NEW YORK — In October 2010, William F. Boyland Jr., a state assemblyman from the Brooklyn borough of New York City, shared fine cuts of meat, wine and whiskey with two businessmen who were trying to buy Boyland’s political influence.

A new analysis of hundreds of thousands of cases in federal courts has found vast disparities in the prison sentences handed down by judges presiding over similar cases, raising questions about the extent to which federal sentences are influenced by the particular judges rather than by the specific circumstances of the cases.