Sixteen female Senators have called on the NFL to impose a “zero tolerance” policy for domestic violence by players. “If you violently assault a woman, you shouldn’t get a second chance to play football in the NFL.”

I sympathize with the sentiment behind the letter, and — if I were a football fan — I would find it hard to feel any connection as a fan with a player who I knew was guilty of violent assault; it might make good business sense for the NFL to fire such players.

But where would it put football players’ wives who are being beaten? If they call the police, and the player is prosecuted, that doesn’t just mean the end of the player’s career; it likely means a loss of millions of dollars to the wife as well as to the husband. They call the police, and their husband is out of a job, they can’t pay their mortgage, and they and their children are potentially headed for poverty.

And of course the women may still love their abusive husbands, and be willing to expose them to a well-deserved prosecution and even public shame, yet not to the loss of the career that their husbands care deeply about. But even if they understandably no longer care about their husband’s happiness, and plan to get a divorce after calling the police, the husband’s job loss would mean that he’s unable to pay child support, keep them and the children in the family home, and so on.

Of course, some women may choose that financial loss over continued abuse, and I respect them for it. But some women may not be willing to make that trade-off, and they thus won’t call the police. Indeed, they won’t tell anyone, for fear that it will leak out.

They may be especially unwilling to say anything when the abuse starts, and doesn’t yet seem to be chronic or extreme. By the time they do call the police (if they ever do), the abuse would have had to be something unendurably bad for them, bad enough to lead them to be willing to ruin their own financial lives as well as their husband’s. And that might be too late; indeed, as best I can tell, it’s better if women try to get police intervention early in the process of abuse rather than later. But will they do that if this early intervention is so costly for them?

Indeed, my understanding is that this is already one reason why some wives don’t report abuse by their husbands: If the husband is arrested and imprisoned, he’ll lose his job, and when that happens the family loses, too. But a zero-tolerance policy, under which the employer obligates itself to permanently fire the husband, and in a situation where the loss of income has such a dramatic financial effect, would only exacerbate the problem. This is an aspect of what I call the anticooperative effect of law: Sometimes measures to fight crime actually cause people to fear cooperating with law enforcement.

Now maybe on balance a zero-tolerance policy would still do more good than harm. The senators’ letter argues, for instance, that the policy would “send a strong message that the league will not tolerate violence against women by its players, who are role models for children across America.” If that’s right, then maybe (1) the deterrent effects plus (2) the norm-setting effects (the message sent to children across America) will on balance protect women more than the anticooperative effects will jeopardize them.

But on the other hand, the anticooperative effect will, at least in some measure, decrease the deterrent effect. “What’s she going to do,” a football player might think to himself, “call the police and lose all the income that she’s gotten used to?” And sometimes that player might be correct in this prediction. If you think this is so, and if you’re skeptical that children are going to be much influenced by this policy — or would be better influenced by hearing more frequent stories of significant criminal and professional penalties under a less punitive policy than by hearing of the zero-tolerance policy and its likely very rare enforcement — you might think that women will be more hurt than helped by exposing NFL wives to the prospect of financial ruin for calling the police.