This is part of a general issue in binary win/loss games.
As you approach the end of a game with a lead in points, the value of scoring more points diminishes. If you don’t adjust your strategy to compensate, you end up taking risks that increase your expected points, but decrease your win probability. Win probability plotting is popular for American Football obsessives.
It’s often very frustrating to be a sports fan, as it’s obvious what’s going wrong with the decision theory in the heads of coaches and players.
This is also one of the standard heuristics in chess. When you gain an advantage large enough, e.g. a couple of pawns, the best course of action is usually to stop trying to gain more advantages and instead trade as many pieces as you can, to avoid counterplay and reach a simple-to-win endgame.
Intermediate players may, at times, enjoy a material advantage and start exchanging pieces. However, they may become too focused on exchanging pieces, as if it were a terminal goal, and neglect their position. Once their pieces are placed sufficiently worse, their material advantage might not count as much anymore, and they might lose their advantage and the game.
I recently witnessed exactly this pattern in a game of two weak amateurs, where the weaker player had won a minor piece. In the end, he lost—not because he blundered back, but because his opponent could gradually improve his pieces to the point where he was actually better despite still being down a piece.
However, simplification (even giving back material) to reach a technically won endgame is a viable plan of action for stronger players, so I think it fits the pattern of a “win-more” problem.
Quibbling: Weak players sure, but club level players rarely mess up simplification that much. They need a larger advantage than stronger players to be sure they’ll end up better after simplification, but they don’t usually misjudge that advantage in my experience. So at club level and beyond it’s very standard and effective stategy.
You are correct—although I have also seen club players misjudge a Queen + pawns vs. Rook + Pawns endgame, thinking it was won when in fact it was only a draw.
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”.
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.
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.
In a failed attempt to make the game “interesting”, the NFL Pro Bowl would do the opposite, and help the team that was behind. They would get the ball again after they had scored if they were still behind. Naturally, that makes it easier to catch up.
This is part of a general issue in binary win/loss games.
As you approach the end of a game with a lead in points, the value of scoring more points diminishes. If you don’t adjust your strategy to compensate, you end up taking risks that increase your expected points, but decrease your win probability. Win probability plotting is popular for American Football obsessives.
It’s often very frustrating to be a sports fan, as it’s obvious what’s going wrong with the decision theory in the heads of coaches and players.
This is also one of the standard heuristics in chess. When you gain an advantage large enough, e.g. a couple of pawns, the best course of action is usually to stop trying to gain more advantages and instead trade as many pieces as you can, to avoid counterplay and reach a simple-to-win endgame.
Does it take a really good player to take advantage of this strategy i.e. is knowing about it a trap from middling players ?
Intermediate players may, at times, enjoy a material advantage and start exchanging pieces. However, they may become too focused on exchanging pieces, as if it were a terminal goal, and neglect their position. Once their pieces are placed sufficiently worse, their material advantage might not count as much anymore, and they might lose their advantage and the game.
I recently witnessed exactly this pattern in a game of two weak amateurs, where the weaker player had won a minor piece. In the end, he lost—not because he blundered back, but because his opponent could gradually improve his pieces to the point where he was actually better despite still being down a piece.
However, simplification (even giving back material) to reach a technically won endgame is a viable plan of action for stronger players, so I think it fits the pattern of a “win-more” problem.
Quibbling: Weak players sure, but club level players rarely mess up simplification that much. They need a larger advantage than stronger players to be sure they’ll end up better after simplification, but they don’t usually misjudge that advantage in my experience. So at club level and beyond it’s very standard and effective stategy.
You are correct—although I have also seen club players misjudge a Queen + pawns vs. Rook + Pawns endgame, thinking it was won when in fact it was only a draw.
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.
I would watch this variant of Everyone Else Football.
In a failed attempt to make the game “interesting”, the NFL Pro Bowl would do the opposite, and help the team that was behind. They would get the ball again after they had scored if they were still behind. Naturally, that makes it easier to catch up.