I started having fun, so played around even more, running thousands and thousands of hitters through my little routine. Here's the span of results of .300 hitters given a certain # of seasons.
Code:
# Low High
5000 .240 .360
10000 .232 .367
50000 .225 .376
100000 .225 .381
500000 .210 .385
1000000 .207 .385
So, basically, if your ratings say you're a .300 hitter, this data says you have well under 1 in a million chances to hit .400. On the good side, you should _always_ hit better than .207.
EDIT: The highest I could get in subsequent testing of 1,000,000 hitters at a time was .392.