Making that Shadow Wilson transcription, I was reminded of this video fellow blogger Jon McCaslin shared with me (and Ted Warren of Trap'd), in which drummer Bernie Dresel shares his formula for comping with the snare drum in jazz:
Basically he says:
• Play lots of & of 1 / & of 3
• & of 2 / & of 4 “doesn't swing”, save it for the end of the phrase
Now: on that Monk record, Shadow Wilson, you'll recall, plays mostly &s of 2s and 4s, all throughout the phrase. The idea that he doesn't swing or doesn't know how to comp would be absolutely ludicrous, if anyone dared to state it.
Dresel mentions developing this formula from listening to Billy Higgins. But we just have to go to the records to discover that he plays plenty of &s of 2/4, all the time. Part of what's nice about the way he does it is that he mixes it up.
As an aside Dresel notes that accenting the cymbal on the & of 2 / & of 4 also “doesn't swing”, which... Elvin Jones famously plays his cymbal that way, as do many others following him, so case closed on that. I also recall Paul Motian somewhere saying that Monk suggested accenting his cymbal that way. I don't have more examples because I never thought it would need defending. It's an established thing.
Certainly a lot of people are active with the snare drum around the & of 1/3— Kenny Clarke and Max Roach, for example. I've written some stuff based on the idea. For a stone beginner with no idea what to do, Dresel's formula is not a terrible place to start.
But it's very, very reductive. Approaching jazz as a formula is a terrible idea. Jazz is not Rockabilly. It's better to do what everyone great did: practice some stuff, play a lot, listen to a lot of records, listen to the people you're playing with, play the tune, and play what you hear. In the video Dresel asks is it random?— the answer is, no, it's based on all those things.