In the National league all players take a turn at bat. But in the American league, a “designated hitter” usually bats for the pitcher, who is likely not to be a strong batter. The theory is that a designated hitter will lead to more hits, more runs, and a higher-scoring game. The data give the average runs per game and total home runs for major league baseball teams during the 2012 season. Is there a discernible difference between the leagues?