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Mathletics by Wayne L. Winston

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23

 

IF PASSING IS BETTER THAN RUNNING,WHY DON'T TEAMS ALWAYS PASS?

In football the offense selects a play and the defense lines up in a defensive formation. Let's consider a very simple model of play selection in which the offense and defense simultaneously select their play:

  • The offense may choose to run or pass.
  • The defense may choose a run or pass defense.

The number of yards gained is given in table 23.1, which we call a payoff matrix for the game. We see that if the defense makes the right call on a run, the opposing team loses 5 yards, and if the defense makes the wrong call, the team gains 5 yards. On a pass the right defensive call results in an incomplete pass for the opposing team while the wrong defensive call results in a 10-yard ...

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