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The analytics are interesting and confirm the intuitions of experienced players. There is one social cost and game theoretic aspect you ommited:The players play for fun and are partly rule-setters themselves, which explains why we're in this equilibrium.

When you have an inverted line-up, there are two boards that have a much less interesting game, so it's rather rude at least to the board 1 of the opposong team who could travel hours on his free day to enjoy his hobby. On the other hand, always playing exactly ccording to rating could result in every season playing he same guy and can be a bit boring. Everybody knows they could misuse the line-up for their own advantage, but if they do that too often, the aggregate of players/league will set strict rules that makes it less fun for everybody.

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