Effective number of games

For each player, let $N$ be the number of tournament games the player has competed, or, for unrated players, the value assigned from Step 1 of the algorithm. Let $R_0$ be the player's pre-event rating, or, for unrated players, the imputed rating assigned from Step 1. Let

$$N^* = \left\{ \begin{array}{ll} 50/\sqrt{1 + (2200-R_0)^2/10... ...leq 2200$} \\ 50 & \mbox{if $R_0 > 2200$} \end{array}\right.$$ (1)

Define the ``effective'' number of games, $N'$, to be the smaller of $N$ and $N^*$. As a result of the formula, $N'$ can be no larger than 50, and it will usually be less, especially for players who have not competed in many tournament games. Note that $N'$ is a temporary variable in the computation and is not saved after an event is rated.

Example: Suppose a player's pre-event rating is $R_0=1700$ based on $N=30$ games. Then according to the formula above,

N* = 50/sqrt(1 + (2200-1700)^2/100000) = 50/sqrt(3.5) = 26.7

Consequently, the value of $N'$ is the smaller of $N=30$ and $N^*=26.7$, which is therefore $N'=26.7$. So the effective number of games for the player in this example is $N'=26.7$.