Once while speaking to a group of coaches, One of us (Hogg) made the comment that it would be possible for batter A to have a higher average than batter B for each season during their careers and yet B could have a better overall average at the end of their careers. While no coach spoke up, you could tell that they were thinking, "And that guy is supposed to know something about math"
Of course, the following simple example convinced them that statement was true: Suppose A and B played only two seasons, with these results: