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Is it worth the risk to give players a second chance? Stephen J. Dubner analyzes how guys who took the game for granted performed when they were given another shot.

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Trade off with troublemakers

By Stephen J. Dubner

Economics is all about trade offs. If you want to buy a top-tier performance car, it'll cost you a lot more than a Camry. If you're looking for an investment that'll set you up for life, you have to be willing to take on more risk.

NFL personnel decisions involve the same kind of trade offs. Better players generally cost more. Bigger players are generally slower. Just look at the NFL draft, and how hard it is to balance all these trade offs when making your picks -- especially when you're spending huge money on a guy whose future is impossible to predict. (We explored this puzzle earlier in "The Quarterback Quandary.")

In this installment of Freakonomics Football, we look at a different kind of trade off -- the decision of how to handle a player who's gotten in trouble off the field. Unfortunately, you don't have to think very hard to come up with a lot of big names from the recent past: Michael Vick, Ben Roethlisberger and Plaxico Burress, to name just a few.

With guys like these, the trade off is pretty clear. The player has already proven his value on the field, so that's the upside. But will his off-the-field trouble follow him back into the game? And then you've got to wonder how his physical performance will be affected by his time off for bad behavior.

It would be nice to be able to give a purely scientific answer to the following question: After getting into big off-the-field trouble, do players tend to perform better, the same, or worse?

Unfortunately, that's a really hard question to answer, for a variety of reasons:

1. The sample size is relatively tiny. While it might seem like a lot of professional athletes get in trouble, the fact is that they inevitably make headlines when they do, whereas you and I won't. This leads to a skewed sense of proportion about how much athlete wrongdoing there is. A former NFL security chief -- who was also a former FBI assistant director -- once told me that NFL players are in fact arrested at a lower rate than young men the same age in the general population, and a variety of independent studies back him up.

2. There are a ton of other variables to wrestle with. Just take Vick and Roethlisberger. Vick was in prison and out of football for a couple of years (during which time he went bankrupt), and then reentered the league as a backup in a new city. Roethlisberger, who wasn't even arrested, missed just four games and came back with his same team. So comparing the return of one to the other is very much comparing an apple to an orange.

3. You also have to face the fact that most guys who get in trouble aren't high-profile guys and, moreover, they often don't come back and play. Imagine there are two groups of players who get in trouble: High-profile guys and low-profile guys. The high-profile guys will almost certainly get another chance to play if only because they're better players to start with. But here's the kicker: They'll also get more scrutiny as a result. As with a lot of things in life, we tend to pay more attention to the noisy examples and forget the others which often constitute the majority.

So how would I think about this question if I were a GM or a coach, considering a player who got in trouble off the field?

First I'd ask myself: Is this guy a generally solid citizen who got in trouble due to a lapse in judgment, or was he a knucklehead to start with, who made it to the NFL despite his character weakness?

Then, if he fits in the second category, I'd ask myself the most important question of all: Am I willing to live with the trade off? Just because I want to drive the Lamborghini doesn't mean I shouldn't buy the Camry.

Coming up next on Football Freakonomics

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Coming Nov. 9