Justice Bradley noted that Northpointe had disputed the analysis. Still, she wrote, “this study and others raise concerns regarding how a Compas assessment’s risk factors correlate with race.”

In the end, though, Justice Bradley allowed sentencing judges to use Compas. They must take account of the algorithm’s limitations and the secrecy surrounding it, she wrote, but said the software could be helpful “in providing the sentencing court with as much information as possible in order to arrive at an individualized sentence.”

Justice Bradley made Compas’s role in sentencing sound like the consideration of race in a selective university’s holistic admissions program. It could be one factor among many, she wrote, but not the determinative one.

In urging the United States Supreme Court not to hear the case, Wisconsin’s attorney general, Brad D. Schimel, seemed to acknowledge that the questions in the case were substantial ones. But he said the justices should not move too fast.

“The use of risk assessments by sentencing courts is a novel issue, which needs time for further percolation,” Mr. Schimel wrote.

He added that Mr. Loomis “was free to question the assessment and explain its possible flaws.” But it is a little hard to see how he could do that without access to the algorithm itself.

The company that markets Compas says its formula is a trade secret.

“The key to our product is the algorithms, and they’re proprietary,” one of its executives said last year. “We’ve created them, and we don’t release them because it’s certainly a core piece of our business.”