Press coverage - not metrics, but I've seen an awful lot of stories come out of events, and most importantly an awful lot of journalists meeting exhibitors, from bloggers to mainstream websites or newspapers. Obviously this doesn't guarantee coverage, but it puts the ball in your hands, once you're stood talking to a journalist while standing over your product it's time to knock it out of the park.
I don't really have any customer data I can share with you, the sort of selling points generally used are more vague - such as "The average spend per visitor at last year's event on products sourced at the show was £767, a total audience spend of £79.8m" (taken from the sales pitch of a 2012 event). The overall focus of selling - though I'm not actually in sales so this isn't my direct area - is about the size of the audience, and what sort of demographic they are.
I don't know if events are a good use of your money when it's as tight as that, i.e. if you can chose between $3k on an event or $3k on a PR company, but only one, as I can't think of any exhibitor I've ever had that paid that little, or that was small enough not to have marketing budget around it.
The single biggest argument I can give, I think, is that if you go to PAX you're going to get more people looking at your game than you'd get clicks for $3k online - and when it comes down to it, are you going to sell your game better by having somebody look at your website, or stand in front of you try out your game?
Incidentally, what adverts are giving you that click-rate, and do you have any calculated CPA figures?
edit: I just want to note that like I said above, my experience comes more from big budget companies like big studio publishers rather than indies, so I can't necessarily say events are or aren't a great idea for people like you, just that they do offer bang for buck.