When the LED's first hit the scene, the industry was confronted with a light source quite different than a hot wire. For one, the LED being a constant current device required more than just driving it directly from a battery source. The other significant difference was in regards to the distribution pattern of light from the source. To keep it simple, the LED has a directional distribution pattern whereas the hot wire emits light in all directions. Both have images of size and not an infinitely small point of light origin and in this regard, the size of optic matters. The larger the optic and larger its focal length, the smaller, relatively speaking, the image size and the less divergent the beam, from true collimation.
I believe all will agree that throw requires collimation unless the object is close at hand or the flux of the light source is simply overwhelming in its intensity. To my thinking, throw is synonymous with collimation. If the subject of this thread were to substitute terms and it read; "The Real Reason for Collimation.." I think the discussion would follow on a very similar path.
In terms of real world where the OP wants us to focus (and for good reason) there are two aspects of far field illumination that effect our ability to perceive an object at distance. One is the level of light reflected back from the object and this is primarily what has been under discussion here. However there is also the consideration of field of view. In particular, how much of the distant object is being bathed in similar intensity from our light source.
Much of the discussion and focus of portable illumination has been in the realm of tactical illumination and whether stated or implied, the object of illumination is often a person. I recall a beam size discussion some years back with a CPF member who also was a government employee of unknown agency and he had a parameter of beam angle based on upper torso illlumination at a specified distance. A 3' diameter circle of light at x feet away will define an optimal beam angle for instance. If one were to set a required lux on target at this distance in addition to the 3' field of view then you could have a reasonably well defined minimum or throw qualification. The actual beam from a light might have greater intensity than the required lux and it might also have a larger beam angle or field of view.
I think we would all agree that you can't come up with a better throwing illumination device than a laser but for all intents and purposes, its field of view (or viewing angle if you are the target) is way to small to be of any value. A truly useful measure or definition of throw should disqualify a laser inherently and without additional qualifications.
To try to wrap this rambling up, I would propose that a definition or measure standard for throw might consist of the maximum distance from the light source in which the minimum lux measured within a circle of diameter
y would be
x. To be clear here, your target would be a lux meter that is moved around with a defined circle (diameter of y) on the same plane perpendicular to the z axis of your light source and with its center in the center of the light's beam. You move further and further from the light source until you find you have the minimum level of lux (
x) being measured somewhere within that circle.
As to an appropriate circle diameter, obviously if you are hunting humming birds, humans or elephants you might have a differing opinion of optimal diameter. :shrug:
If the industry standard that has been mentioned but not given in detail above encompasses this consideration then forgive my ramble. From the little I gather about the standard as discussed here in this thread, it does not seem to address a field of view consideration.