Kevin Vallier, a philosopher, considers on Facebook the optimal journal submission strategy:

I was implicitly assuming the best strategy was to start with the best journals, receive rejections, and then work my way down, lest my piece get accepted by a sub-par journal first. But now I’m thinking it may make more sense to start from “the bottom” or at least mid-tier journals and work my way “up” if I can assume that my pieces will generally be rejected several times, even by the mid-tier journals. I think I was overestimating the risk of publishing my work in mid-tier journals and underestimating how much rejections can improve the quality of the paper. In light of this, I want to construct a “journal ladder” that political philosophers and political theorists can “climb” towards the best journals.

Let’s put some numbers on this to see what makes sense. The expected utility from submitting to a high quality journal first is:

HighFirst = Ph* HV + (1 – Ph)*(Pl*mult)* 1

The first term, Ph*HV is the probability of acceptance at a high quality journal times the value of acceptance at a high quality journal. If the paper is rejected, which happens with probability (1-Ph), then you go to a low-quality journal where the paper is accepted with probability Pl times the multiplier which you get because of suggestions and comments from the referees at the high quality journal. The value of the low-quality journal is set to 1 so HV>=1.

Now what about low first:

LowFirst = Pl*1 + (1 – Pl) (Ph*mult)*HV

if you submit to the low quality journal and are accepted you get Pl*1, if the low quality journal rejects which will happen with probability (1-Pl) you submit to the high quality journal which accepts with probability Ph*mult and if accepted you get HV.

Now let’s put some numbers on this. The probability of acceptance at a high quality journal is 5-10%. The rate at the AER in recent years, for example, has been about 7.5%. Let’s say 10% and for a low-quality journal 20%. These rates are conditional on being the type of paper that is submitted to the AER not any random paper. (These rates are also reasonable for philosophy journals.). What’s the value of HV, the high quality journal relative to the low quality journal? Let’s say between 1 (equally valuable) and 10. And the multiplier? 1.5 would be very generous. 1.1 might be reasonable on average, 1.2 if you are lucky. Given these numbers let’s consider LowFirst-HighFirst so positive numbers mean that the LowFirst strategy is better, negative numbers that the HighFirst strategy is better. Here’s what we get:

The way to read this is that if the multiplier is a hefty 1.5 then LowFirst is superior to HighFirst if a high quality journal has a value of at least 3.5 (relative to the low quality journal at 1). If the multiplier is 1.3, however, then LowFirst is optimal only if the high quality journal is more than 8 times as valuable as the low-quality journal. And for a multiplier of 1.2 LowFirst is never optimal.

Thus the LowFirst strategy is better the higher the relative value of a high-quality journal, the bigger the multiplier and also the lower the acceptance rate at the low quality journal . The lower the acceptance rate at the low-quality journal the lower the cost of submitting it there in order to earn the multiplier.

I conclude that the high-value first strategy is usually optimal. All the more so since there are good substitutes for submitting to a low quality journal. Namely, submit the paper to a conference, circulate the paper to friends, enemies (especially) and others to get comments. The multiplier with this approach will be at least as large as with the submission approach and the opportunity cost will be lower.