What exactly are the odds of being published? Statisitically they're very low, but that doesn't have to be cause for concern as you'll see as you read on.
Editors and publishers agree that the odds of being published are only 1-2%. That is, they only accept, and publish, one or two out of every hundred manuscripts they receive.
Sounds depressing, doesn't it? (Still better odds than the lottery of course!)
However, it doesn't have to be so depressing.
When people do the lottery every ticket has an equal chance of winning. However, not every manuscript has an equal chance of being accepted.
The truth of it is that the majority of manuscripts received by agents and publishers are absolutely appalling.
Teresa Nielsen Hayden in her famous Slushkiller article estimates that up to 95-99% of manuscripts range from the author being functionally illiterate, through authors working through their psychological problems in the manuscript, to the high end of books that are merely derivative and unoriginal.
The remaining manuscripts will be considered - say that's 5% of the total. Of these, 1% will be published by that publisher, i.e. 1% of 5%. Which is 20% of the serious contenders. Those are much better odds, aren't they!
And of the 4 out of 5 which are still rejected, they're rejected for reasons like the publisher just thinking that the manuscript just didn't suit them. That manuscript is very likely to find a home with another publisher. So the odds of being published are high for that particular manuscript.
So, if you write an original and engaging story with lively and full-drawn characters, with all the words spelled correctly (occasional typo forgiven) - the odds of being published - as long as you show persistence - are actually pretty good.
I have a phrase: there's always room for excellence. Write an excellent book and you're on your way. That always comforted me because writing an excellent novel was very much something that was in my control. Not that I was arrogant enough to be sure my novel would be excellent. But excellence was definitely something to strive for, and if it wasn't excellent it didn't deserve to be published anyway.