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kpreid comments on The Problem of "Win-More" - Less Wrong Discussion
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I wonder if other sports could use a model similar to the Triwizard Tournament. The outcome of the first two events sets the handicap for the third event, which is the only one that really counts. Be ready for some bad ideas.
Adapting this to American Football, it could be that your score after the first three quarters is converted into an advantage in downs or yards in some fashion for the last quarter.
Baseball - each run in the first 8 innings counts as an extra out in the last inning.
In Everyone Else Football... umm... I'm having a hard time coming up with something not boring but less insane than "each goal you score in the first three quarters is an extra ball that goes on the field in the last quarter and can only be scored into your opponents' goal".
This isn't very much “a sport”, but it came to mind that Team Fortress 2's Payload Race game mode works exactly like this on multi-stage maps. The handicap (starting farther ahead/behind) is very small and usually overwhelmed by team organization and the outcomes of combat, though.