Everything I am about to say will be old hat for many readers. Even so, I like to provide public service announcements to law students. In that spirit, here is a valuable lesson: law — or at least the practice of law — is about math. In particular, law revolves around expected value, and by extension decision theory, which means math. The D.C. Circuit’s opinions this week illustrate this lesson well.

“Math,” of course, is a scary word for many law students. When undergraduates think about law school, oration, not computation, comes to mind. They read news clips about the Supreme Court and never see equations. They watch lawyers on television and no one ever even mentions “the one,” much less forgets to carry it. Undergrads may even look at LSAT prep materials and, while the test contains the dreaded “logic games,” that isn’t really the same as “math.” And after these students come to law school, unless they look hard, they won’t see numbers anywhere.

This is a problem. A lawyer that doesn’t understand math is no friend to clients.

Think about it this way. Litigation, in large part, is a complex game of Deal or No Deal. As with that game show, the key to success is understanding expected value, discounted for risk preferences. And a lawyer must recognize that at each stage of the game, as uncertainty decreases, the math changes. When it comes to the game show, a good player can do the math; a bad player cannot.

The same principle applies to litigation. At the outset of a case, uncertainty is everywhere. What are the facts and how well will the lawyer be able to present them? What are the open legal questions? How much will litigation likely cost your client? How much will it likely cost the other side? Before going to court, a lawyer has to think through all of that and more to try to find an expected value. If the expected benefits are greater than the expected costs, it may make sense to pursue the matter. If not, a lawyer does a client no favors by encouraging suit. All the while, of course, as new information comes to light, the calculations change. And then usually, after enough uncertainty is gone, the case will settle. Who is “right” about the substantive law, therefore, is part of the larger equation, but only part. Many plaintiffs who are right about the law will determine it is not cost-justified to bring suit; many defendants who are right about the law will determine it is not cost-justified to mount a defense. To make these decisions well, a lawyer better understand math, at least intuitively. (I teach Civil Procedure. Once you understand the “game,” this class is not boring; almost every procedural skirmish plays a role in determining expected value. This can be a sobering thought.)

This principle of expected value, of course, applies to administrative law too. The perfect example is Sackett v. EPA. Sackett is a case about math, although the justices hardly used numbers at all. In Sackett, the Supreme Court — unanimously — concluded that an EPA “compliance order” is final agency action. The Court did this because the justices recognized that EPA could exercise coercive power through compliance orders; indeed, the Court called it “strong arming.” After all, after EPA concludes that someone has violated the Clean Water Act, it can either bring an enforcement action or issue a compliance order. If EPA prevails in the enforcement action, the person must pay a fine. If, however, EPA previously issued a compliance order, and if the person failed to follow that compliance order, the statute says that the fine will be significantly increased. As the Court recognized, this dynamic creates coercive power with real-world effects. If an agency issues a compliance order, even someone with a strong argument may conclude it is rational to comply, especially if they cannot seek immediate judicial review.* (Of course, immediate judicial review is no silver bullet. The fact that the CWA’s coverage can be mushy itself sometimes encourages acquiescence. After all, because there are also per day fines for violating the statute, a mere letter from the EPA threatening to bring an enforcement action often can induce compliance.) The upshot is that lawyers advising clients need to understand the situation, and, again, that requires math.

This week’s D.C. Circuit opinions are also good illustrations of the importance of being able to calculate expected value. Most obviously, look at Mike-sell’s Potato Chip Co. v. NLRB, written by Judge Silberman and joined by Judges Millett and Williams. On its face, this case appears to concern potato chips, unions, and when an “impasse” occurs in labor law. In reality, however, this case is about math. Mike-sell’s Potato Chip Co. has “fallen on economic hard times.” The Company decided it needed to lower its costs, including through lay-offs. Its employees, however, are unionized. When the time came to renegotiate the collective bargaining agreement, the “Company . . . showed the Union its books [and] sought . . . to lower costs by reducing its obligations in wages, pension and health care. The Union [for its part] wished to maintain existing pensions and health benefits and restore wage cuts it had given up in prior negotiations.” The negotiations were complex. Just days before the agreement was slated to end, the Company and Union met for another round of negotiations. Then this: “At 8:00 pm, without agreement on the major issues, the Company suggested a further meeting two days later on November 16 – a day before the expiration of the agreement. The Company stated that it did not intend to extend the agreement. The Union indicated its representatives were not available on the 16th, but it would be in touch to propose further days.” On the 16th, the Company sent a letter saying its offer was the final one. The Union said it wanted to continue negotiating. “The Union representative said it was only scheduling conflicts preventing a meeting prior to the expiration of the contract on November 17. On the 18th, the Company sent the Union another letter, declaring an impasse and stating it would unilaterally implement its last offer, which it did the next day. The Union, for its part, insisted that the parties were not at impasse.”

