Should teams opt for a two-point conversion?
``Professional football coaches often make more than $1 million a year. They work long hours, sometimes sleeping in their offices, looking for a small edge that will give their teams a victory and a chance to advance to the playoffs.
But when faced with a crucial decision during close games, many coaches make a mistake that a middle-school math student might recognize.
The problem comes when a football play known as the two-point conversion collides with a mathematical principle known as expected value... In the N.F.L. this season, two-point attempts worked 37 percent of the time. So the expected value of a two-point try was 0.74: 0.37 (the success rate) times 2 (the value of a successful attempt). The expected value of an extra point, by contrast, was about 0.94...
Week after week, after scoring a touchdown, teams try to add two points by running or passing the ball into the end zone from the tow-yard line, rather than take the safer route of kicking it through the goalposts for one point ... Bill Parcels, the New York Jets' coach this season, did it against the New England Patriots ... Behind by five points to the Patriots in the third quarter, Parcells went for two, hoping to pull within three points, the value of a field goal. The difference between trailing by four points and five points, on the other hand, seemed trivial ... The Jets... missed their two-point try, forcing them to make another one later on, which they also missed. Had they scored the extra point both times, the Patriots would not have been in position to kick a last-second game-winning field goal.
`Frequently, coaches will do something that is in direct violation of the laws of probability,' said Harold B Sackrowitz, a statistics professor at Rutgers University. He as designed an alternative card that has columns for both the score and how much time is left in a game."
Source: David Leonhardt, ``In Football, 6+2 Equals 6,'' The New York Times, January 16, 2000.
Questions for study/discussion: