We are looking to see if there is a "home run effect." This tests whether a pitcher's pitching performance in a game deteriorates after he gives up a home run to an opposing batter.
Hypothesis: This "home run effect" should not exist. However, if it does exist, only bad pitchers should be affected.
Finding: The value of the home run effect is completely random. There is also no relationship between total ERA and an ERA after a home run. Of course, a pitcher may continue to pitch poorly after a home run, but this is not predictive of the situation after he hits another home run in the next game.