Ok here we go, several things. First of all, I would like to point out that this is why djozz's images showed that spotlight with the center blocked out projected a concentrated point instead of a ring of light:
This is how you get a high lux reading, not high throw, past that point at the left the rays diverge and you end up with no good beam.
Next, this is the light rays coming from the focal point of the parabolic lens. This is how you get maximum throw, all light beams collimated. Please ignore the half dozen other reflectors in the bacground, those are inactive.
This is just the 9" mirascope reflector (green) being used. 9" diameter, 1.5" depth.
Now, this is how I test beam divergence. The origin is offset 2mm from focal point, so this is the light coming from the LED at the greatest possible offset angle (in this case it would be an XHP70 which has about 4mm side length)
Ok, now let's take a look at what happens with small vs large reflectors. First the 9" mirascope, then a larger 35" reflector, similar to what is used in the old military searchlights.
As you can see, the larger reflector has much smaller "skew" due to the offset. This means the light that is not coming from the middle of the LED, eg. the edge, still gets very well collimated.
This is because even though the two mirrors have the same curvature (and collect the same 120 degrees of light) the larger lens is farther away (because of a longer focal distance)
So the light rays coming from the center of the LED, vs the edge of the LED, have a much smaller difference angle when they hit the reflector, and are bounced back also at a much smaller difference angle.
This is why for long range lights, the size of the light source matters a lot. Instead of using a huge reflector, you can use a smaller light source and get also a huge amount of throw.
This is why the maxabeam uses a 0.25mm short arc lamp. Even though it only makes a few thousand lumens, it can reach many kilometres with only a 8" or 6" reflector or whatever it uses (i forget).
Lesson is, the light needs to be going straight forward to be collimated, not like the first image, that is bad. That is what you use for burning paper and matches, not for lighting up kilometres away :D