rated 2100-2399,16 if you are rated 2400+; use 16, 12, 8 for 1/2 K events).
7. Add your pre-event rating (Ro) to this calculationto get your new rating.

1. Example 3: You have an established rating of 1500.You play six games against opponents rated 1700, 1600, 1850, 1900,1800, and 1550, drawing with the first, beating the second, losingto the third, drawing with the fourth, losing to the fifth, beatingthe sixth.
   1. Subtracting each opponent's rating from your rating, you obtain-200, -100, -350, -400, -300, and -50.
   2. For -200 the We is 0.240, for -100 the We is0.360, for -350 the We is 0.118, for -400 the Weis 0.091, for -300 the We is 0.151, and for -50 the Weis 0.429.
   3. Summing the We scores gives 0.240 + 0.360 + 0.118 +0.091 + 0.151 + 0.429 = 1.389.
   4. Your W is 0.5 + 1 + 0 + 0.5 + 0 + 1 = 3.
   5. Subtract 1.389 from 3 to get 1.611.
   6. Multiply 1.611 by 32 to get 51.552.
   7. This rounds off to 52. Your new rating is 1500 + 52 = 1552.