The Cosby Cup was donated by businessman A. Morgan Cosby. The OHA playoffs at the time consisted of play-downs from a limited number of teams. At the start, there was Lindsay, Ottawa, Kingston Queen's University, Toronto Osgoode Hall, Toronto St. George's and Toronto Granites. These were the only teams of the OHA upon its founding, but the league started adding divisions in 1896, splitting into junior, intermediate and senior. The Cosby was awarded to the senior champions until the John Ross Robertson trophies were donated in 1899. The Cosby was given permanently to Queen's University.