🕸📝Fergus Duniho wrote on Thu, Jan 12, 2006 05:16 PM UTC:
Michael Howe asks:
what, therefore, is the refutation to my concern that a player's rating be retroactively affected by the performance of a past opponent whose real playing strength has increased or decreased since that player last played him?
A system that offers estimates instead of measurements is always going to be prone to making one kind of error or the other. This is as true of Elo as it is of GCR. Keeping ratings static may avoid some errors, but it will introduce others. The question to ask then is not how to avoid this kind of error or that kind of error. The more important question to ask is which sort of system will be the most accurate overall. Part of the answer to that question is a holistic system. Given that the system estimates relative differences in playing strength, the best way to estimate these differences is a method that bases every rating on all available data. Because of its monodirectional chronological nature, Elo does not do this. But the GCR method does do this. This allows it to provide a much more globally consistent set of ratings than Elo can with its piecemeal approach of calculating ratings. Since ratings have no meanings in themselves and mean something only in relation to each other, a high level of global consistency is the most important way in which a set of ratings can be described as accurate. Since a holistic method is the most important means, if not actually necessary, for achieving this, a holistic method is the way to go, regardless of whatever conceivable errors might still be allowed.
Michael Howe asks:
A system that offers estimates instead of measurements is always going to be prone to making one kind of error or the other. This is as true of Elo as it is of GCR. Keeping ratings static may avoid some errors, but it will introduce others. The question to ask then is not how to avoid this kind of error or that kind of error. The more important question to ask is which sort of system will be the most accurate overall. Part of the answer to that question is a holistic system. Given that the system estimates relative differences in playing strength, the best way to estimate these differences is a method that bases every rating on all available data. Because of its monodirectional chronological nature, Elo does not do this. But the GCR method does do this. This allows it to provide a much more globally consistent set of ratings than Elo can with its piecemeal approach of calculating ratings. Since ratings have no meanings in themselves and mean something only in relation to each other, a high level of global consistency is the most important way in which a set of ratings can be described as accurate. Since a holistic method is the most important means, if not actually necessary, for achieving this, a holistic method is the way to go, regardless of whatever conceivable errors might still be allowed.