What would be one small detail that, if changed, might change the outcome of the story.

In the beginning of Catching Fire Katniss said that when her father passed away she would have sold her body to Cray, a peace keeper in District 12, if she was a little older as a source of money towards Prim and her mother. Instead, she hunted for food. Also, if she was a little older, she might not have been able to take her sisters place in the reaping, so the book would have either focused on Prim in the Hunger Games, or Katniss watching her sister throughout the Hunger Games.