Expected and achieved points

The achieved points ${\displaystyle W}$ are the sum of the game results in which a win counts 1 point, a draw counts ½ point, and a defeat 0 points. The expected points ${\displaystyle W_{e}}$ are calculated with the following approximation:

${\displaystyle W_{e}={\frac {1}{1+10^{(Z_{G}-Z_{A})/400}}}}$

${\displaystyle Z_{A}}$: present DWZ

${\displaystyle Z_{G}}$: present DWZ of the competitor

The expected points are calculated for each game of chess and then added. The exact values of the expected points can be looked at in the table of the DSB. The formula provides good approximations.

The development coefficient

Another constituent is the development coefficient ${\displaystyle E}$. It consists of the fundamental value ${\displaystyle E_{0}}$, the acceleration factor ${\displaystyle a}$ and the braking value ${\displaystyle B}$:

${\displaystyle E=a\cdot E_{0}+B}$

with

${\displaystyle E_{0}=\left({\frac {Z_{A}}{1000}}\right)^{4}+J}$

where the component ${\displaystyle J}$ depends on the age of the player:

${\displaystyle J={\begin{cases}5,&{\text{for teenagers (up to 20 years)}}\\10,&{\text{for junior adults (21 - 25 years)}}\\15,&{\text{for adults (over 25 years)}}\end{cases}}}$

and

${\displaystyle a={\frac {Z_{A}}{2000}}}$

The factor ${\displaystyle a}$ is furthermore defined as ${\displaystyle 1\geq a\geq 0.5}$. Additionally, it is only calculated if the player is less than 20 years old and has achieved more points than expected. The acceleration factor a is 1 if that is not the case. The acceleration factor helps young players to improve their DWZs more quickly.

${\displaystyle B=e^{\frac {1300-Z_{A}}{150}}-1}$

The braking value B is only calculated for players with a DWZ of under 1300 points and only if the achieved points are less or equal to the expected ones, else the braking value is 0. The braking value makes the DWZ of poor players decrease not so rapidly.

Besides, ${\displaystyle E}$ depends on the number of the previously evaluated tournaments. The index ${\displaystyle i}$ is 1 in the first DWZ and is increased by 1 after every tournament evaluation.

Also consider that:

${\displaystyle 5\leq E\leq {\begin{cases}\min(30;5i),&{\text{if }}B=0\\150,&{\text{if }}B>0\end{cases}}}$

This formula is only considered when a DWZ already exists, viz. ${\displaystyle i}$ is not only 0. So ${\displaystyle E}$ is normally increased to 5, if the coefficient is less than 5, or decreased to 30 if ${\displaystyle E}$ is higher than 30. If a braking factor is present (${\displaystyle B>0}$), ${\displaystyle E}$ can also go beyond 30.

The next step is to round ${\displaystyle E}$ to the nearest integer.