Each Baseball Stars subset includes at least one player form each major league time at the time. In addition, two players printed in both sizes had team changes and these really help to pinpoint the year. Ed Lopat started the year pitching for the New York Yankees but was traded to Baltimore on July 30, 1955. He would end his career for the Orioles, who released him on October 10th. He is shown in both sets as a Yankee:
Boston and Kansas City were the only two teams with two players in the "large" set, so Lopat was the only Bronx Bomber present. He dates the set at 1955, as does the inclusion of Johnny Schmitz:
Johnny is clearly a Senator in the "small" set but Washington traded him to Boston after the 1955 season. In addition, he indeed led the Senators staff with a 2.91 ERA in 1954. Based on Lopat and Schmitz, I am dating both Hocus Focus sets as 1955 issues.