The key question for the D.C. Circuit was how to determine whether an impasse exists. And here, math plays a role. As the Court explained: “To take a step back, the doctrine that an employer is entitled to institute its last offer after impasse is an ancient one in labor law. Its stated purpose is to accelerate negotiations. But it should be obvious that it presents an employer – at least one negotiating in good faith – with a powerful weapon. Therefore, typically a Union will seek to frustrate its use by attempting to avoid an impasse.” If an “impasse” requires both sides to agree that negotiations aren’t working, the doctrine would largely be dead because unions would not agree to give companies this leverage. But just because an “impasse” can exist without the union’s consent does not mean that a company can declare an impasse with no risk. “If an employer, such as Petitioner, facing financial difficulty wishes relief from existing collective bargaining costs and therefore puts into place significantly diminished compensation, its risk is considerable because the Board, if it finds a violation of 8(a)(5) (no impasse existed), will order extensive back compensation, as it did in this case.” This creates a dilemma, especially when it is difficult to determine whether a court is likely to agree that there was impasse. The more legal uncertainty there is, the more dangerous it is to declare an impasse; in other words, legal uncertainty changes the expected value. In Mike-sell’s Potato Chip, Judge Silberman recognized the mathematical reality, and so declared: “An employer, facing a deadlock and planning a post-impasse institution of its last offer, is entitled to an understanding of clear legal principles that will govern its behavior.” The Court thus rejected the idea that courts should reflexively defer to the “Board’s expertise” about whether an impasse exists but instead emphasized that there must be “principles” to guide the impasse analysis. In this particular case, however, the Court concluded that no impasse occurred because the Company “had not displayed the requisite firmness on the key issues in negotiations, it had not made a last offer – a necessary if not a sufficient condition – nor declared an impasse in the crucial bargaining session.”

The week’s other case also illustrates the importance of expected value. In NOVA Southeastern University v. NLRB, written by Judge Rogers and joined by Chief Judge Garland and Judge Ginsburg, the Court confronted a potentially interesting issue: If a company hires a contractor who in turn hired employees, must the company allow the contractor’s employees to engage in labor activities at the company’s site? Unfortunately for the Company, the Court agreed with the NLRB that such employees are also entitled to protections because of a case from 2012. This is where expected value kicks in. In determining whether it was “worth it” to challenge the NLRB decision, the Company had to decide the likelihood that the D.C. Circuit would find the 2012 decision distinguishable. That the Court didn’t distinguish the earlier case does not, by itself, mean that the Company made a mistake in seeking judicial review. Nor, at the same time, is it clear that the Company made a good decision. To evaluate its choice, we would need to assess expected value, remembering that sometimes even when you make a good decision, bad things happen — or vice versa.

So what’s the takeaway from this week? Law students, pay attention to math. Your career depends on the answer to this question: Deal or No Deal? (Also, visiting a potato chip factory is a lot of fun.) 

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* A highly stylized explanation (not tied to the CWA) illustrates why this is so. Imagine that an activity produces a net benefit of $10,000. Imagine further that a private person can say with 99% confidence that any legal challenge to the activity would fail. One would expect the activity to continue. Now imagine, however, that an agency issues a compliance order commanding the activity to cease or else pay $25,000 a day in fines. Even though the odds of losing are still only 1%, the person will be strongly tempted to comply if he cannot seek immediate judicial review (ideally, from his perspective, with a stay pending review). After all, after enough time, the potential fine, even discounted by 99%, would exceed the activity’s benefit. Of course, the law may not have set per-day penalties. Instead, judges set penalties from a range after balancing various factors. This complicates the math but does not change the underlying situation. And also, needless to say, agencies do not act when it is 99% certain they will lose. This is a deliberately far-fetched, simplified example; the same sort of analysis works with different inputs.

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