Assessing Likelihood of Success in the Fourth Circuit

By Steve Klepper

There is a divide on the Fourth Circuit on how to calculate a litigant’s odds of success. When a party seeks a preliminary injunction, the factors include the likelihood of success on the merits. Three recent Fourth Circuit decisions address the “multiplicative problem” when the movant must win on several issues.

The most recent offers what I’ll call the “Steph Curry Hypothesis.” Judge Quattlebaum, in United States v. Herrera-Juarez, calculated that a movant with a 75% chance of success on each of three dispositive issues cannot establish a likelihood of success:

It’s a mathematical truth. If an applicant must prevail on three independent issues, his chance on each must be very high. Otherwise, he can’t succeed overall.

To explain, consider Steph Curry. He may be the greatest shooter in the history of basketball. His career free throw percentage is 91.2%. But as good as Curry is, if he takes ten foul shots, the likelihood that he makes all ten is only 39.8%. That’s because each shot he takes is independent of any other.

Here, the same principles apply. If we were to assume that [the movant] has a 75% likelihood of success on each issue [out of three], he only has a 42% likelihood of overall success.

This view did not prevail—this passage is from a dissent. Still, it raises a fundamental question about how lawyers should respond when clients ask, “What are my odds?”

To some judges, when there are multiple points on which a party could lose, the “likelihood of success overall is the product of their probability of success on each of the independent, dispositive issues.” Am. Fed’n of Teachers v. Bessent, 152 F.4th 162 (4th Cir. 2025) (“AFT”) (Richardson, J., joined by Agee, J.).

Six months after AFT, the full fifteen-judge Fourth Circuit, sitting en banc, “disavow[ed] any suggestion that district courts should assign numerical probabilities to a plaintiff’s chances of success on each issue and then multiply those probabilities together to determine whether the plaintiff’s “overall odds” of success are high enough to warrant a preliminary injunction.” Am. Fed’n of State, Cnty. & Mun. Emps., AFL-CIO v. Soc. Sec. Admin., 172 F.4th 361, 366 (4th Cir. 2026).

Writing for a nine-judge majority, Judge Heytens criticized the AFT opinion’s numerical approach:

AFT suggests district courts should perform unfamiliar tasks for dubious benefits. The law often deals in probabilities that are “incapable of precise definition or quantification into percentages,” Maryland v. Pringle, 540 U.S. 366, 371, 124 S.Ct. 795, 157 L.Ed.2d 769 (2003) (discussing probable cause), and we doubt the value of asking district courts to spend time pondering whether a plaintiff has a 75% (versus a 70% or 80%) chance of prevailing on a given issue. See Kevin M. Clermont, A Theory for Evaluating Evidence Against the Standard of Proof, 127 Penn. St. L. Rev. 345, 367 (2023) (noting that “[c]ognitive limitations leave humans able only weakly to judge likelihood on any sort of scale”). In addition, AFT never defines what it means for two issues to be “independent” in a legal or mathematical sense … , nor does it address how district courts should deal with the familiar statistical problem known as conditional probability. What should district courts do when the parties disagree about whether (and if so, how) the plaintiff’s success on one issue would impact its odds of success on another? Are some arguments so weak that a court may definitively reject them without asking how they impact the plaintiff’s “overall odds” of prevailing in the suit? …. And what about novel legal issues or those of first impression, where a district court may struggle to identify the precise probability of one outcome or another?

Better, we think, to stick with the traditional approach …. [P]laintiffs seeking a preliminary injunction must show they are likely to succeed on the merits of their lawsuit. Plaintiffs need not clear a different or additional hurdle in cases involving multiple issues or defenses. All statements to the contrary in AFT are abrogated.

Judge Richardson, writing for six judges, called the abrogation of AFT “the very definition of dicta,” because the Court ultimately denied relief on other grounds.

“To be clear,” Judge Richardson wrote, “I have not suggested that district court judges must assign a specific number to the plaintiff’s probability of success on each issue and then multiply them out.” In his view, a multiplicative approach is a “framework that guides that discretion in evaluating a plaintiff’s likelihood of ultimate success. Indeed, equity demands—not forbids—the application of basic probability principles when it asks courts to engage in an inherently predictive inquiry.”

