This particular site is top 5,000 Alexa. The content changes every minute, and Google is fast at picking up those changes. The last cache of the homepage was 7 minutes ago from Google.
There's definitely a correlation between my sites' Google rankings, their organic traffic, and their crawl rate. The other sites I run are Alexa top 30,000 and top 100,000. They all feature dynamically changing content, but Google is definitely using a higher crawl rate on my higher ranking sites. This isn't a surprise though, Google has limited resources like everyone, and they'll focus those resources in a way that provides the most benefit.
Edit: If you're talking about the correlation between daily ranking and daily crawl rate for an individual site, then no, I'm not aware of any patterns. For example, the graph is flat for organic traffic and total indexed pages, but the crawl rate jumps up and down as mentioned, and it doesn't appear to relate on a daily basis.
