Why don't coaches understand fundamental math?

[pzhon]

Not only are the teams losing out, so are the announcers. I think the fans would value comments like, "They should go for the touchdown. Going for it won't win more points here, but failure means turning over the ball on the goal line. That is worth 1 point more than kicking the ball off after a successful field goal," or, "They need to realize they are in a desperate situation since losing by 3 points is the same as losing by 30. They need to play for there to be 3 or 4 more touchdowns in this game, even if that means they get those touchdowns only 1 time in 3. They have to go for it here."

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I'd be curious to see what the average log of the effect of coaching decisions on the result is, rather than just the flat averages.

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What do you mean? If a mistake drops a team's winning chances from 10% to 5%, that is both cutting their chances in half, and increasing their opponent's chances by less than 6%.