As most baseball fans know, batting average is simply the ratio of the number of hits to the number at bats. That makes it a linear relationship: for any given number of at bats, a .400 hitter (hypothetically, since there has not been one since Red Sox slugger Ted Williams did it about sixty years ago)will have obtained twice the number of hits as a .200 hitter. But consider a similar statistic known as the batting average of a pitcher's opponents. Strange as it may seem, if you plot the number of hits given up by the pitcher per game versus the opponents' average, you will notice a non-linear relationship!
Here's why:
Let A = batting average for opposing hitters