As a former editor of all kinds of journals (creative and academic/critical), I know what the editorial process is like. Most journals have small staffs and little time. If you are sending to a big journal, probably the initial readers are grad students (if you are lucky) and ungrads (if you're not lucky).
If by some accident or act of God you survive that process, you get read, looked at, reviewed by the next level. Here's where you have to hope that the editor or assistant editor or co-editor has some time to read your story or poem and realize how good it is.
If he/she doesn't, you should hope he/she recognizes your name. Otherwise, your story gets returned.
I bet if we looked at stats about whether or not an editor has ever accepted a story or poem by someone he/she didn't know, we would see that the likelihood of that happening was about close to the odds of you or me winning the mega-millions lottery, Leslie.