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559 andrew gelman stats-2011-02-06-Bidding for the kickoff


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Introduction: Steven Brams and James Jorash propose a system for reducing the advantage that comes from winning the coin flip in overtime: Dispensing with a coin toss, the teams would bid on where the ball is kicked from by the kicking team. In the NFL, it’s now the 30-yard line. Under Brams and Jorasch’s rule, the kicking team would be the team that bids the lower number, because it is willing to put itself at a disadvantage by kicking from farther back. However, it would not kick from the number it bids, but from the average of the two bids. To illustrate, assume team A bids to kick from the 38-yard line, while team B bids its 32-yard line. Team B would win the bidding and, therefore, be designated as the kick-off team. But B wouldn’t kick from 32, but instead from the average of 38 and 32–its 35-yard line. This is better for B by 3 yards than the 32-yard line that it proposed, because it’s closer to the end zone it is kicking towards. It’s also better for A by 3 yards to have B kick fr


Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 Steven Brams and James Jorash propose a system for reducing the advantage that comes from winning the coin flip in overtime: Dispensing with a coin toss, the teams would bid on where the ball is kicked from by the kicking team. [sent-1, score-1.596]

2 Under Brams and Jorasch’s rule, the kicking team would be the team that bids the lower number, because it is willing to put itself at a disadvantage by kicking from farther back. [sent-3, score-1.88]

3 However, it would not kick from the number it bids, but from the average of the two bids. [sent-4, score-0.416]

4 To illustrate, assume team A bids to kick from the 38-yard line, while team B bids its 32-yard line. [sent-5, score-1.562]

5 Team B would win the bidding and, therefore, be designated as the kick-off team. [sent-6, score-0.487]

6 But B wouldn’t kick from 32, but instead from the average of 38 and 32–its 35-yard line. [sent-7, score-0.321]

7 This is better for B by 3 yards than the 32-yard line that it proposed, because it’s closer to the end zone it is kicking towards. [sent-8, score-0.821]

8 It’s also better for A by 3 yards to have B kick from the 35-yard line, rather than from the 38-yard line, it proposed if it were the kick-off team. [sent-9, score-0.5]

9 In other words, the 35-yard line is a win-win solution–both teams gain a 3-yard advantage over what they reported would make them indifferent between kicking and receiving. [sent-10, score-1.053]

10 While bidding to determine the yard line from which a ball is kicked has been proposed before, the win-win feature of using the average of the bids–and recognizing that both teams benefit if the low bidder is the kicking team–has not. [sent-11, score-1.837]

11 Teams seeking to merely get the ball first would be discouraged from bidding too high–for example, the 45-yard line–as this could result in a kick-off pinning them far back in their own territory. [sent-12, score-0.648]

12 “Metaphorically speaking, the bidding system levels the playing field,” Brams and Jorasch maintain. [sent-13, score-0.39]

13 “It also enhances the importance of the strategic choices that the teams make, rather than leaving to chance which team gets a boost in the overtime period. [sent-14, score-0.843]


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