“These free speech slam-dunks, with their colorful facts, were among the Roberts court’s cases that have attracted the most press attention, but they are hardly indicative of a conservative majority with an expansive view of First Amendment freedoms,” Monica Youn, a lawyer with the Brennan Center for Justice at the New York University School of Law, wrote in a report titled “The Roberts Court’s Free Speech Double Standard.”

Floyd Abrams, the prominent First Amendment lawyer, said he was unimpressed by the new findings. “Statistics cannot tell the story of the willingness of a court to defend free expression,” he said. “Cases do. It is unpopular speech, distasteful speech, that most requires First Amendment protection, and on that score, no prior Supreme Court has been as protective as this.”

Ms. Youn’s study was posted on the blog of the American Constitution Society, a liberal legal group. At the request of The New York Times, two scholars — Lee Epstein, who teaches law and political science at the University of Southern California, and Jeffrey A. Segal, a political scientist at Stony Brook University — examined the data Ms. Youn relied on and confirmed the essence of her empirical conclusions. Professors Epstein and Segal also added several refinements.

In its first six terms, from 2005 to 2011, the Roberts court issued 29 free speech decisions in argued cases, and it ruled for the free speech claim in 10 of them, or 34.5 percent of the time. The three prior courts issued 506 such decisions and ruled for the free speech side 54 percent of the time. The difference is statistically significant.

But most of the difference can be explained by the decisions of the court led by Chief Justice Earl Warren, from 1953 to 1969, a famously liberal court that ruled in favor of free speech 69 percent of the time. The court led by Chief Justices Warren E. Burger, from 1969 to 1986, ruled in favor of free speech 46 percent of the time, and the one led by Chief Justice William H. Rehnquist, from 1986 to 2005, ruled that way 49 percent of the time.

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By this measure, the Roberts court’s commitment to free speech is also lower than that of the Burger and Rehnquist courts, but those differences, singly or in tandem, are not statistically significant.

David L. Hudson Jr., a scholar at the First Amendment Center at Vanderbilt University, said the studies lacked nuance by, for instance, treating every decision as equally important. His criticism illuminated a gap between the two disciplines used to assess the Supreme Court: political science codes and counts, while law weighs and analyzes.

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Mr. Hudson said the Roberts court’s record was mixed. It “has been terrible in public employee free speech claims,” he said, but it “really landed the plane” in the funeral protest, animal cruelty and video games cases.

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A majority of the Roberts court’s pro-free-speech decisions — 6 of 10 — involved campaign finance laws.

“What really animates” the Roberts court, Erwin Chemerinsky wrote recently in The Arizona Law Review, “is a hostility to campaign finance laws much more than a commitment to expanding speech.”

Mr. Abrams countered that it was precisely the most controversial decision of the Roberts court that illustrates its commitment to the First Amendment.

“This court has been prepared to defend core First Amendment principles even when doing so would subject itself to the harshest, sometimes most frenzied, criticism,” he said. “Two words — Citizens United — illustrate that proposition.” That decision said that corporations and unions have a First Amendment right to spend freely to support candidates in elections. Mr. Abrams was one of the lawyers on the winning side.

Professor Chemerinsky, who is the dean of the law school at the University of California, Irvine, said it was necessary to look at a broader set of decisions to assess the Roberts court’s commitment to free speech. The court, he wrote, has a “dismal record of protecting free speech in cases involving challenges to the institutional authority of the government when it is regulating the speech of its employees, its students and its prisoners, and when it is claiming national security justifications.”

In 2010, for instance, five months after the Citizens United decision, the court ruled in Holder v. Humanitarian Law Project that the First Amendment did not protect benign assistance in the form of speech to groups said by the government to engage in terrorism.

“The Roberts court’s overall record,” Professor Chemerinsky wrote, “suggests that it is not a free speech court at all.”

If free speech cases are not in fact a signature project of the Roberts court, they are nonetheless of exceptional interest to Chief Justice Roberts himself. The chief justice has the power to assign the majority opinion when he is in the majority. In general, he has assigned such opinions to himself about 10 percent of the time.

But in free speech cases, he has assigned the majority opinions to himself about a third of the time. When he did, he was almost twice as likely to vote in favor of the free speech claim as against it.