Why is small sample size so difficult to grasp. It really exists, as does gravity, the speed of light, etc.

Probability tables give you the variance of an event occuring. For a basic head/tails occurance, the sims give the following numbers:

With 1000 flips of the coin, you still have around a 10% variance. Drop that down to 500 flips, and you have a close to a 20% variance. Drop that down to 250, and you have close to a 25% variance.

This variance becomes even greater when you have multiple outcomes of an event(such as out, walk, hit, HR) thus with a pitcher, only throwing 200 innings, you end up with variance in the 50% range(or even higher on occasions).

If you add up all the PB leagues stats for a player, you will end up with a fairly close approx. of the pitchers stats(it should a touch higher since we use the top 80% of players). You will also have a high range for that player(2-3 run difference).

Try running your DMB sim. Follow one teams pitchers(chose a team in a neutral park). Watch the variation each year. Add up their ERA's after you run 20 sims, as well as record the highest and lowest ERA, and you will get a wide range(2-3 runs), but the average should be very close to actual.