Eye test

I was reading Moneyball and Michael Lewis said you could tell a .275 hitter from a .300 over a sample of 15 games about 40% of the time. I got bored and did it in R with the 1986 MLB season. How could we bump that accuracy up to 90%? Either compare the .275 and .300 hitters over 100 games, or compare Jody Davis and Wade Boggs for 15.