How much is that correlation due to influx of a high, ready to play, draft pick?
Jazz don't have that.
What's the correlation to coaching changes?
Rookies almost never have massive effect on the win total of their teams. I posted about a nice ESPN article about it a while ago that summarized it pretty well:
https://jazzfanz.com/showthread.php?32535
The "NBA ready" rookies who help you "win now" are to a huge extent a myth. It usually takes 2-3 seasons for the rookies to start becoming serious contributors.