In this time period football was rapidly growing. Many teams were being created and joining the American Football League and the National Football League. Baseball was the most popular sport at this time and was allowed to continue on normally through world war 2 by FDR's Green Light Letter. A lot of the sports lost professional players who went o fight in the war while others suffered from lack of wood and rubber.
Video of a football game in the 1940's.
http://www.huntleyarchives.com/searchresult.php?keywords=&option=all&filmCategory=Sport&filmDecade=1940&filmSound=&filmColour=&filmNumber=90117
http://www.huntleyarchives.com/searchresult.php?keywords=&option=all&filmCategory=Sport&filmDecade=1940&filmSound=&filmColour=&filmNumber=90117