[eastbay]

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It seems like jcm gave a compelling argument that multiple points from the same tournament violates the necessary condition that observations be independent of each other. I have only basic training in statistics, but it seems to me that since having X chip distribution necessarily leads to a distribution of the number of observations of finish A that is different than Y chip distribution, then without removing this effect from ther results, they are not independent. I know that's nothing new but I guess I cast my vote on the side of one point per tournament.

Slim

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First problem is that independence is not a binary thing. It's shades of gray. If you want to be a purist, you could say that no two games where two players faced each other twice were permissible, since they may have learned about each other, and the resulting data is not independent in that case. The second result depends on what was learned in the first. But, at some point you have to draw the line, and do some computing rather than just disposing.

Second issue is that even two most certainly dependent data points may get used in such a way that dependence doesn't matter.

In any case, we vote the same way about the first thing to try.

eastbay