5. Applications

Rating systems typically maintain a pool of rated players and apply their formulas to contests among the players as they occur. This straightforward approach is not without its problems:

• Although the emphasis is on up-to-date ratings, the underlying data are usually an assortment of old and new.

• While some ratings are stable, others are upwardly mobile, and both together cause deflation in the pool at large.

• Data samples vary in size from the occasional to the perennial player, with resulting variation in sampling error.

• Finally, the rating pool itself is changing as players come and go.

In such an environment it is asking a great deal of players to be patient while the minimizing effects of the rating process take hold. A system that restricts itself to upward adjustments, much like master points in bridge, is an appealing alternative and will be investigated further on.

The Elo System attempts to keep ratings current by limiting sample size in its established rating, which thus becomes a kind of moving average, described more fully in the following section. Unlike ordinary moving averages, where sample size is restricted to the last N games, established ratings are based on attenuated sample weight. The effect of a rated event with an original sample weight of 1/N gradually becomes attenuated as more data are processed, but the effect is never completely lost. The established rating thus becomes a weighted moving average. Even though recent data are more heavily weighted, rating changes cannot keep pace with changes in playing strength.  Timely adjustments of established ratings, in short, do not guarantee currency of the data on which they are based.

A more rigorous application of the rating process involves simultaneous calculations for a defined data set. In 1969 such an application produced the first International Rating List [E1]. Recursive calculations on a computer were applied to the complete interplay of 210 contestants over the previous three years. This was regarded primarily as a method for initializing the rating pool, but the effect was to produce a self-consistent set of ratings with clearly defined boundaries. Linear programming, as exemplified by this method, has the drawback of being computationally intensive, and it is an open question whether the masses of data processed by a large rating system could be handled in this manner.

The issue, in the final analysis, is between descriptive statistics and statistical inference.  The attempt to establish a clearly defined, self-consistent rating pool focuses on the descriptive value of rating statistics.  The current fashion, attempting to infer trends from probability assumptions, is a far more hazardous undertaking.