Supreme Court Chief Justice John G. Roberts Jr. (Win McNamee/Getty Images)

Chief Justice John G. Roberts Jr. is a stickler for evenly distributing the workload of the Supreme Court, but he plays favorites among his eight colleagues when assigning the court’s most important decisions.

Not surprisingly, Roberts calls his own number more than anyone else’s and assigns the second-highest number to Justice Anthony M. Kennedy, the pivotal justice on the ideologically divided court, according to a new study by Harvard law professor Richard J. Laz­arus, published in the Harvard Law Review.

On the other hand, Roberts has never assigned Justice Sonia Sotomayor the court’s opinion in a major case in her six terms on the court, Lazarus found, an omission that he wrote “could be a bit portentous.”

In looking broadly at the chief justice’s 10 years on the job, Laz­arus found that Roberts hesitates in assigning big decisions to the court’s most conservative and liberal members — Antonin Scalia and Clarence Thomas on the right, and Sotomayor and Ruth Bader Ginsburg on the left.

Roberts pays “little regard to seniority” in assigning major decisions, Lazarus found.

Relatively speaking, Roberts turns more to Justice Samuel A. Alito Jr. on the conservative side of the bench and Justice Stephen G. Breyer on the left.

“For the closely divided cases in particular, the chief appears to place a premium on opinion writers who can write more narrowly and therefore can be more trusted to maintain the majority established” when the justices vote on cases at their private conference, Lazarus wrote.

Lazarus acknowledges the “inside baseball” nature of his study. But it examines how Roberts in his first decade of leading the high court has used one of the few powers that come with being chief justice rather than an associate justice.

Roberts has jokingly referred to the “odd historical quirk” that gives the chief justice only one vote, just like every other justice. But when he is in the majority — and Lazarus calculated that Roberts has been on the prevailing side in more than 86 percent of the cases in his decade on the court — he can either write the opinion himself or choose who gets the assignment. (When Roberts is not in the majority, the senior justice in the majority either writes the court’s opinion or makes the assignment.)

Roberts is more successful than any other chief justice in making sure that each justice writes the same number of opinions during a specific term, Laz­arus found.

But not all Supreme Court decisions are created equal. Some are more interesting than others or more important.

“Some, including those in which the vote is closely divided, require opinions that are much more difficult to write than others,” wrote Lazarus, a former director of the Georgetown Law Center’s Supreme Court Institute, who teaches a course with Roberts during the court’s summer breaks about Supreme Court history. “And some are stultifyingly dull.”

Roberts has referred to the latter category as “dogs,” and the study found that he takes his share of them.

But equality “dissipates” when it comes to assigning the majority opinions in the 14 percent of high-profile cases Lazarus defines as “salient.”

Roberts gave himself 34 percent of those cases when he could and assigned Kennedy 31 percent of them.

“The most likely explanation is that many of the salient cases in which the chief and Justice Kennedy are together in the majority are closely divided cases in which Justice Kennedy is the ‘swing’ vote,” Lazarus wrote. “One of the easiest ways to reduce the risk of the swing justice swinging the other way is to assign the opinion to that justice.”

Sotomayor, on the other hand, “is the only justice to have received no salient opinion assignments from the chief during her six terms on the court,” Lazarus wrote. “Zero is inherently unique and in this particular context could be a bit portentous.”

President Obama’s other nominee to the court, Justice Elena Kagan, fares better; Lazarus found that Roberts has an “increasing potential to favor Justice Kagan.”

Another disfavored justice, according to the study, is Roberts’s fellow conservative Scalia, the court’s most senior member. Alito, who joined the court just after Roberts, gets as many high-profile assignments as Scalia, Laz­arus said, despite Scalia’s seniority. Lazarus speculates that Alito’s style is closer to Roberts’s than Scalia’s.

“The chief, for instance, has expressed a general preference for narrower rather than broader rulings, while Justice Scalia has in his own opinions ridiculed the chief for what Justice Scalia describes as ‘faux judicial restraint,’ ” writes Lazarus.

“For that same reason,” Lazarus writes, “perhaps the chief believes that Justice Alito is more likely to produce an opinion that can be more quickly joined by others, without the need for pushback by other justices unhappy with some of Scalia’s rhetorical flourishes.”