http://alumnus.caltech.edu/~raj/writing ... Order.html
As often happens, people need to be careful about what the data show.
Batting order does matter. The best order would beat the worst order over the course of a season by about 6-9 games.
BUT, most teams don't use the worst order. They use what is labeled in this study as the "conventional" order. And the difference between the best order and the conventional order is what is very, very small, only about 4 runs over the course of the season.
So, the difference between the best and the worst order is big.
But, the difference between what most teams do and what would be best is very small.