How often should my papers be rejected? When submitting papers to scientific journals, it makes sense to aim slightly above the paper's level - after all, if you submit too high, you get rejected and can resubmit, while if you submit too low you end up just publishing there. Or so it seems to me.

An extreme strategy (which is equally impractical and evil) would be to make a list of all journals ranked from best to worst, and keep submitting to the highest ranking one that you haven't tried yet, until one of them accepts. With a strategy like that, the chance that the paper gets accepted in any particular submission is close to zero. At the other end of the spectrum, if almost all of your submissions are accepted then it's very likely that you're selling yourself short. 

Now, it's impossible to know with any level of precision what's the probability of acceptance of a given paper at any particular journal. But it is possible to observe a general trend, and try to adjust your confidence up or down. Hence, the question:

If one is reasonable in their choice of journals, how frequently should their papers be rejected?

In other words, at what point should I start making a conscious effort to submit to better journals? At which point should I start submitting to worse journals?

For instance, my current strategy is to try and figure out how good a paper is, and first submit to a journal that's about the best that could possibly accept it, and then go down from that by a small but noticable margin. In a small sample size, about half the time the paper was submitted on the first attempt, and about half the time on the second, and so far I haven't had to submit anything three times. Hence, my papers get rejected around 33% of the time. Is this a reasonable frequency, or should I be more modest (or possibly more aggressive) in my choice of journals?

My field is pure mathematics, but I'm also interested in perspectives from other fields.
You could use the
principle of maximum entropy.

Thus, the first submission should be accepted about 50% of the time. When the first is rejected, next the second submission should be accepted about 50% of the time and so on.

This way you "make every time count": you maximize the amount of information (in the sense of information theory) that you receive from each decision.