Judge Quattlebaum, joined by Judge Richardson and Judge Rushing, authored a separate opinion emphasizing that assigning numerical probabilities is “a common way lawyers and clients make informed decisions” about whether to pursue a case and when to settle. He runs through a scenario in which a lawyer tells the client: “I just read the Fourth Circuit’s opinion that says it’s just too hard to give you percentages on likelihood of success. So, while I think we’ll win, I can’t give you any numbers.” Judge Quattlebaum predicts: “Without some sense of numerical percentages, the client can’t make informed decisions. Frustrated, it’ll likely fire the lawyer who follows the majority’s thinking and replace her with someone who can give it more concrete help.”

Two weeks after the en banc opinions, Judge Quattlebaum revisited this debate when making his Steph Curry analogy in his Herrera-Juarez dissent. He cited Judge Richardson’s view that the abrogation of ABT was dicta. Noting that nine of his colleagues had “bristled” at multiplying probabilities in multi-issue cases, Judge Quattlebaum wrote: “Frankly, I don’t understand why. With genuine respect, this is not a matter of opinion. It’s not a matter of judicial philosophy. It’s a mathematical truth.”

I agree on some underlying assumptions, including that clients want numerical probabilities in making decisions in litigation or settlement, and that lawyers often give such odds, though usually with caveats about imprecision.

But I part company on how to calculate odds when there are multiple issues that are, at least on paper, independent. To use the Steph Curry analogy, if a plaintiff were to have a 91.2% chance of success on each of ten issues the defendant raises on appeal, I wouldn’t say the plaintiff has only a 39.8% chance of winning.

Rather, the plaintiff’s chances of running the table on all ten issues would be about the same, and perhaps even worse, than if the defendant raised only one. The Supreme Court has endorsed Justice Robert Jackson’s view that multiplying issues on appeal is more likely to help than to hurt:

Legal contentions, like the currency, depreciate through over-issue. The mind of an appellate judge is habitually receptive to the suggestion that a lower court committed an error. But receptiveness declines as the number of assigned errors increases. Multiplicity hints at lack of confidence in any one …. [E]xperience on the bench convinces me that multiplying assignments of error will dilute and weaken a good case and will not save a bad one.

Jones v. Barnes, 463 U.S. 745, 752 (1983) (quoting Robert Jackson, Advocacy Before the Supreme Court, 25 Temple L.Q. 115, 119 (1951)).

Similarly, if a plaintiff has a 75% chance of success on each of three potentially dispositive issues, I think most lawyers would say the odds of running the table are closer to 75% than 42%.

Justice Robert Jackson’s observations suggest that, even when issues are analytically distinct, they are not independent variables when the same decisionmaker (jury, trial judge, or appellate panel) resolves them.

I’d be fascinated to see an experiment in which mock judges are given the same set of facts and apply them to different combinations of analytically distinct issues. Some would decide only issue A, only issue B, or only issue C; some would decide two issues (A&B, A&C, or B&C); and some would decide issues A, B, and C together. Maybe I’m wrong, but I suspect that the odds would be much closer across the scenarios than the multiplicative approach assumes.

The multiplicative approach could have a range of unintended consequences, including for postconviction claims based on ineffective assistance of counsel. The multiplicative approach assumes no downside, only upside, when raising analytically distinct defenses or objections. Postconviction counsel could establish both deficient performance and prejudice simply by identifying more and more omitted defenses and objections until the prosecution’s multiplied odds fell below 50%.

No court has taken such an approach in the postconviction context. Rather, the Supreme Court adopted Justice Robert Jackson’s anti-multiplication view when ruling against a postconviction petitioner alleging ineffective assistance of appellate counsel.

Math is only as reliable as the assumptions that enter a calculation. Assumptions in other contexts, such as postconviction relief, suggest flaws in the multiplicative approach to likelihood of success.