Rules for organizing, conducting, and participating in online Heroes of Might and Magic III tournaments.

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I wonder if any sports use a ranking system in a similar way? I can't recall any examples.

It was used (and may still be used). In the group stage of the Champions League in football. In case of a tie in points, the head-to-head record, goal difference, and number of goals scored were considered. And if all of these were equal, the club's (or country's) ranking was taken into account. But the ranking was never used to determine which team would advance, as the other criteria were sufficient.