While I'm certainly not perfect by any means, I try my very best to write stories where the characters are believable. How do I do that?

Watch an episode of the show before each and every chapter you write. It doesn't matter if the subject is pertinent to your characters or not. Watching it always reminds me of certain nuances of the characters that help me stay on track. That is why people are here after all. They want to continue reading about their favorite characters from MLP. That is why the top stories on this site tend to feature believable character dynamics. If you'd like to go even deeper into making your characters believable, check out some analysis videos on the tube. Ink Rose and Silver Quill are good sources for understanding how characters act, what's considered out of character, and what parts about them to people respond to. Like many others, it is very hard to like a story when the characters in it are completely different. Do what you can to make them believable, and your readers will thank you for it.

Trust me on this. Watch the show, and you're writing will come much more naturally.