"I see around 6000 submissions annually, and take on about 2-3 new clients a year."
Based on other things I've read, I'd say this might not be a typical answer. Many agents take on fewer new clients each year and receive more queries.
Let's break down those numbers, shall we?
I don't have exact stats, obviously, but I'm betting at least half, maybe even 3/4 or more of those submissions can be immediately eliminated from competition, either because the author queried too soon with a manuscript that is not yet ready or because the author failed to do the requisite homework and queried an agent who does not rep that kind of story. None of us wants to believe we're one of those writers, but if we're not, chances are good we have been.
If we've sufficiently polished our manuscript and done our homework, this means our odds are improved from impossible to merely astronomical.
In a typically perverse writerly kind of way, this gives me some positive feels.
It's not like the agent is accepting everybody else's manuscript and declining mine. Better books than mine are likely being rejected on that same day.
I've had other writers tell me they love my story, people who didn't have to tell me anything at all. This means there might still be that one agent out there who doesn't automatically push my query into the pile of 5,998 that will not make it.
There are a lot of agents out there. If they all choose one or two, or even three, new writers, that's still a lot of new writers. Maybe I'll be one of them. Maybe you will.
And if not, we'll keep chugging along because we believe in our stories, but mostly because we just love writing them.