Research Article Biology, Engineering and Medicine Biol Eng Med, 2019 doi: 10.15761/BEM.1000165 Volume 4: 1-3 ISSN: 2399-9632 Mathematical model of journal acceptance and rejection rates Peter R Greene 1 * and Antonio Medina 2 1 Department of Bioengineering, BGKT Consulting Ltd., Huntington, New York, USA 2 Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Mass, 02139, USA Abstract Journals nowadays typically have an acceptance ratio for submitted technical reports at a rate less than 1 in 5 (20% acceptance for some journals, p=0.20). Te purpose of this report is to determine how exactly the likelihood of success subsequently improves, with several sequential submissions, assuming random selection. More commonly for the very busy journals, the rate is less than 1 in 10 (p=0.10 “acceptance probability”). Te likelihood of failure q=(1-p) will diminish according to a power law as (1-p) ^ N, where N is the number of sequential submissions. For journals that are not as busy, where the acceptance probability is higher, p=0.20, the statistics show that at least 3 submissions are required to achieve a 50% likelihood of success, and 10 submittals are required to achieve a 90% likelihood of success. In recent years, there have appeared completely new scientifc and medical journal groups, not necessarily “predatory”, with 10 or 20 diferent sub-specialities in each group. Beall (2016) discusses practical implications in terms of the so-called predatory journals. *Correspondence to: Peter R Greene, Department of Bioengineering, BGKT Consulting Ltd., Huntington, New York, 11743, USA; Tel: +1 631 838 03 95; E-mail: prgreenBGKT@gmail.com Key words: journal submission rates, likelihood of acceptance, rejection ratios, predatory journals, 1-parameter mathematical model Received: February 05, 2019; Accepted: February 19, 2019; Published: February 21, 2019 Highlights • Journals nowadays typically have an acceptance rate less than 10%. • Repeat journal submissions are necessary to achieve a reasonable likelihood of success. • A single-parameter mathematical model is developed, showing that 7 repeat attempts are necessary to achieve a 50%-percent likelihood of success. • It is shown that these results are relevant to the newly developing “predatory” journals, now numbering more than 2,000. Introduction Nowadays scientifc journals typically have an acceptance ratio for submitted technical reports at a rate less than 1 in 5 (i.e. 20% acceptance for some journals, p<0.20), and more commonly for the very busy journals, a rate less than 1 in 10 (i.e. p<0.10 acceptance probability for most journals nowadays). Equivalently, we can consider the problem in terms of q, the rejection ratio or rejection probability: q=1– p=0.80 to 0.90 [1]. The new and rapidly developing phenomenon of predatory journals is an important consideration nowadays, especially in the biomedical fields, so an attempt is made to address these statistics using a simple 1-parameter mathematical model. This model can be used to predict an estimate of the # of repeated submission attempts required (depending on the journal’s advertised acceptance rate) and subsequently an estimate of the likely time-delay factor. The purpose of this report is to calculate and demonstrate how exactly the likelihood of success significantly improves, with several sequential submissions, assuming random selection. Methods It is standard procedure for authors to resubmit repeatedly, applying to several journals sequentially (parallel submittals are specifcally not allowed, as each journal usually requires a written pre- assurance of “exclusivity”). Each individual subsequent submission (assumed to be independent events) has a 10% to 20% chance of success, the likelihood of failure F is given by: Equation (1) F=q= (1–p) for N = 1 attempt Te likelihood of failure F will diminish with increasing N as: Equation (2) F=q ^ N= (1 – p) ^ N where N is the number of sequential submissions. For this simplifed 2-state “success or failure” model, the result is only a success likelihood S or failure likelihood F (other possibilities are possible, but not considered at this stage), so: Equation (3) S+F=1.0 Combining Equations 1,2, and 3 above, the probability of success S is found to improve with repeated attempts N, according to the following power law: Equation (4) S=1–q ^ N=1– (1–p) ^ N