"Ear training, instrumental skill, theory"
All accomplished musicians who improvise play what they hear in their heads. Let's unpack this statement.
Let's break it down further.
"They hear something in their heads." A developing musician must listen to the musical style they wish to improvise in: Jazz, Rock, Classical, whatever. How much listening? A lot. Last year at the Jazz Education Network convention in Louisville Kentucky there were several interesting young musicians in attendance. One, a young bassist, walked around with his ear buds in all day long. Complete immersion. With immersion, the knowledge students are acquiring in theory class starts to make sense. Theory is only helpful if you can hear it in the playing of others. Until you can, it likely won't make much sense to you. Or, will it be helpful in your playing. (An effective way to help your understanding grow is to transcribe music. Check out the video below for more information.)
"They can execute rapidly in real time." Learn to play your darn instrument. Learn how to practice. Then practice, as much as you can, alone and with others.
You've got to learn your instrument. Then, you practice, practice, practice. And then, when you finally get up there on the bandstand, forget all that and just wail.
I'm a professional pianist and music educator in West Toronto Ontario. I'm also a devoted student and teacher of the drums.