Richie -- haven't really noticed any difference in correlations on big days like the Derby.

In general, the win pool is the most efficient pool but the theory that there's a high degree of "dumb" money in the win pool on days like the Derby is certainly plausible. I've never taken a deep dive into the Derby to see if it holds water, but I don't recall anything anecdotally that's stood out over the years. The Patch example from last year was a good one - would've expected to see it in play a little bit there if the theory was valid, but then again it's only one data point so can't read much into it.

From what I've seen the correlations between the win pools and the Will Pays are just as good on big days as the rest of the year. They might even be a little better on big days, as larger pools tend to be more efficient, and the wisdom of crowds is also more in play. There are of course anomalies from time to time - recall the Palace Malice Belmont Boscar and I posted about awhile back (7-1 in the Will Pays, went off 13-1 on the tote), but that's more the exception than the rule.

Regarding the Pk3, Pk4, etc., they're less useful a predictor of win odds than the Will Pays because the horse-to-horse variability increases with each successive leg you add (ie. the error compounds).