OK, pocket cameras.
The
Nikon SB800 has a guide number (in meters) of 125 at ISO 100 with its zoom head set to telephoto (105mm coverage). That's a "beam angle" of 20x27 degrees (
http://www.scantips.com/speed2.html) and the flash duration is 1/1050th second (same link). 20x27 degrees is about .35x.47 radians or .35*.47/(4*pi) steradians (is that right?) or 0.013 steradians.
The 125 guide number means at 1 meter you'd use f/125 (close to f/128) so this is 4x the exposure of f/64, the
However, because of that 20x27 mm narrow angle, that light is going over just 0.16 or so square meters. So spreading it out to 1 square meter (remember lumens = lux/square meter) we get 9 million * 0.16 or about 1.4 million lumens!
Remember that this is a fairly hefty 4AA-powered flashlight which will give you maybe 100 flashes on full power per set of batteries, or a total runtime of around 1/10th of a second. If you dialed the power back by a factor of 10000 so you were getting just 143 lumens (a more normal 4aa or 2x123 flashlight) the resulting 17 minute (10000 * 1/10th sec) runtime wouldn't be all that impressive, so the efficiency of these flashes is not that high. Of course you can't really dial back the power like that and get the same efficiency, that was just for comparison.
Cool question! Anyone up for checking the answer please do so, I could have easily made a mistake. It was fun researching this.