Good stuff @SimpleMike. I'd be interested in seeing the covariance data for 1.0 -- one song pairing (besides the obvious ones like Mike's Groove, Horse > Silent, etc.) that I saw popping up in the same shows repeatedly throughout my year-by-year listening exercise from '97 - '00 was Taste and Theme from the Bottom. Especially in '97, those two had an insanely high coincidence in the same show.

One nit to pick:

They do not pick certain songs that are easier to transition between seamlessly.

You'd be surprised (and I'd be interested in an analysis of this as well) -- Piper and Twist are both in G, so they flow together nicely. DWD and Free? They're both in D. While other pairings may not be in the same key throughout the whole song -- and many of Phish's songs have multiple sections in multiple keys and modes, and that's not even including Type II jams that may modulate entirely to another key -- there are other pairings that lead into one another via some other musical pattern, whether a walk-up or walk-down (like the end of AC/DC Bag, for example, whose walk-up may be extended chromatically for an arbitrary amount of time until they reach the desired key for the next song), or dropping from the I at the end of the first song to the minor sixth at the start of the next, or a whole-step up or down to give a different effect, or my favorite, a jam that modulates effortlessly at some point and suddenly finds itself in the key of another tune (think Tweezer (in Am) -> Heavy Things (in C) from 10/31/14). When these decisions by the band (read: Trey) are made wisely and executed precisely, we as fans say things like "that set had good flow". So I think it's important to realize that, while predicting the next song might be near impossible at times, it's not completely chaotic -- there is a method to the madness. It certainly helps that their repertoire is vast -- so while they may like to go from songs in G to songs in Em, they've got loads of options for each and any patterns would be invisible to us when just looking at the songs.

I do understand your point though, but I might rephrase it a bit: one of the best things about Phish is their ability to take sets of songs seemingly out of thin air and -- when they're at their best -- effortlessly weave them together as if they were meant to be one longer song. Think Magna Tweezer > Caspian (-> Tweezer Jam in G!) or the Blossom "Cheezer", or that entire second set from 8/12/15.

Thanks again for the nice write-up!