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Convergence

Posted By: Rich Munitz
Date: Friday, 8 July 2011, at 5:42 p.m.

In Response To: Convergence (Bob Koca)

Suppose two populations are of different skills and have converged so that the difference in average rating within each population reflects the average skill difference between the two groups. If there is a single new player rating given to everyone regardless of population, this will be the average rating of the combined population. Since the two populations are of unequal skill and have converged to their proper levels, the new player rating will be higher than the average rating of the weaker population and will therefore raise the average rating of the group. Similarly it will drag down the average rating in the stronger population. While the two groups will always retain average ratings where the stronger group is higher than the weaker group, the ratings will no longer properly reflect the skill difference between the groups. In fact, if population size increases fast enough, the two population ratings can be made arbitrarily close to one another. Setting initial rating to current population average avoids this pull to the center.

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