WASHINGTON — President Barack Obama won a series of major cases before the Supreme Court on health care, gay rights, affirmative action and abortion, helping to preserve significant parts of his legacy.

But, over hundreds of cases in eight years, his reception at the court, on the whole, was chilly.

“Barack Obama’s win rate before the Supreme Court is extremely low, lower than any president of this century,” said Eric Posner, a law professor at the University of Chicago and an author of a new study on the subject.

On average, presidents win in the Supreme Court about two-thirds of the time. The Obama administration won just 50.5 percent of its cases. That record, the study said, “may be the worst since the Zachary Taylor administration,” which began in 1849.

Supporters of Mr. Obama point out that he faced a generally conservative court inclined to be hostile to his generally liberal policies. His critics say his losing streak was a judicial response to his expansive deployment of executive power.