Rising in the serps, falling in PR

What difference does it make?

[MatthewHSE]

I've read the posts saying how PageRank is irrelevant, but I never really believed it until lately. My rationale was that Google wouldn't be using PR if it wasn't used in their algorithm somehow.

But my perspective has recently changed. Over the past two PR updates, I've noticed that my homepage PR dropped from 6, down to 5, and now it recently dropped to 4. And yet, search engine traffic is finally beginning to pick up on my site, to the point that it's at least ten times as much now as it was when my PR was 6. Furthermore, I'm currently in 23rd position for one of my main keywords, which is a pretty competitive search term. Given the trend my site has been on lately in the serps, I expect to be on the first page sometime soon.

So tell me, once again, just what is the connection between PR and the actual results? Must say, I don't see a connection at all.