How did the rise of organized sports and commercial amusements reflect and shape social divisions at the end of the century.
It's somewhere in my textbook calle dout of many a history of the american people volume2. Chapter 19 and 20.
Out of Many is the textbook that I have used most often in my teaching US History at the college level. In my opinion, the text argues that the organized sports did more to bring people of different classes together. However it does talk about how the National League (baseball) was more for middle class people (no alcohol sold, no games on Sunday, higher prices) than the American Association. So that is both reflecting and shaping social divisions. Having sports become a big deal also leaves lots of women out and deepens division between the sexes. (End of Ch. 19 -- "National Pastimes")
The other thing you should look at is "Gentility and the Middle Class." Look at the part where it talks about the middle class being able to buy toys for their kids (and bikes for themselves). This gave them a different experience than the lower classes had.
There will have to be more detail given in answering this question. For example, specifying which sports might allow a more detailed analysis. Without knowing these specifics, I would say that the emergence of golf at the turn of the century might help to reflect strong social divisions present between those that had wealth and those who did not. Golf and the country club culture associated with it was a direct result of the rising acquisition of wealth at the turn of the century. In terms of commercial amusements, Hollywood films were not fully democratized yet, in that the films represented a segment of the social order that reflected wealth and privilege. A possible exception to this might have been Chaplin and his depiction of the lovable tramp. Only in the late 20s and 30s do we see the depiction of the common man as one put on film for the audience to not only pay money to see, but with which there is a greater sense of identification and association.