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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.

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    I don't think there's a right or wrong answer here. Your personal "target" rate would depend on how you balance the competing priorities of "publish in the best journal" versus "get it accepted fast". Different people will weight these differently depending on their personal preferences, career situation, the quality of the specific paper, etc, and both your extreme strategies could be valid in appropriate situations. – Nate Eldredge Oct 19 '17 at 19:33
  • This also seems to apply to conferences, not just journals (in those fields where conferences are the main method of publication). – JAB Oct 19 '17 at 19:36
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    If you keep submitting your work to journals that are way too high for the potential impact or quality of your work, the editors of those journals may start to remember your name and have a special eye on you next time you submit, even though next time it might be appropriate to submit to such a journal. Take home message: don't start at Nature and Science every time you want to submit something. – Mark Oct 19 '17 at 19:56
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    I think you're looking at this the wrong way: It's not a question about getting accepted or not, but of getting reasonable (constructive) feedback on your work. I posit that as long as you are getting such feedback on your first submission that leads to a noticeably better second revision (that gets accepted, possibly after another round of minor polishing), you're targeting the right level. On the other hand, feedback that boils down to "didn't bother to read, but doesn't look interesting enough" or "looks good, should be published as is" is a sign you submitted too high or low, respectively. – Christian Clason Oct 20 '17 at 13:07
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    @JeffE: I'm sure you mean it in a constructive way, but it could sound a little dismissive. It goes without saying that everyone in the academia is trying to do the best research they can (or so it seems to me). But unless I throw away every result I get which is not at the level of Annals of Mathematics, I still need to figure out how high to send them. And I think there is value in publishing papers in a journal of the appropriate level. Arguably, that's the key reason for the continued existence of journals now that we have arXiv. – Jakub Konieczny Oct 20 '17 at 20:19
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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.

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    Note that anyone can still submit to Nature or Annals of Mathematics with this method... just not too often. – Bjørn Kjos-Hanssen Oct 19 '17 at 22:12
  • This looks interesting. Can you make an example of the "submission strategy" that this would generate? – Federico Poloni Oct 20 '17 at 15:25
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    @FedericoPoloni Say, if I notice that out of those of my papers that get rejected twice, pretty much all are accepted on 3rd submission, then I'd think "Maybe I should try to submit to a journal more at the level of my 2nd submission rather than stoop to the usual level of my 3rd submissions". – Bjørn Kjos-Hanssen Oct 20 '17 at 16:19
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    Or are you thinking of something mathematically precise, with convergence guarantees @FedericoPoloni ? :) – Bjørn Kjos-Hanssen Oct 20 '17 at 16:21
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    I was just curious to see if you had a specific "mathematical" process in mind. But I am not sure if a meaningful analysis is possible -- one would need first to decide where to put the balance between better venues vs. faster acceptance time and not bothering editors --- otherwise the best strategy is clearly "always submit to the best journal in your field, then when rejected to the 2nd best, etc.". – Federico Poloni Oct 20 '17 at 17:31

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