Race figures in many of the new term’s most important cases, including two to be heard in October, and that seems to be part of a new trend. “The court hasn’t had a lot of cases recently dealing with race in the criminal justice system,” said Jeffrey L. Fisher, a law professor at Stanford.

In June, a dissent from Justice Sonia Sotomayor brought a new perspective to the issue. Citing James Baldwin’s “The Fire Next Time” and Ta-Nehisi Coates’s “Between the World and Me,” she insisted that the brutal history and contemporary reality of racism in the United States must play a role in the court’s analysis.

That dissent may prove influential, said Justin Driver, a law professor at the University of Chicago. “One item to keep an eye on this term,” he said, “is the extent to which the Black Lives Matters movement makes its presence felt on the court’s docket.”

On Wednesday, the court will hear arguments in Buck v. Davis, No. 15-8049. It arose from an extraordinary assertion by an expert witness in the death penalty trial of Duane Buck, who was convicted of the 1995 murders of a former girlfriend and one of her friends while her young children watched. The expert, presented by the defense, said that black men are more likely to present a risk of future danger.

The justices will decide whether Mr. Buck, who is black, may challenge his death sentence based on the ineffectiveness of the trial lawyer who presented that testimony.

“The Buck case raises questions that could not be more relevant to ongoing conversations sparked by police shootings about implicit bias and stereotyping of African-American men as violent and dangerous,” Ms. Wydra said. “The Roberts court, and particularly the chief justice himself, has often been reluctant to acknowledge the reality of systemic racism in this country, but the egregious facts of the Buck case make it impossible to avoid.”

On Oct. 11, the court will consider another biased statement, this one ascribed to a juror during deliberations in a sexual assault trial. “I think he did it because he’s Mexican, and Mexican men take whatever they want,” the juror said of the defendant, according to a sworn statement from a second juror.