Be like Tebow

Never followed him in college, but am intrigued by Denver Broncos quarterback Tim Tebow. And his experience has lessons for the actuarial exams.

If you follow football, you know Tebow led his team back from 15 points behind late to win Sunday’s game. Apparently Tebow has crude quarterbacking skills. His only skill, it seems, is winning.

But his ties to the actuarial world arrive via Advanced NFL Stats, a site that crunches football numbers the way the Sabermetricians have long done for baseball.

We’ve heard one statement over and over since Tebow joined the Broncos last season: Kyle Orton gives the Broncos the best chance to win.  I disagree.  While Orton is the better and more consistent quarterback, Tebow gives the Broncos the best chance to win.

A bit counterintuitive. Tebow apparently hashes things up most of the time. But when he plays well, he is fantastic.

And when you are on a bad football team (which the Broncos are), you don’t want consistency, because then you will consistently lose. You want Tebow playing, and you hope he is operating at his rare top level, because then you might win. If he plays poorly, it’s no big deal – you were going to lose anyway.

Blogger Keith Goldner puts it into three distributions, one for the Broncos with Tebow at QB, one for the Broncos when led his safe, competent alternative, Kyle Orton.

The third distribution is the performance of Denver’s opponent in a typical week. If Orton is quarterback, Denver wins when the green line is to the right of the red line. With Tebow at quarterback, Denver wins when the blue line is to the right of the red line.

Notice that the mean performance of each quarterback – where the distributions peak – is the same. So, on average, there’s no difference between the two. However, look at how much more frequently the blue Tebow line surpasses the red line – much more frequently than the green Orton line does.

The lesson: When you think you’re going to lose, you are better off gambling. You benefit by increasing the variability of the result.

This has a direct application to some of the upper level actuarial exams, especially on the casualty side. The multiple choice sections have a guessing adjustment. If the MC gives you five choices you get one point for a correct answer, no points for leaving the question blank and negative 1/5 point for filling in the wrong answer. Some trivial math shows that the expected value of guessing is zero. Should you guess?

Tim Tebow tells us what to do, because like his performance vs. Orton’ – the expected performance – doesn’t change. But by guessing you increase the variance of your score. If you think you’re going to fail, you might as well guess and hope for luck. But if you think you are going to pass, you should not guess – luck is more likely to work against you.

(Early joint SOA/CAS exams don’t have this adjustment. So you should guess in any case – a problem in game theory instead of probability.)

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