Q: What are the chances of acceptance of an article that has not been desk rejected?

Detailed Question -

I submitted a paper to a journal and they asked me to resubmit it after I take care of some formatting issues. The status was "With editor" for nine days and on the tenth day, it changed to "Under review." It has been under review for 25 days now. Does this mean the editor has somehow approved the quality of my work? What are the chances of getting an acceptance?

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Answer:

Status descriptions vary across journals. While some journals use the status "Under review" exclusively for external peer review, some use it for both internal and external review. So, it is difficult to say whether your paper has actually been sent out for peer review or whether the "Under review" status merely refers to the internal editorial screening. Since the status did not change from "With Editor" to "Reviewer assigned" before changing to "Under review," there is a possibility that your paper is still undergoing the initial screening. The next status change will make things clearer. 

Regarding your question about the chances of acceptance, it is actually difficult to say. Typically, a significant percentage of papers submitted to reputable journals are desk-rejected. For example, Elsevier journals desk reject 30 to 50 percent of all submissions. Therefore, avoiding desk rejection implies that you have crossed the first big barrier. Even if your paper does not get accepted, it is indeed a big deal that you will be getting peer reviewer comments as these will help improve your paper and take it a step closer to publication.

Good luck!