This document provides approximation formulas for players to compute and update their USCF ratings. The actual rating system is quite complex, and performing the computations by hand is virtually impossible. It should be noted that, on occasion, the formulas presented below produce ratings considerably different from ratings calculated under the actual algorithm, so that the formulas below should serve only as a rough guide. A detailed description of the new system's formulas is posted at the USCF web site (www.uschess.org), and is available on request from the USCF.
Provisional and established ratings:
Players' ratings are considered provisional if they have played 25 or fewer games (rather than 20 under the old system), and established if having played more than 25. There are two different formulas to compute ratings. The criterion for using the different formulas depends on whether the player has completed 8 tournament games. The formula for ratings based on 8 or fewer games is called the ``special'' rating formula, and the other is called the ``standard'' formula. A provisional rating is updated using the special formula if the number of completed games is 8 or fewer, and the standard formula if the number is greater than 8. Established ratings are based on the standard formula.
Special rating formula:
If a player has a rating based on 8 or fewer games, or is
unrated, then the new rating can be approximated by the old
provisional rating formula, that is
Example: Suppose a player rated 1500 based on 6 games
competes against players rated 1400, 1550 and 1650, winning
the first, losing the second and drawing the third. In this
, , ,
, , and . Then,
from the special rating formula,
It should be noted that, from the approximating formula, a player could gain rating points by losing to a high rated player, or lose rating points with a win over a low rated player. The actual rating procedure corrects for these possibilities. Furthermore, the actual formulas first calculate ratings for unrated opponents, thereby making use of all game outcomes.
Standard rating formula:
To approximate one's rating using the standard formulas,
a player needs to know (or approximate) the number of games
played in tournaments, only if less than 50. Let be the
number of previous games, but set to 50 if the number of
games is 50 or more. Then, if the player
has a pre-tournament rating less than then 2200, the player
Example: Suppose a player's pre-tournament rating is
, based on games. Then, according to
the formula above,
The next step in the calculation is to determine the value
of , the value that governs the magnitude of rating changes.
For a full- event, letting be the number of games the
players completes in the tournament,
To calculate , the winning expectancy for each opponent
must be calculated and then summed. The formula for the
winning expectancy between a player with rating and an
opponent with rating is given by
The bonus, , is automatically 0 if the player has competed against
fewer than 3 distinct opponents, or more than twice against
any opponent. If the player has competed
against 3 or more opponents, no more than twice against
each, then a comparison is made
between the value and ,
where is the larger of and 4 (in other words,
3-round events are treated as 4-round events when computing
the bonus amount).
is larger or equal, then the bonus is 0. But if is larger,
then the bonus is the difference
Example: Suppose a player is rated 1300 based on 45 games, and competes in a full- event against 4 distinct opponents rated 1250, 1400, 1500, and 1550 winning three and drawing one. With these results, .
First, we compute the value of as
The value of for this player in this tournament is given by
Rating floors exist at 100, 1400, 1500,
1600, , 2100. No player's rating can drop below 100.
A player's rating floor is calculated by subtracting
200 points from the highest attained established
rating, and then using the floor just below. For example,
if a player's highest rating was 1941, then subtracting 200
yields 1741, and the floor just below is 1700. Thus the
player's rating cannot go below 1700. If a player's highest
rating was 1588, then subtracting 200 yields 1388, and the
next lowest floor is 100, which is this player's floor.