The time period listed in the question spans roughly from the American Civil War (which began in 1861) to the end of World War Two (which concluded in 1945). As it so happens, baseball had a key role in America both before and during the Civil War. Since the eighteenth century, American colonists had been amusing themselves with a variation of cricket that looked a lot like baseball. The industrial revolution further popularized the sport. Finally, in 1845, the New York Knickerbocker Baseball Club was created. This group would settle on the rules that would become the foundation for baseball.
Baseball’s ascension fits closely with the rise of the United States of America, which might be why it’s referred to as “America’s national pastime.” The configuration of baseball, according to some, connects to the imputed values of America. ''Whoever wants to know the heart and mind of America, had better learn baseball,'' said the prolific historian Jacques Barzun.
But during the time period listed in the question, baseball also acted as an extension of America’s racist identity. Black players and white players played in different leagues. Until 1947, when Jackie Robinson joined the Brooklyn Dodgers, Black players had to play in the Negro League. Taking into account baseball’s history of segregation, it’s possible to argue that baseball not only shaped America’s idealistic identity but its ignominious reality as well.
In 1936, Germany used the Summer Olympics to help shape and manipulate their identity. Three years earlier, Adolf Hitler and his Nazi party came to power in Germany. Now, they could use this major sporting event to perpetuate the supposed physical superiority of the Aryan race and to calm other country’s fears about their aims. To give countries the impression that they were a welcoming, tolerant society, the Nazis removed anti-Semitic signage and instructed Germans to treat Black people well.
According to some reports, Hitler’s deceptive marketing was a success. After the games, countries considered Germany a respectable nation again and were less fearful about their intentions. Of course, very soon, the international community would discover that the identity that Hitler presented during the Olympics was misleading.