...When it's dark I'll try and do some tests with various brollies and reflectors and see what the flash meter says. I haven't got a softbox like FITP sells, but I've got a small 65cm studio version somewhere which should be similar, plus a few brollies etc.
As promised, a few tests to see how much light you get out of various brollies and a softbox, shooting outoors.
Flash gun was a Canon 580EX on full power, zoom head set to 35mm, everything is at ISO400, and the distance from reflector surface to flash meter 2m.
First the naked flash, fired direct, gave f/16.9 (that's 1/10th of a stop shy of f/22).
Firing into a 33in silver brolly dropped that to f/11.6 - 1.3 stops down on naked.
Firing into a 33in white brolly dropped it another 0.7 stops f/8.9 - 2.0 stops down on naked.
Firing through a 33in transluscent umbrella lost 0.4 stops more at f/8.5 - 2.4 stops down on naked.
Firing into a 65cm (26in) softbox - without any supplementary diffusing panel inside - gave f/11.2, which is 1.7 stops down on naked.
Fitting the flash with a Stofen diffuser inside the softbox, to spread the light more evenly for a better result lost another 0.5 stops at f/8.7, which is 2.2 stops down on naked. (Stofens normally lose more light than that, but the softbox collected the spill from the sides and 'recycled' it.)
I also took the flash indoors and did identical tests in the living room - light walls and white ceiling - and they were all 1-1.5 stops higher than outside.
These tests are only a guide, and things can change quite a lot depending on things like bigger/smaller umbrellas, how far they are positioned from the flash, setting of the zoom head etc. But at least they are like for like as far as I could manage.
Conclusions:
The moment you move outside, you lose at least one stop of light.
A silver umbrella or small softbox is most efficient, only losing 1.5-2 stops over direct flash. That's workable if it's not bright and sunny.
A white or shoot through umbrella loses 2-2.5 stops. You'll need a dull day for that.
Bearing in mind that a daylight exposure in bright sun would be 1/200sec (x-sync) at f/22 with ISO400 (sunny 16 rule) only a powerful hot shoe flash fired direct can equal that at 2m range.
So if if want to go head to head with nature, and even beat sunlight to get those atmospheric dark skies and backgrounds, you will need studio flash power of 400 Joules or more. But if you wait until the sun goes down, you're in with a fighting chance

Dull days are good for strobists
