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These ratings, calculated for Williams, Paul, incorporate all games (against rated opponents) played in the year before the "Date of rating", along with the ratings that were already calculated one year previously. If a player has an insufficient number of games in recent years, there may be gaps in the list, even though you may see ratings listed on previous and/or subsequent dates. Whenever a player has played no rated games for three straight years, or dies, they are removed from the list.

Definition of columns in the above list:

Date of rating is the "effective date" of the rating. The rating calculation does not include any games occurring after the "Date of rating".

World Rank refers to the player's world rank on that date.

Rating is the calculated rating for the player, as of the "Date of Rating". This represents the player's estimated strength on the following day.

+/- is the standard deviation of the player's rating estimate. It is based on a geometric average of the number of rated games played in past years. Players who play very frequently will have a smaller +/- value, indicating a greater confidence in the accuracy of their rating. Players whose +/- value exceeds 76 are classified as "Inactive" due to their infrequent play against rated opponents. Mathematically, a player's rating is an estimate of their exact strength on the day after the "Date of Rating". The +/- value represents the standard deviation of that estimate; the player's true strength on that date should be within one standard deviation of their calculated rating approximately 68% of the time, and within two standard deviations of their calculated rating approximately 95% of the time.

Age is the player's exact age in years, on the "Date of Rating". If a player's age is displayed as a link, that means that this rating was active at the time of their next birthday. Click on the link to see the sorted list of all players' ratings on their birthdays when turning that same age.

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