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+1 @ Brian's process of ambient, then strobe. Even without a meter the process is effective with Sunny 16 ROT.
Using the camera's meter in averaging mode, set the exposure to give a proper background exposure. (Subject not in the frame.)
Sunny 16 @ background @ ISO 200 is 1/200 @ f16
Next, use your flash meter to set the strobe's output to give the same exposure at the subject location.
Subject in shade (no flash) @ same 1/200 would require f6.3 (2 1/2 stops diff), thus a need for fill light to raise the subject to match the background. If your strobe/modifier output has an effective GN @ ISO 200 of say 160 ft (easy math), then light placement would be GN160 / f16 = 10ft from subject to attain a proper exposure for the subject.
You can then adjust the strobe's output and/or the shutter speed to vary the precise ratio of strobe to ambient, but going equal is a good starting point.
As Brian also noted, your last exposure was overexposed for the background, as one would expect if you had an aperture / shutter @ f9 & 1/160. This is why you determine your ambient background exposure first and add fill to the subject based on the necessary f-stop for the background.
Brian is correct that you can adjust your shutter/aperture combination, but the camera's sync speed can be a limiting factor that restricts you from opening up your aperture very much and still retaining a proper exposure for your background with an offsetting shutter adjustment. As such, the overexposed background is a common occurrence if you open up the aperture too much.
As to balance of strobe & ambient, Brian mentions that equal is a good starting point. I agree that it makes for the easiest calculation / starting point. My preference is to have my strobe slightly under @ -2/3 or so, such that it doesn't have quite as strong of a "strobe" look.
The salient point being made here is that ambient is based on aperture and shutter, whereas flash is based on aperture and flash to subject distance (for a given GN/power output), with shutter being of little consequence except for sync limitations.
From that, we can realize that the common lynchpin connecting the two is the aperture. The fine tuning of ambient exposure is via shutter, the fine tuning of strobe exposure is via power/distance.
But ... I'm still wondering how you got a 1/160, f13 exposure reading in the shade
I'm also wondering if the fact that you got the SAME reading with your flash @ 50% means that you are NOT adding any (significant) flash to the subject. This could be the case if you are metering in flash+ambient mode.
Based on what you've said your readings were, I'm inclined to think that your meter was in reflective metering mode (seeing all the light behind the camera) and/or ambient+flash mode (getting the bulk of its light from ambient) when you took your flash reading.