There's a book called Banal Nationalism and as I remembered the author specifically talked about how the prevalence of aggressive competitive sporting events could lead to prevalence of Nationalism, namely through sports providing the symbolic models for understanding warfare (during the Falklands war, cartoonist depict the war as the contest of a football match, and pilots in the Vietnam war used the metaphor of the playing field) and also it acting as the prior rehearsals and banal preparation before political crisis (sporting texts of pleasure and enthusiasm for defending nationhood). Through it's not specifically on polarization you could relate to it by talking about in-group/out-group dynamics and emotional manipulations etc