The question is: how do I define and when do I find success in writing? Like almost everything else having to do with writing, the answer is: it depends.
It depends on what type of writing it is and what its purpose is. If I am writing an academic paper or an essay for school, I tend to feel successful once my teacher has read it and told me they liked it (even if they have some pointers for what to do different, if it is an overall positive review, I am pleased). If I am journaling, I feel successful if my thoughts and prayers flow straight from my head through my hand onto the paper, even though no one will ever read it. If I am writing the first draft of a story, I feel successful when the characters come alive to me and I feel emotionally invested in the story, even though no one will ever see this draft, or possibly any draft ever.
The lower my expectation for a certain piece of writing, the easier it is to feel successful. I believe this is why journaling or prayer writing is so rewarding to so many people. When I write in my journal, it's usually a prayer to God or else just musings on some aspect of life that made me feel or think today. It is more like a free writing session than an organized attempt to inform, entertain, or persuade.
When I'm writing a paper for a school assignment, not only is it much harder to actually do, but my standards for my writing are much higher. I obsess over the placement of every paragraph to make sure it has a clear and logical flow. I worry over the introduction and conclusion. I edit and re-read it and sometimes get others to proofread it. It is a much longer process to feel good about, and if I'm told it's not a good paper, it's harder to accept than if someone were to tell me that my journaling wasn't good. But at the same time, when a peer or professor tells me my essay was a good one, the feeling of accomplishment is much more exhilarating than if someone liked my journals.
Another type of writing I do quite often is letter-writing. I only write to people who are very close to me, and so it is much like journaling. I don't worry about how much sense it makes, as long as it makes sense to the one person I am writing to. My letters are messy, often more emotional, and not thought through ahead of time. The success in writing a letter comes when I sign off and know that my friend will read and understand what I mean to say.
Success is hardest for me to define when I think about my novels and stories. They are written as if to be published and so for a larger audience. But, when I'm drafting, I know that I am only writing for myself. No one else will ever know about the worlds and characters in my head unless I choose to pursue that. And while it is one of my deepest desires to one day be able to publish my books (and I would no doubt feel a great deal of triumph) I don't let myself think about that when I write; I would be paralyzed if I assumed it was going to get published from the beginning. So instead, I feel like I did a good job with my story when I feel invested and emotionally connected with it.
Just like success in life, success in writing is a slippery thing to define. But rather than try and bash its head, like a fish you caught, so it lays still and can be examined, defined, and achieved every time, maybe it's better to let the feeling of success swim free. And we can count ourselves lucky every time it brushes our fingers through the water.