2.6.2 Static and Dynamic Rating

Let us look at an example explain the procedures. You sit in a train and want to measure its speed. You have got a wristwatch and there are milestones outside. To make the measurement coarser (just like the rating measurement) the wristwatch has no second hand. Like the players change their strength, the train is accelerating slowly.

There are two concepts:

• Static: Ignore the acceleration. You measure the speed for the first mile. In order to get a finer measurement, you accumulate the time for the first and the second mile. You observe that the second speed is greater. You repeat the step and again the speed increases. In the end you get the mean speed for the whole distance, but you cannot tell, how fast the train was after three miles.

• Dynamic: Do not ignore the acceleration. The next step is to make up a plan, how the speed changes. If the changes are small and if there are no special objections against it, a linear change should be considered. This step is called modeling. If the model is reasonable, you get a good result. If not, the results are questionable. Back to our example: If the train accelerates continously the dynamic model yields the correct speed after three miles and the acceleration.

Studying the above example carefully, shows that a dynamic measurement has a couple of drawbacks: First, you must be sure to have a reasonable model. Second, you have to introduce another system parameter (the acceleration in the example), which makes the measurements more unstable.

Back to rating. Obviously, to observe the change of rating, a player must have played in many tournaments. Therefore dynamic rating can only be applied to players, who have played very often. There is another condition for dynamic rating: If the player has not played since a long time the assumption of a linear change of his rating becomes more and more questionable. Therefore, to be rated dynamically, a player must have played recently.

This divides the players into two groups: One group can be rated dynamically. The other group (the larger one) can only be rated statically. If one player changes from one group to the other, his rating changes abruptly causing the ratings of other players to change too.

In the end, dynamic rating gives a more reasonable estimate of the strength at the expense of more noise.