Sunday, November 12, 2006

The Guessing Penalty

The Giants are "idiots" for attempting a 52-yard field goal that was returned by the Bears for a crucial touchdown in Sunday night's loss.

At least that's what you believe if you're a Chicago-area radio host. After all, the only bad decisions are those which end up hurting you, right? If you're like the many radio hosts I heard on my drive home from watching the game, you certainly feel this way.

I liken this approach to how many students react the first time they hear of the "guessing penalty" on standardized tests. On the SAT, to prevent test-takers from artificially enhancing their scores by randomly guessing on questions that stump them, the student is penalized for incorrect answers in such a way that random guessing will even out in the long run. For example, if a question has five choices, each correct answer is worth +1 point, and an incorrect response costs you 1/4 of a point.

Many students see that they are penalized for incorrect responses and, not understanding the mathematics behind the system, decide not to guess at all unless they are confident in an answer, even if they have it narrowed down to two choices.

When taking an SAT prep course, the first thing the instructor does is demonstrate how the guessing penalty really works. First, they will show that if you guess randomly on five questions and get one right, as you will on average, you break even. Then they will demonstrate that narrowing the choices down to two or three makes guessing very profitable.

For example, if you narrow each of eight questions down to a coin flip between A and B, you will average getting four right and four wrong, for a total profit of +3 points to your score. Guessing when you can narrow it down to two choices, even if you have no preference between the two, is worth +3/8 of a point to your score on average.

What does this have to do with football? Let's say you narrow down eight questions to two choices each, but because you're extremely unlucky, you get all eight wrong. If you could see your test results, you would likely lament guessing on those questions, just like Tom Coughlin probably regrets attempting the field goal. That doesn't make it the wrong decision.

In hindsight, it seems so easy to assume that the field goal would likely fall short, providing a golden opportunity for a lengthy return reminiscent of Nathan Vasher's 108-yard runback against the 49ers in 2005. However, at the time, kicking was a perfectly reasonable move. The Giants were down by four points with 12 minutes to play, facing fourth-and-15 at the Bears' 35. Most people would completely rule out going for the first down here; I wouldn't, but kicking was still the best play. A punt probably gains them an average of 25 yards of field position over kicking the field goal and missing. The chance at three points was far more valuable.

It's popular to be a monday-morning quarterback, but the world needs analysts who can separate the truly bad decisions from the good ones gone awry. The Giants may not have played a good game on Sunday, but the decision to kick didn't cost them the win.

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