Instead of thinking deeply about the problem here's a rote formula I use to get basic 50% fill-flash that works all times all places:

Incident light flash-meter the subject.
Note the f-stop reading and set one stop smaller; say for example the flash-meter reading is f8 then set f11 on the lens.
Then set the shutter speed for correct over-all exposure of the scene at that aperture; for f11 in this example.

The result is a correctly exposed over-all scene but the shadows where you originally placed the flash meter are opened nicely from about Zone IV to Zone V, the mid tones move from Zone V to Zone V+1/2, and the higher values scarcely move at all. Most casual viewers accept this photograph as a beautifully lit clear and detailed picture and don't even notice the flash effect.