When you set out to disseminate your research, be ready to take comments and criticisms. The logic of a statistical argument isn’t always straightforward, and it’s quite possible that your study doesn’t show what you think it shows. Even though you won’t necessarily get the formal, blind-refereed, peer review that you would in academia, the informal peer review process of the sabermetric community is still very effective in spotting flaws in an analysis, so be ready for constructive criticism as you shop your paper around.
You’ll also get some criticism that you don’t agree with. That’s how life is: People disagree on what a result means or how a methodology works. It’s important to engage readers who disagree with you, even if you think they’re wrong. There’s nothing more frustrating than a researcher who posts a piece and refuses to discuss criticisms of it. Be civil and meet questions head on.
Of course, not everyone is logical and reasonable and will agree that you’re right (even if you are, which you might not be.) At some point, the discussion may fail to advance any further, and you might have to agree to disagree. That’s OK. And, a nice bonus is that a public discussion on the internet will attract others, and you probably won’t have to do all the defending yourself.
Finally, there are always idiots online who just don’t get it, or who will insult you for the sake of insulting you. Just keep a thick skin.