Statistics - NOT in simple models.

Statistics have no place in simple models because NOBODY has a 'feel' for statistics . We can illustrate this with a really simple statistical system, the coin flip. An honest coin gives 50-50 odds on each flip - either heads or tails. Consider though, what happens if we get 10 heads in a row. If they are betting, most people will shift their bet to tails, with the feeling that the coin has to come up tails more often in the next few flips to 'even things out'. In a trial of several thousand flips, though, you can expect 10 in a row of either heads or tails to occur multiple times. What has gone before has absolutely no effect on the current flip. The odds remain 50-50, but our feelings about the odds vary dramatically, even when we know they don't change.
Good statisticians know that expectations can influence not only our perception of the odds but even the way we report the events. This is why they go to extreme measures to set up 'double-blind' experiments, so the experimenters and the subjects don't know what to expect.
Feynman illustrated another problem with statistics, that of remembering only 'significant' results. His line was approximately:
"On the way in from the parking lot today I noticed the license plate ABR165. Now, consider the odds that THAT particular license would be there today. It's over 10 million to one!"
The point was that the license had to have SOMETHING on it. If we consider it significant, we note it and say "wow !" and otherwise we don't notice it. We never remember when we have a premonition that a phone call will be bad news about a relative and it turns out to be a telemarketer.
We set up simple models to force ourselves to look at what is actually happening without fooling ourselves. Statistics are an extremely powerful tool for checking reality, but the probability of self-delusion is so high that they are most useful in disproving a simple model, rather than setting one up.