The difference between real and purebaseball often exists as we see with the examples of Pujols and Berkman but within the game, a player can have extremely different stats in different leagues. There are just a lot of random events that contribute to overall stats. Example: I have Brian Lawrence on three different teams (all traditional). On one team, he's my best starter, on another he's in the middle of the pack and on the third, he stinks. Here are the three stats lines:

Brian Lawrence 4 6 0 15 94.3 111 62 56 11 23 55 5.34 10.59 5.25

Brian Lawrence 8 4 0 16 104.7 90 35 27 6 27 56 2.32 7.74 4.82

Brian Lawrence 4 6 0 18 100.3 105 56 49 16 25 57 4.40 9.42 5.11

There's a world of difference between an ERA of 2.32 and 5.34.