There's variation in the SIM. Its part of how simulations work. Here's an example, one of the leagues I played, 12 of 16 teams used Addie Joss, 1908. He didn't perform identically for every team, which IN PART is a result of the composition of the team he is on and the teams he faces, and the stadiums, etc.,. But even without those factors, the SIM is based on an approximation of real life play. If it wasn't, then you wouldn't even need to play the league, because you could predict the results entirely from the draft.
The outcome of any simulation is based on mathematical probabilities. Those probabilities are distributed as a normal curve. A large number of simulation produces a normal curve; any particular simulation, however, can fall anywhere within the parameters of the normal curve, and may not represent an average outcome. This means that you need a certain number of runs of the SIM to generate the entire range of the curve to determine the mean effect.
In the SIM, even the fatigue affect will be randomly distributed -- its constructed the same way for all the players experiencing fatigue, BUT, the fatigue effect will be random for each particular at bat either from the pitcher's or the hitter's perspective. Its the sum of all the at bats that generates the normal distribution of the fatigue effect in any particular league under the conditions in the league.
As noted in previous posts, perhaps the best way to determine this effect is through the experimental design. But, this would still require a number of experimental design permutations and cross-referencing of the design outcomes. One design would be for every team to be the same and to play in the same stadium and to have the same batting order, pitching rotations and all the same advanced settings and managerial settings. In that case, you would have 16 players at each position to compare who are all the same, and with 16 cases you would come closer to getting an approximation of a normal curve than if you had one case. Statistically, there is a minimum number of cases you would need to ensure that you replicated the normal curve of any distribution to allow you to generalize from the results.
In the SIM, you can control some level of the variability, but not directly, by playing all the games in neutral parks. But, the neutral effect of parks is an estimation based on a normal distribution, and the outcome of every at bat isn't 0 -- the sum of the at bats in the park over the entire season should, if the SIM acts correctly, be 0. But, since the SIM is based on probability and a normal distribution, there is always the chance that the outcome isn't exactly 0. Mathematically, the SIM has a variation, a standard deviation, and a confidence interval, and given enough cases, these can be replicated, But with one SIM, you don't know if you replicate the mean and the distribution.