Before the first game of the season, a player does not have a batting average, it is not zero, it is null. So the first game of the season and a no hitter is not the correct answer because the players go from not having a batting average to zero. Why do players not have a batting average before the first game of the season? Batting averages are computed as the number of hits divided by the number of at bats, hits/at bats. If the "at bats" equal 0, then you are dividing by zero which is not mathematically possible. The result of division by zero is called infinity.

Here is a correct answer, there are many. In the first game of the season, some players get hits at each at bat and the others all make outs. So some players have zero batting averages and others have perfect batting averages of 1.000. In the second game, the same thing happens again, so at the end of the SECOND game, the players still have the same batting averages of zero and 1.000. The key is that whatever happened in the first game of the season happens exactly the same in the second game of the season. It is the SECOND game of the season that is the key to the correct answer to this question.