Nate Silver emphasizes an important point about when statistical models can really shine: when there is a rich source of data and lots of opportunities to test the predictive power of your models. This is why baseball statistics provide such a great platform for teaching modelling techniques.
Silver N (2015) Rick Data, Poor Data. ESPN. The Magazine (February 22). Available online at: http://m.espn.go.com/general/story?storyId=12317383